the value of pi in the bible by periander a esplana

The Value of Pi (π) in the Bible πeriander א. esplana

1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 3809525720 1065485863 2788659361 5338182796 8230301952 0353018529 6899577362 2599413891 2497217752 8347913151 5574857242 4541506959 5082953311 6861727855 8890750983 8175463746 4939319255 0604009277 0167113900 9848824012 8583616035 6370766010 4710181942 9555961989 4676783744 9448255379 7747268471 0404753464 6208046684 2590694912 9331367702 8989152104 7521620569 6602405803 8150193511 2533824300 3558764024 7496473263 9141992726 0426992279 6782354781 6360093417 2164121992 4586315030 2861829745 5570674983 8505494588 5869269956 9092721079 7509302955 3211653449 8720275596 0236480665 4991198818 3479775356 6369807426 5425278625 5181841757 4672890977 7727938000

The Value of Pi (π)in the Bible

The Solution to the Mathematical “Problem” No. 1 in the Bible

PERIANDER A. ESPLANA

http://www.pdfonline.com/easypdf/?gad=CLjUiqcCEgjbNejkqKEugRjG27j-AyCw_-AP


The Value of Pi (π) in the Bible(The Solution to the Mathematical “Problem” No. 1 in the Bible)

PERIANDER A. ESPLANAwww.geocities.com/perianthium786

6/24/08

THE SO-CALLED MATHEMATICAL PROBLEM NO. 1 IN THE BIBLE

Biblical Errancy, Issue No. 23, November, 1984:"And he made a molten sea, ten cubits from one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about" (1 Kings 7:23). How could a circle be 10 cubits in diameter and 30 cubits in circumference? Since pi is 3.14, the circumference must be 31.40 (3.14 x 10) cubits.

THE EXPLANATION OR SOLUTION TO THE SO-CALLED MATHEMATICAL PROBLEM NO. 1 IN THE BIBLE

Let us analyze the “Biblical Errancy, Issue No. 23, November, 1984” on its criticism of 1 Kings 7:23:"And he made a molten sea, ten cubits from one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about" (1 Kings 7:23). How could a circle be 10 cubits in diameter and 30 cubits in circumference? Since pi is 3.14, the circumference must be 31.40 (3.14 x 10) cubits.

Obviously, the stupid author of “Biblical Errancy” is not asking for any enlightenment for he started his “commentary on biblical math” with the following words: “From a scientific perspective, one of the more interesting aspects of the Bible concerns the number of times numerical calculations are inaccurate. Poor addition, erroneous

measurements and fallacious counting are all too evident.” After he gave ten (a – j) “examples,” he continued: “Besides fallacious counting and adding, biblical authors had

difficulty measuring and computing.” Then, he gave three (k – m) “examples” in which he prioritized 1 Kings 7:23 in the list and he discussed it immediately by reviewing a book on biblical inerrancy. All these so-called examples of mathematical problems in the Bible were merely misinterpretations of his perverted mind. All these so-called problems in all the issues of “Biblical Errancy” were already explained and solved in Dr. Peter S. Ruckman’s “Problem Texts” and in Dr. Gerardus D. Bouw’s “The Book of Bible



Problems.” In this e-book, I will clearly proved the outright foolishness and downright ignorance of the infidel in his criticism of 1 Kings 7:23.In his criticism, the stupid infidel asked a question:

“How could a circle be 10 cubits in diameter and 30 cubits in circumference? Since pi is 3.14, the circumference must be 31.40 (3.14 x 10) cubits.”

You will noticed that in his first question, he already assumed “problem” in the text for he immediately followed it with his statement on pi and a review of the book of Dr. Gleason Archer entitled “Encyclopedia of Biblical Difficulties” in its discussion of the said “problem” text. In the infidel’s question, he indicated the impossibility of a circle which has a diameter of 10 cubits and a circumference of 30 cubits. The impossibility existed only in his foolish mind, as the following scholars will show:

Dr. Norman L. Geisler and Thomas A. Howe:“1 KINGS 7:23 - Doesn’t the calculation in this verse represent an inaccurate value of pi?PROBLEM: According to 1 Kings 7:23, Hiram constructed a ‘Sea of cast bronze ten cubits from one brim to the other; it was completely round. Its height was five cubits, and a line of thirty cubits measured its circumference.’ From this report we learn that the ration of the circumference to the diameter is three to one. However, this is an inaccurate value of pi which is actually 3.14159.SOLUTION: This is not an error. The biblical record of the various measurements of the different parts of the temple are not necessarily designed to provide precise scientific or mathematical calculations. Rather, the Scripture simply provides a reasonable approximation. The rounding of numbers or the reporting of approximate values or measurements was a common practice in ancient time when exact scientific calculations were not used.” (N. L. Geisler and T. A. Howe, When Critics Ask: A Popular Handbook on Bible Difficulties, Wheaton: Victor Books, 1992, p. 182)

Dr. Henry M. Morris:“Critics who try to find scientific ‘mistakes’ in Scripture nearly always settle on this verse as one of their prime examples. Solomon’s sea, ten cubits in diameter, had a circumference of 30 cubits, supposedly showing that the writer thought the value of π, or ‘pi’ (the ratio of a circle’s circumference to its diameter) was exactly 3.0, instead of 3.1416. The critics do not understand the principle – always applied in careful scientific calculations – of ‘significant figures.’ The dimensions as given were not intended as precisely 10 or 30, but were obviously round numbers. To say that the diameter was 10 means only that it was somewhere between 9.5 and 10.5. Similarly, the circumference was somewhere between 29.5 and 30.5. Thus the implied value of π was somewhere between 29.5/10.5 and 30.5/9.5 – that is, between 2.81 and 3.21. The precise value of π is clearly within this range, and it would have been incorrect to try to specify a more precise value. (H. M. Morris, “1 Kings 7:23 annotation” in The New Defender’s Study Bible, Nashville: World Publishing, Inc., 2006, pp.541 – 542)

Dr. Ethelbert W. Bullinger (1837 – 1913):“Here the proportion of the diameter to the circumference (1:3) was revealed, while human wisdom was still searching it out.” (E. W. Bullinger, “1 Kings 7:23 annotation” in The Companion Bible, Grand Rapids: Kregel Publications, 1990, p.459)

Dr. Math:“The Bible does not state that pi = 3.0. It states that a particular object (the circular basin in front of the Jerusalem Temple) had a diameter of 10 cubits and a circumference of 30 cubits. So the correct question is not, "Is it proper to round pi to 3.0?" but "Is it proper to round the circumference of this circle to 30 cubits?" Or better, "Are a diameter of 10 cubits and a circumference of 30 cubits consistent within reasonable measurement error?"



We do not know the precision of the measuring instruments used to measure the diameter and circumference of this circle. But here is what I would naturally understand if I saw this figure in a scientific journal: in the absence of an explicit indication of precision, the absence of a tenths digit implies that the figure is accurate to the nearest 1 cubit - that is, plus or minus 0.5 cubit.

So let's suppose that the diameter was measured, or specified in the design, to be 10 cubits plus or minus 0.5 cubit. Then the actual circumference would be in the range from 9.5 pi to 10.5 pi, or 29.8 to 32.98 cubits.If we make the same assumption about the precision of the circumference measurement, we get a range of 29.5 to 30.5 cubits. Notice that the two ranges have considerable overlap. There is therefore no inconsistency between the diameter and the circumference as reported in the Bible.If you have further questions of this nature, I hope you will be careful in stating them so that the facts are properly represented.”(Note: To read the entire math forum on this question of rounding pi with the answers of Dr. Mathdefending the Bible, see the Appendix A of this e-book)

Now, I hope that you clearly see how foolish the infidel when he dogmatically asserted that the circumference of 30 cubits is wrong and that“the circumference must be 31.40 (3.14 x 10) cubits.” Let us further analyze the infidel’s criticism: “How could a circle be 10 cubits in diameter and 30 cubits in

circumference? Since pi is 3.14, the circumference must be 31.40 (3.14 x 10) cubits.” I will show to you the perfection of the Bible and the foolishness of the infidel. In the infidel’s statement that “Since pi is 3.14, the circumference must be 31.40 (3.14 x 10) cubits,” he exposed his utter ignorance of mathematics. He thought that his “little” knowledge of logic and math enabled him and gave him authority to criticize God Himself by finding errors in His words: the inerrant Bible. What an arrogant exhibition of infidel’s stupidity and insanity! Pi (π) is NOT 3.14 only!!! It can also be rounded as 3.0, 3.1, 3.142, 3.1416, 3.14159, 3.141592, 3.14159265358979323, or if you want up to 1,001 decimal digits of pi (π): 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859502445945534690830264252230825334468503526193118817101000313783875288658753320838142061717766914730359825349042875



546873115956286388235378759375195778185778053217122680661300192787661119590921642019893

As of now, pi is already digitally computed in a trillion decimal places, and still computing… Did you now see the infidel’s ridiculous stupidity when he tried to correct the inerrant Bible? A rabbi who lived 1,000 years ago had something to say for this postmodern stupid infidel:

Rabbi Moses ben Maimon Maimonedes (1135 – 1204 A.D.):“Four thousand years ago, the Babylonians used the approximation 3 1/8 = 3.125. Then or earlier, according to ancient papyri, Egyptians assumed a circle with diameter nine has the same area as a square of side eight, which implies π = 256/81 = 3.1604….Some have argued that the ancient Hebrews were satisfied with π = 3: ‘Also, he made a molten sea of ten cubits from brim to brim, round in compass, and five cubits the height thereof; and a line of thirty cubits did compass it round about.’ (I Kings 7:23; see also 2 Chronicles 4:2) In Judaism's defense, several millennia later, the great Rabbi Moses ben Maimon Maimonedes (1135 - 1204) is translated by Langermann, in ‘The ‘true perplexity' [2, p. 753] as fairly clearly asserting the Pi's irrationality.‘You ought to know that the ratio of the diameter of the circle to its circumference is unknown, nor will it ever be possible to express it precisely. This is not due to any shortcoming of knowledge on our part, as the ignorant think. Rather, this matter is unknown due to its nature, and its discovery will never be attained.’ (Maimonedes)In each case the interest of the civilization in π was primarily in the practical needs of engineering, astronomy, water management and the like. With the Greeks, interest was metaphysical and geometric.” (Jonathan M. Borwein, “The Life of Pi: From Archimedes to Eniac and Beyond,” Prepared for Mathematics in Culture, July 29, 2004, pp. 4 – 5)

This genius rabbi had already written in advanced that Pi is an irrational number (mathematically proved in 1761 by Johann H. Lambert) and a transcendental number (mathematically proved in 1882 by Ferdinand von Lindemann). It cannot be expressed exactly as a quotient of two integers. It is a non-terminating number with non-terminating decimal. We can, therefore, see the perfection of the Bible by expressing its measurement in personal unit of measurement (cubits) which was not only very useful or practical but also very relevant during the ancient time:

Dr. Gerardus D. Bouw:“The problem is that π is an irrational number. That is a mathematical term which means that it cannot be expressed as a fraction. If God were to give the actual values, the Bible, as a book, would need an infinite number of pages just to write down the diameter or the circumference. Clearly, this is not practical.” (G. D. Bouw, The Book of Bible Problems, Cleveland: Association for Biblical Astronomy, 1997, pp. 102 –103.

Dr. Eric Weisstein:“The Bible contains two references (I Kings 7:23 and Chronicles 4:2) which give a value of 3 for π (Wells 1986, p. 48). It should be mentioned, however, that both instances refer to a value obtained from physical measurements and, as such, are probably well within the bounds of experimental uncertainty.” (Eric Weisstein, “Pi” at http://mathworld.wolfram.com, compiled by CRC Concise Encyclopedia of Mathematics)



Russel Grigg:1.The first concerns the meaning of the word cubit, and how it would have been used in measuring the vessel. A cubit was the length of a man’s forearm from the elbow to the extended fingertips. The Hebrew cubit was about 45 centimetres (18 inches). It is obvious that a man's forearm does not readily lend itself to the measurement of fractions of a forearm. In the Bible half a cubit is mentioned several times, but there is no mention of a third part of a cubit or a fourth part of a cubit, even though these fractions of ‘a third part’ and ‘a fourth part’ were used in volume and weight measurements. It therefore seems highly probable that any measurement of more than half a cubit would have been counted as a full cubit, and any measurement of less than half a cubit would have been rounded down to the nearest full cubit. From 1 Kings 7:23 (‘a line of thirty cubits did compass it round about’), it appears that the circumference was measured with ‘a line’, i.e. a piece of string or cord on which the distance was marked, and this length would then have been measured off in cubits by the measurer, using his own or someone else’s forearm, or possibly a cubit-long rod. Similarly the diameter would have been marked on a line and ‘cubitized’ in the same way. If the actual diameter was 9.65 cubits, for example, this would have been reckoned as 10 cubits. The actual circumference would then have been 30.32 cubits. This would have been reckoned as 30 cubits (9.6 cubits diameter gives 30.14 circumference, and so on). The ratio of true circumference to true diameter would then have been 30.32÷ 9.65 = 3.14, the true value for pi, even though the measured value (i.e. to the nearest cubit) was 30 ÷ 10 = 3.While the above seems reasonable, and the Ask ‘Dr Math’ Forum agrees that there is no error in the Bible here, we have no way of knowing for certain whether the measurements were approximated in this way.

Arie Uittenbogaard:“Theory vs practice.Pi is a number without a unit because when we divide so-many meters by so-many-more meters, the [meters] cancel out of the equation and a pure relational number remains. And that means that the decimal tail of pi may go on for ever in theory, but not in practice. Practically, the ratio between C and D is as accurate as the unit in which both were measured. Most civilized countries nowadays use the meter as standard of length, and the mother of all meters is a bar of platinum stored in a Paris clean-room that is kept at precisely 20 degrees Celsius. Because if that bar of platinum gets a little warmer or colder, the bar becomes a little larger or smaller and the meter itself changes.The standard unit of length in Biblical times was the cubit, which corresponds to about an arm-length. And there's the rub: the cubit was by no means standardized and its usage yielded no mathematical precision from which to deduct a ratio that is the same every time. Most commentaries will state that the cubit was approximately 17.5 inches, but that's not entirely accurate. The cubit denotes any length that is roughly the same as an arm length. 17 inches is a cubit, and 18 inches is a cubit as well. The same goes for the other unit of length, used to indicate larger distances: the day's journey, which corresponds to the distance that a healthy pedestrian might cover if he keeps at it and doesn't take too many breaks.The circumference of the vessel described in 1 Kings 7:23 was precisely 30 cubits, which comes down to about thirty arm-lengths of a medium seized gentleman. The diameter of the vessel was precisely 10 cubits, which comes down to ten arm-lengths of the same or some other gentleman. The ratio between the two was exactly 3, which comes down to nothing but a hardy handshake between two gentlemen.In his lovely little book The Joy Of Pi, David Blatner inserts an anonymous statement (page fifty-four): What is pi?Mathematician: Pi is the number expressing the relationship between the circumference of a circle and its diameter.Physicist: Pi is 3.1415927 plus or minus 0.000000005.Engineer: Pi is about 3.Point well taken. 1 Kings 7:23 says nothing about the theoretical value of pi. It just states that a line of thirty cubits went around a ten cubit vessel.The realness of number theoryBut suppose that a measuring line dropped from heaven and the vessel maker now had a standard length of exactly 10 meter (and God said, "You're using meters now...!") and the vessel maker made the vessel precisely 10 meters in diameter. That means that the circumference of that vessel was precisely 10 times pi



= 31,41592... meters. Or in words: Thirty-one meters, plus forty-one centimeters, plus five millimeters, plus nine micrometers (that's pretty much the limit of accuracy used in modern engineering), plus a few picometers, plus the width of a few molecules, plus the width of some atoms, plus an electron more or less, plus a couple of the smallest units of length possible in the universe, called Planck-Wheeler lengths.Smaller detail than that is not possible, but pi goes on! Pi goes on and on to describe smaller and smaller detail, but all of it is fictional and untrue.

Pi lies. Pi lies by nature of its transcendence, and has no relationship to reality. In fact, by its very nature, the more accurate we represent pi in numbers, the less accurate it represents nature!Because pi is transcendent, it can not be written down in a finite string of numbers, not even in the Bible even if the Hebrews had decimal notation, which they didn't. Pi is also not rational and can therefore not be written down as the ratio between two other numbers. Pi can not even be caught in any finite algebraic equation. In other words, the number pi can not be fully written down in any way! It leans heavily on the concept of infinity, like the whole number sequence does, and infinity does not occur in nature.If the Bible were to contain an accurate representation of something that isn't true to begin with (pi), it should use a method that has no precedent in nature and look like an infinite series; like these:

- or -

The Bible shows no such thing. When the Bible was written, no such notations existed. And even if it did, it would only have served to display a numerical tower of Babel.The only practical function pi in all its extend has is to test new computers for their speed and accuracy. And the number of pi-digits that we can calculate is a measure for our technological abilities. It used to be fire: the hotter the fire, the more advanced a nation was and the stronger its weaponry and tools were. Nowadays it's computer power. And even though there's nothing wrong with using computers (we're using one now to show you all these things, aren't we?) the rub lies in the place we give our power to compute in constructing a model of reality around us, and the hope we invest in it that it may some day deliver us from all our shortcomings and failures.”(http://www.abarim-publications.com/Bible_Commentary/1Kings7v23.html)

James Patrick Holding:“The ancients did measure pi more precisely in some cases -- but this is found in places like the Rhynd Papyrus, a book of mathematical equations. The Kings and Chronicles writers were evidently literate, but there is no evidence that they were mathematicians. We would rightly expect accuracy of greater order from specialists in mathematics like the writer of the Rhynd Papyrus, and from Babylonian astrologers. But such an expectation is ludicrous from a non-mathematician.Put it this way: If we ask how many gallons of fuel a rocket contains, we expect a detailed answer like "4,942,827.78 gallons" from a NASA engineer, if he is involved in a techincal discussion with other engineers. If he's talking to the press, and he is savvy, he'll say "4.9 million gallons" rather than bewilder the scientifically inert with more detail. Your average hobbyist (or even a reporter) will say "5 million gallons". Are any of them incorrect? No, because there is a semantic contract that correlates the level of precision with the level of expertise. Unless the Bible authors were mathematicians on the level of Archimedes (one of the other few ancients to go this far in looking at pi), then it is ridiculous to expect precision to that level from them.”(http://www.tektonics.org/lp/piwrong.html)



In other words, it is not only possible to express diameter and circumference in imprecise, rounded numbers but also it is the only actual measurement that can be applied by man to physical objects. You must remember that imprecision or approximation by rounding or truncation in mathematics is not equivalent to mathematical error. What is really IMPOSSIBLE is the ignorant infidel’s wishful thinking of computing the precise ratio of diameter of a circle to its circumference by means of a measurement of physical objects! What is really IMPOSSIBLE is the stupid infidel’s foolish thinking of writing a precise measurement of physical objects which will express the complete value of pi by means of precise measurement of diameter and circumference!

The ignorant infidel did not know that pi (π) could be defined or expressed algebraically, geometrically, analytically, and algorithmically! See http://mathworld.wolfram.com/PiFormulas.html And 1 Kings 7:23 in itself is NOT written to define pi (π) for pure mathematicians in particular but simply to express approximately the practical measurement of the molten sea in Solomon’s temple for all men in general.

But if you really want to know the value of pi (π) in the Bible as used in 1 Kings 7:23 in a much wider CONTEXT, the truth is indeed stranger than fiction, you can read the amazing proofs from Appendix B to Appendix D.

Visit also the website of the mathematician Vernon Jenkins to see how the value of the constants π, α and e can be found encoded in the text of the Bible at http://homepage.virgin.net/vernon.jenkins/index.htmhttp://www.whatabeginning.com

On a lighter note, you can also see at Appendix E some of the “solutions” which will make you laugh.

Don’t ever trust the ignorant infidel when he or she tried to criticize or correct the Bible by using his or her perverted mind to justify his or her sins and immorality. Sin really drives all infidels crazy. All their foolish arguments are mere expression of their arrogant stupidity and fanatic bigotry.



Appendix AROUNDING PI

Source: http://mathforum.org/library/drmath/view/52573.html

The Math Forum – Ask Dr. Math

Date: 06/01/99 at 11:37:02From: Sam GibsonSubject: Can Pi be rounded to 3.0?

I have been challenged to prove that the value of Pi cannot be rounded down to 3.0. I balked at this, thinking that it is obvious that it would make all calculations needing Pi incorrect, but I can find nothing that would say that this is improper. At the same time, I find nothing that says that Pi cannot be rounded to 5, either.

Can you help?

Thanks!Sam Gibson

Date: 06/01/99 at 12:09:26From: Doctor PetersonSubject: Re: Can Pi be rounded to 3.0?

Hi, Sam.

I'm not sure of the context of this question. Any number can be rounded to any precision you want; you can round pi to the nearest ten if you want, and you'll get zero. Rounding it to the nearest unit, giving 3, makes perfectly good sense if that is what you want to do.

The real question is, what is lost if you round pi down to 3? You're reducing its value by .14/3.14 = 4.5%, so any calculations you make will have that much error; but for many purposes that would be perfectly acceptable.

Whenever we work with pi we are rounding it to some number of digits, so all such calculations are incorrect. The only issue is how much accuracy we need for a particular application.

I hope that helps.

- Doctor Peterson, The Math Forum http://mathforum.org/dr.math/

Date: 06/01/99 at 12:21:44From: Doctor RobSubject: Re: Can Pi be rounded to 3.0

You can round pi to anything you want, but you won't have pi when you are done. If you try to use that number to find the circumference of a circle with a given diameter, you will get answers that are not accurate.

Actually, I think what the challenger wants is for you to prove that pi > 3.1, so that when rounded to two significant figures, you don't get 3.0. This can be done as follows.



Start with a regular hexagon inscribed in a circle with diameter d. The perimeter of the hexagon is p = 3*d, so Pi > p/d = 3. Now bisect each side of the hexagon, and connect the points where the perpendicular bisectors meet the circle to the vertices of the hexagon, thus forming a dodecagon (regular 12-sided polygon) also inscribed in the same circle. You can show that the perimeter of this polygon is p = 3*(sqrt(6)-sqrt(2))*d, so pi > p/d = 3.1058... > 3.1, which is what you wanted.

The small isosceles triangles formed will have base d/2, base angles of 15 degrees (or Pi/12 radians), and vertex angle of 150 degrees (or 5*Pi/6 radians). You can use trigonometry to find the lengths of the other two sides of the triangle (the Law of Sines comes to mind), once you know the sine of 15 degrees, which is [sqrt(6)-sqrt(2)]/4, and that the sine of 150 degrees is 1/2.

- Doctor Rob, The Math Forum http://mathforum.org/dr.math/

Date: 06/01/99 at 12:40:32From: Sam GibsonSubject: Re: Can Pi be rounded to 3.0

Hi Dr. Peterson,

The purpose of this little experiment was to show that there is an error in the Bible. In 1 Kings 7:23, a circumference of a circular object is given as 30 while the diameter is given as 10. Obviously, when using the equation 2Pr (where P = pi) to find the circumference this would make pi equal to 3. I was wondering if it is considered proper to round pi down to 3. I understand that pi is always rounded no matter what, but is it proper to round it that much?

Thanks.Sam Gibson


Thank you very much. I am actually doing this to show that there is an error in the Bible at 1 Kings 7:23 and have run into a person who claims that there is no error here and that it is proper to round the value of pi to be 3.0.

The verse claims that there is a circular object that has a circumference of 30 and a diameter of 10. You have shown that this can not be.

Thanks again.

Sincerely,Sam Gibson

Date: 06/01/99 at 16:08:16From: Doctor RickSubject: Re: Can Pi be rounded to 3.0

Hi, Sam.

I beg to differ. The question that you asked, and that Dr. Rob answered, is not the same question that you have now stated. Dr. Rob has not proved your claim at all.

The Bible does not state that pi = 3.0. It states that a particular object (the circular basin in front of the Jerusalem Temple) had a diameter of 10 cubits and a circumference of 30 cubits. So the correct question is



not, "Is it proper to round pi to 3.0?" but "Is it proper to round the circumference of this circle to 30 cubits?" Or better, "Are a diameter of 10 cubits and a circumference of 30 cubits consistent within reasonable measurement error?"

We do not know the precision of the measuring instruments used to measure the diameter and circumference of this circle. But here is what I would naturally understand if I saw this figure in a scientific journal: in the absence of an explicit indication of precision, the absence of a tenths digit implies that the figure is accurate to the nearest 1 cubit - that is, plus or minus 0.5 cubit.

So let's suppose that the diameter was measured, or specified in the design, to be 10 cubits plus or minus 0.5 cubit. Then the actual circumference would be in the range from 9.5 pi to 10.5 pi, or 29.8 to 32.98 cubits.

If we make the same assumption about the precision of the circumference measurement, we get a range of 29.5 to 30.5 cubits. Notice that the two ranges have considerable overlap. There is therefore no inconsistency between the diameter and the circumference as reported in the Bible.

If you have further questions of this nature, I hope you will be careful in stating them so that the facts are properly represented. Doctor Math does not want to have inaccurate statements attributed to him/her!

- Doctor Rick, The Math Forum http://mathforum.org/dr.math/


Doctor Rick,

I am not quite sure I am understanding you. I do not think that I misrepresented the question at all.

What I asked is simply, can pi ever be expressed as being equal to 3.0. The Bible makes this claim and it is mathematically incorrect.

You wrote:"in the absence of an explicit indication of precision, the absence of a tenths digit implies that the figure is accurate to the nearest 1 cubit - that is, plus or minus 0.5 cubit."

Why? The Bible does not say approximately or about 10 cubits. It states that it is 10 cubits. I am not sure why we could take that to mean anything other than 10 cubits which is what we would need to do if we accept a range from 9.5 cubits to 10.5 cubits.

"So let's suppose that the diameter was measured, or specified in the design, to be 10 cubits plus or minus 0.5 cubit. Then the actual circumference would be in the range from 9.5 pi to 10.5 pi, or 29.8 to 32.98 cubits."

First, we would need to understand why this is acceptable to do when we have been given a figure of 10.

"If we make the same assumption about the precision of the circumference measurement, we get a range of 29.5 to 30.5 cubits. Notice that the two ranges have considerable overlap. There is therefore no inconsistency between the diameter and the circumference as reported in the Bible."

Same problem as above. The figure given is 30, not "approximately 30" or "about 30."



"If you have further questions of this nature, I hope you will be careful in stating them so that the facts are properly represented. Doctor Math does not want to have inaccurate statements attributed to him/her!"

I probably won't have future questions like this. Again, the question that I asked was: "Is it proper to round pi to 3.0?" This would need to be the case if we understand the diameter to be 10 and the circumference to be 30.

Thanks again.

Sam Gibson

Date: 06/01/99 at 19:22:51From: Doctor RickSubject: Re: Can Pi be rounded to 3.0

Hi again, Sam.

No, you didn't misrepresent the question, but you didn't give enough information for either Dr. Peterson or Dr. Rob to interpret the phrase "can be rounded." Both said that pi can be rounded however you like. Dr. Rob made a reasonable guess at what criterion you might have in mind, supposing that you needed to prove that pi > 3.1. Re-read Dr. Peterson's answer, please:

"I'm not sure of the context of this question. Any number can be rounded to any precision you want; you can round pi to the nearest ten if you want, and you'll get zero. Rounding it to the nearest unit, giving 3, makes perfectly good sense if that is what you want to do.

The real question is, what is lost if you round pi down to 3? You're reducing its value by .14/3.14 = 4.5%, so any calculations you make will have that much error; but for many purposes that would be perfectly acceptable.

Whenever we work with pi we are rounding it to some number of digits, so all such calculations are incorrect! The only issue is how much accuracy we need for a particular application."

We need to start from the actual question posed to you in order to decide what are the appropriate criteria -how accurate we need to be in this particular application. Then we can see whether approximating pi as 3.0 meets these criteria.

>What I asked is simply, can pi ever be expressed as being equal to >3.0. The Bible makes this claim and it is mathematically incorrect.

The Bible does not make this claim. If we are going to be mathematically precise, the Bible never says that there is such a thing as pi. The figure of 3.0 is not found there. It simply reports two measurements which imply a value of pi. Therefore in my analysis, I started from the measurements as given and derived reasonable precision criteria from them. This information was not available in the original question.

>You wrote:>in the absence of an explicit indication of precision, the absence of >a tenths digit implies that the figure is accurate to the nearest 1 >cubit - that is, plus or minus 0.5 cubit.>>Why? The Bible does not say approximately or about 10 cubits. It >states that it is 10 cubits. I am not sure why we could take that to >mean anything other than 10 cubits which is what we would need to do >if we accept a range from 9.5 cubits to 10.5 cubits.



Look back at Dr. Peterson's answer. Every measurement we ever make is an approximation. I don't know your background, but I studied physics and before we had our first laboratory, we learned about how to write our measurements so that they would accurately reflect the precision of our measuring instruments. Ifthe smallest markings on my ruler are millimeters, then I would not write a measurement as 11.423 millimeters; the closest I could measure with that ruler would be plus or minus 0.5 millimeter, so I might write 11.5 mm +- 0.5 mm or even just 11 +- 0.5 mm. Such a measurement precision is part of every measurement, whether it is written or not.

>> So let's suppose that the diameter was measured, or specified in >> the design, to be 10 cubits plus or minus 0.5 cubit. Then the >> actual circumference would be in the range from 9.5 pi to 10.5 pi, >> or 29.8 to 32.98 cubits.>>First, we would need to understand why this is acceptable to do when >we have been given a figure of 10.

See my last paragraph. I don't know what the actual precision of the measurements was; I can only make a reasonable guess. I know it was not exactly 10, because as I said, no real-world measurement is exact.

>> If we make the same assumption about the precision of the >> circumference measurement, we get a range of 29.5 to 30.5 cubits. >> Notice that the two ranges have considerable overlap. There is >> therefore no inconsistency between the diameter and the >> circumference as reported in the Bible.>>Same problem as above. The figure given is 30, not "approximately 30" >or "about 30".>>> If you have further questions of this nature, I hope you will be >> careful in stating them so that the facts are properly represented. >> Doctor Math does not want to have inaccurate statements attributed >> to him/her!>>I probably won't have future questions like this. Again, the question >that I asked was: "Is it proper to round pi to 3.0?" This would need >to be the case if we understand the diameter to be 10 and the >circumference to be 30.

I hope I have made myself clearer this time. Under some conditions, as Dr. Peterson said, 5% accuracy is enough. My analysis showed that, with some guesses about the precision of the measurements, it seems that 5% may indeed have been enough in the context. In any case, it's not right to take Dr. Rob's answer as "proof" of your claim. Dr. Rob was answering a different assumed question, namely, how can you prove that pi is greater than 3.1.

- Doctor Rick, The Math Forum http://mathforum.org/dr.math/



Appendix BDoes the Bible say pi equals 3.0?

by Russell Grigg

Source: http://www.creationontheweb.com/content/view/1731/

However, even if it is assumed that the measurements given were precisely 10 and 30 cubits, the following appears to provide a definitive answer. 2. Verse 26 of 1 Kings 7 says that the vessel in question had a brim which ‘was wrought like the brim of a cup, with flowers of lilies’ (KJV), or a rim ‘like the rim of a cup, like a lily blossom’ (NIV), i.e. the brim or rim turned outward, suggesting the curvature of a lily. It is believed by Bible scholars to have looked like the drawing below.

Let us consider the details given in 1 Kings 7:23 and 2 Chronicles 4:2. These are: 1. The diameter of 10 cubits was measured ‘from brim to brim’ (v. 23), i.e. from the topmost point of the brim on one side to the topmost point of the brim on the other side (points A and B in the diagram). 2. The circumference of 30 cubits was measured with a line, ‘round about’ (v. 23), i.e. the most natural meaning of these words is that they refer to the circumference of the outside of the main body of the tank, measured by a string pulled tightly around the vessel below the brim. It is very obvious that the diameter of the main body of the tank was less than the diameter of the top of the brim. And it is also obvious that the circumference of 30 cubits could have been measured at any point down the vertical sides of the vessel, below the brim. For a measured circumference of 30 cubits, we can calculate what the external diameter of the vessel would have been at that point from the formula:

diameter = circumference ÷ pi

= 30 cubits ÷ 3.14

= 9.55 cubits.

Thus the external diameter of the vessel at the point where the circumference was measured must have been 9.55 cubits. It is thus abundantly clear that the Bible does not defy geometry with regard to the value of pi, and in particular it does not say that pi equals 3.0. Skeptics who allege an inaccuracy are wrong, because they fail to take into account all the data. The Bible is reliable, and seeming discrepancies vanish on closer examination.



Appendix CSource: http://www.math.ubc.ca/people/faculty/israel/bpi/bpi.html

On The Rabbinical Exegesis of an Enhanced Biblical Value of

Shlomo Edward G. Belaga C. N. R. S., Université Louis Pasteur

7, rue René Descartes F-67084 STRASBOURG Cedex FRANCE

AMS 1980 Mathematics Subject Classification: 01 A 15, 01 A 17 Key words: history of Pi, Rabbinical exegesis.

Abstract:

We present here a biblical exegesis of the value of , , from the well known verse 1 Kings 7:23. This verse is then compared to 2 Chronicles 4:2; the comparison provides independent supporting evidence for the exegesis.

1.The Hebrew Bible often speaks the language of numbers and measurements [Feldman 1965]; the Western tradition rarely , if at all [Hoyrup 1989], understands this language, and the case of the Biblical value of could be seen as both a remarkable exception of this rule and its striking confirmation.

As a recent publication in The American Mathematical Monthly puts it, ``the ancient Hebrews regarded as being equal to 3'' [Almkvist, Berndt 1988, p. 599]. This claim (as several identical claims made by both working mathematicians [Borwein, et al. 1989] and historians of science [Bell 1945], [Beckmann 1971]) is based on the plain meaning of the following verse of the Hebrew Bible, 1 Kings 7:23, giving the dimensions of a tank in the First Temple :

``And he made a molten sea [tank], ten cubits from the one brim to the other: it was round all about, and its height was five cubits: and a line of thirty cubits did circle it round about''. [Holy Scriptures, p. 412]

As a matter of fact, after mentioning this verse, people either can not , or do not want , to hide (or are even happy for some ideological reasons, to emphasize ) their surprise by such a

low accuracy of the Biblical approximation, , especially in the light of well-documented evidence that the ancient Babylonians and Egyptians used for much better approximations [Neugebauer 1969], [Gillings 1972] many hundred years before this part of the Hebrew Bible was written:



Thus, it seems both appropriate and interesting at this point to give a Rabbinical interpretation of the above verse and the way the number , implicitly defined in this verse, has to be computed [Max Munk 1962 , 1968] (see also two popular and slightly different accounts in [Posamentier, Gordan 1984] and [Roiter 1993]). We do not claim, however, that the Rabbinical folklore has preserved either the mathematical method which was used in this approximation of

, or its historical origins: all that was left to us is an extremely natural and concise mnemonic

rule of the reconstruction of (see more about it in [Max Munk 1962, 1968]).

Such an absence of mathematical justification is, of course, well known to historians; as, e.g., a

researcher writes about the value of : `` Just how this remarkably close approximation was found, we do not know, but we can offer a suggestion on examining the diagram of RMP 48''(cited in [Gillings 1972, p. 142]). In our case, no diagrams were preserved; one could even doubt that such diagrams ever existed: ``ancient Hebrews'' have never regarded mathematical or, for that matter, any other scientific knowledge per se as deserving to be developed, preserved, and disseminated in the written form, as they were not interested (with the Jewish Temple being a notable exception) in creating numerous and splendid monuments of their religion and culture.

2. The key to an alternative reading of the verse 1 Kings 7:23 is to be found in the very ancient Hebrew tradition (see, e.g., [Britannica 1985], [Banon 1987, pp. 52, 53]) to differently write (spell) and read some words of the Bible; the reading version is usually regarded as a correct one (in particular, it is always correct from the point of view of the Hebrew grammar, and this is why it could be easily either remembered or reconstructed from the written version), whereas the writtenversion slightly deviates from the correct spelling. (Another approach, involving the comparison between written forms of the same words in 1 Kings 7:23 and Chronicles 4:2 is cited in [Posamentiern, Gordan 1984] ; see more about this version of the exegesis in 4).

Such a disparity is a common feature for all Books of the Hebrew Bible; and in any such casethere exists (or existed: some of this knowledge was definitely lost) a Rabbinical folklore (in fact, strict Rabbinical hermeneutical rules [Steinsaltz 1976, part three: Method], [Britannica 1985], [Banon 1987]) of interpretation of the difference in question.

In our case there is such a disparity for the word ``line'': in Hebrew, it is written as ``QVH (Qof, Vav, Hea)'', but it has to be read as ``QV (Qof, Vav)'' (the reader is advised to look at any edition of the Hebrew Bible with the Hebrew text and its translation; all disparities are either marked by an atersik, or the reading version is written on the margins).

Tradition asserts that not only does this disparity testify to an approximate character of the given length of the line circling around the ``sea''(tank), -- a much more accurate approximation to ,

, is hidden in the choice of the written version!

The letters of the Hebrew alphabets were traditionly used (well before the building of the First Temple [Guitel 1975]) for numerical purposes and, thus, have had numerical values . Using these values, one can calculate values of words (as sums of values of letters, but also in several other, less obvious and/or more involved ways); these methods became later known as gematria[Michael Munk 1983, p. 163], [Britannica 1985]. Here are the standard numerical equivalents of the letters of the Hebrew alphabet:

Aleph=1, Beth=2, Gimel=3, Daled=4, Hea=5, Vav=6, Zain=7, CHet=8, Tet=9, Yod=10, Caf=20, Lammed=30, Mem=40, Noon=50, Samech=60, Aiin=70, Pea=80,

TSadik=90,



Qof=100, Reish=200, Shin=300, Tav=400. cm

In particular, the numerical equivalent of the written version ,``QVH'', is Qof+Vav+Hea=100+6+5=111, whereas the numerical equivalent of the reading version, ``QV'', is Qof+Vav=106.

Using these numerical equivalents, one defines as follows:

Thus,

3. Quantitatively, this is quite a remarkable approximation! However, it is even more remarkable qualitatively. Here is a finite section of the (infinite) continued fraction of the number :

and here are the convergents (see, e.g., [Khintchine 1963]) corresponding to the first five sections of :

One immediately observes that, firstly, , and, secondly, is

the second (after ) best convergent with a denominator under 30,000 ! Notice also that the preceding convergent, [3:7]=22/7, was known to ancient Greeks.



4. It is worthwhile to mention here a remarkable fact, namely, that in the case of the verse 1 Kings 7:23 we have an independent confirmation of the above mentioned written vs. readingdisparity.

Namely, it could be easily seen that the verse 2 Chronicles 4:2 of the Hebrew Bible repeats 1 Kings 7:23 almost verbatim [Holy Scriptures, p. 988]. Looking at the Hebrew text, one immediately observes that the Hebrew word translated as line is traditionally spelled (written) here identically to its reading version. Thus, even if somebody would rebuff as irrelevant the problem of interpretation of the disparity written vs. reading version of the word line in 1 Kings 7:23 (because he does not trust the oral tradition of transmission of Biblical texts), he would still have to explain the disparity between two different written versions of the same word (with only one version being grammatically correct) in two almost identical verses of the Bible! This last disparity is chosen as the point of departure for the Rabbinical exegesis in [Posamentier, Gordan 1984].

One could ask, why would be this important hint to the enhanced value of omitted from the Books of Chronicles? An answer might be that the Books of Chronicles were written more than four hundred years after the Books of Kings, and the author of the Chronicles (traditionally identified with the Scribe Ezra) was much more preoccupied with rebuilding the Temple and preserving the spirit of the Torah, than with the ``correct'' value of hidden in the descriptions of dimensions of the sacred objects in the First Temple; still, Ezra has faithfully reproduced these dimensions in his book.

A methodological remark: whereas the exegesis based on comparison of written-vs.-readingversions of a verse is a very general method in the Rabbinical tradition [Munk 1962, 1968], [Banon 1987], the above exegesis exploits a more rare event: the existence of two almost identical verses.

5. The following question arising from the above analysis has to be, at least briefly, touched upon: if the author of the first Book of Kings (traditionally identified with Prophet Jeremiah) actually knew

the value and intentionally exploited the aforementioned written-vs.-reading disparity to encode it, why couldn't he simply write this value down in his text?

The answer might be that the value , implicitly given in the text, plays an important rôle as an approximation which was regarded (and is still regarded) as best suited for all ritual purposes in the everyday life of a common practitioner (possibly, mathematically illiterate) of the Jewish law. Thus, our verse serves, in fact, (and so, we conjecture, was it conceived by its author) as the [only] textual basis for the following legal definition of : ``Any [circle] which has a circumference of three fists has a diameter of one fist'' [Mishnah 1983, p. 23] (this important dictum is encountered in at least four different places of the Babylonian Talmud [Max Munk 1962, 1968]).

Still, all legal texts thoroughly investigate the problem [Max Munk 1962, 1968], [Scherman 1980], [Mishnah 1983, p. 22] and confirm that the real value of is ``slightly bigger'' than 3, with some commentators advancing an almost modern point of view on irrational nature of (the irrationality of was strictly proved only in the late eighteenth century); thus, Rambam comments:``...the [exact] ratio of the diameter of a circle to its circumference cannot be known [is irrational]...but it is possible to approximate it...and the approximation used by scientists [Greeks and Arabs] is the ratio of one to three and one seventh... Since it is impossible to arrive at a perfectly accurate ratio, ... they [the Jewish Sages] assumed a round number and said: `Any [circle] which has a circumference of three fists has a diameter of one fist'. And they relied on this for all the measurements they needed'' [Mishnah 1983, p. 22].



It should be stressed that the purposed interpretation of the two-level semantical structure of a Biblical verse (in our case, 1 Kings 7:23), one level for legal purposes, and another one for ``connoisseurs'', is not only a typical phenomenon in the Rabbinical tradition -- in a sense -- such a multi-level approach to texts is the main methodological legacy of this tradition [Steinsaltz 1976, Part Three: Method], [Banon 87]. As Rabbi Moshe ben Nachman writes: ``Everything that was transmitted to Moses our teacher through the forty-nine gates of understanding was written in the Torah explicitly or by implication in words, in the numerical value of the letters or in the form of the letters, that is, whether written normally or with some change in form, such as bent or crooked letters, and other deviations...'' [Ramban 1971, Vol.1, p. 10].

Of course such an approach makes sense only if applied to texts which are faithfully transmitted from generation to generation; in fact, Judaism possesses elaborate institutions for such a transmission . In this sense, it is (and always was) similar to modern science, with its elaborated institutions of training and supporting professionals, whose duty is to discover, accumulate, and transmit knowledge.

6. With all this understanding, gained thus far, we are, as yet, unable to elucidate the way the exegesis of the verse 1 Kings 7:23 has come to us: was it rediscovered by Rabbi Matityahu Hakohen Munk on his own [Max Munk 1962, 1968], or was it transmitted to him? Is there another source in the Rabbinical literature for the exegesis?

A formidable a priori difficulty in answering these and similiar questions is related to unpleasant two thousand years old legacy of Judaism: as a religion, it invariably remained during this period an underdog, prone to persecutions and derision. This external pressure, together with related to it scarcity of social resources, explain why Rabbis have strictly separated legal matters (as, e.g.,

the legal definition of ) from ``esoteric'' knowledge available to them (our exegesis possibly included). In fact, it would be a nightmare scenario for Rambam, or any other Jewish scholar who lived two hundred years ago, or more, to advance a better approximation of , without being able (as we now are) to confirm this value scientifically.

This fundamental difficulty still remains the main obstacle to scientific ``customization'' of the vast body of esoteric knowledge accumulated, commented upon, and faithfully transmitted by Jewish scholars. The author hopes to be able to contribute more to our better understanding of this precious intellectual and spiritual heritage. cm Acknowledgements. Any acknowledgements would be both incomplete and difficult to appreciate without some rather personal remarks about the history of the writing of the present paper.

The author has acquired the knowledge of the Rabbinical exegesis of the verse 1 Kings 7:23from Rabbi Haim Roth, of Mevasseret Yerushalaim, eleven years ago (the winter of 1979-1980); since then, several scholars in Talmudic studies have confirmed the existence of the exegesis, however, no sources for it were ever mentioned.

The author decided to publicize the exegesis, in the fall of 1990, after he stumbled upon two recent papers in The American Mathematical Monthly (written for a wide mathematical audience and devoted to new methods of computation of ), which claimed, in a matter-of-fact manner, that ``the ancient Hebrew regarded as being equal to 3'', citing, of course, the verse 1 Kings 7:23 !

The first draft of the paper appeared in October 1990, with a very gratifying reponse from both the Talmudic and scientific communities. The comments of Rabbi Naftali Gut, of Zürich, were most inspiring. Rabbi Dr. Henri Biberfeld, Rabbis Daniel Mund and Arye Posen, of Montréal, suggested several important Talmudic and Halachic sources. Rabbi Dr. Nachum L. Rabinovich, of Maaleh Adumim, read the paper and suggested an important correction. Discussions with Prof. Louis



Charbonneau, of Montréal, and his colleagues were helpful in adjusting the presentation to the tastes of practitioners of history of mathematics; the references [Feldman 1965], [Hoyrup 1989] belong to Prof. Charbonneau. Later, he introduced the author to Prof. Roger Herz-Fischler, of Carleton, to whom belongs the reference [Zuidhof 1982]. Monsieur Luc Gagnon, the student of Prof. Jacques Lefebvres, Montréal, supplied the reference [Posamentier, Gordan 1984]. Several manifestations of utmost disbelief (in few cases, bordering on ridicule ), on the part of colleagues with, apparently, no previous exposure to Jewish studies, helped the author to contain excitement and avoid self-congratulation.

Finally, and miraculously, Prof. Edward Reingold, of Urbana, whose enthusiasm for the subject was most encouraging, introduced the author to Rabbi Dr. Zeharia Dor-Shav, of Bar-Ilan, who, by sheer coincidence, has just become aware about the existence of an exegesis and started to look for its source. In a week or so, the crucial references [Max Munk 1962, 1968] were found and transmitted to the author -- and all this has happened in the last week of April 1991, after eleven years of unsuccessful search for such a source! After hearing about the author's difficulties to locate the (Hebrew) references in Montréal, Prof. Reingold has found the articles in Urbana and sent the copies to the author.

Still, with all the aforementioned interest and encouragement, the risky endeavor to bridge the gap between the Rabbinical tradition and modern history of science would be impossible without the steadfastness and support of the author's family.

REFERENCESNote: The Rabbinical literature on the subject which are dealt with (or only briefly mentioned) in this paper is enormous. However, the present author has intentionally restricted his choice to such English (and, in three cases, French) references which are widely available in modern libraries. The only (and, unfortunately, unavoidable) exceptions are the original papers of Rabbi Max Munk, written in Hebrew and never translated in any of Western languages. G. Almkvist, B. Bernd 1988: Gauss, Landen, Ramanujan, the Arith- metic -Geometric Mean, Ellipses, , and the Ladies Diary, The Amer. Math. Monthly, 95, 585-608. D. Banon 1987: La lecture infinie: Les voies de l'interprétation midra- chique, Éditions du Seuil, Paris. P. Beckmann 1971: A History of (Pi), The Golem Press, Boulder. E. T. Bell 1945: The Development of Mathematics, McGraw-Hill, New-York. J. Brook 1988: The God of Isaac Newton, in: eds. J. Fauvel, et al., Let Newton Be!, Oxford Univ. Press, pp. 166-183. J. M. Borwein, P. B. Borwein, D. H. Bailey 1989: Ramanujan, modular equations, and approximations to Pi, or How to compute one billion digits of Pi, The Amer. Math. Monthly, 96, 201-219. Britannica (The New Encyclopedia) 1985, Vol. 14: Biblical literature and its critical interpretation, Vol 22: Judaism, Chicago. W. M. Feldman 1965: Rabbinical Mathematics and Astronomy, Hermon Press, New-York. R. J. Gillings 1972: Mathematics in the Time of the Pharaohs, The MIT Press, Cambridge. G. Guitel 1975: Historie comparée des numérations écrites, Flammarion, Paris. J. Hoyrup 1989: The Mathematical Context of the Bible, Technical Report N 2, universityCentre, to appear in Anchor Bible Dictionary. The Holy Scriptures, Koren Publishers, Jerusalem, 1977. A. Ya. Khintchine 1963: Continued Fractions, P. Noordhoff, Groningen. F. Manuel 1974: The religion of Isaac Newton, Clarendon Press, Oxford. Mishnah, The Artscroll Series, 1983: Seder Moed, Vol. 1(b): Eruvin, Mesorah Publications, New-York. M(ax) Munk, Rabbi 1962: Three Geometry Problems in Tanach and Talmud (in Hebrew), SINAI(Mossad Harav Kook) 51 (5722) 218-227.



M(ax) Munk, Rabbi 1968: The Halachik Way for the Solution of Special Geometry Problems (in Hebrew), HADAROM (Rabbinical Council of America) 27 (5728) 115-133. M(ichael) L. Munk, Rabbi 1983: The Wisdom in the Hebrew Alphabet, Mesorah, Brooklyn. O. Neugebauer 1969: Vorlesungen über Geschichte der antiken mathematischen Wissenschaften, Erster Band: Vorgriechische Mathematik, Spring- er, Berlin. A. S. Posamentier, N. Gordan 1984: An astounding revelation on the history of , The Mathematics Teacher 77, N 1, pp. 52, 47. Ramban 1971: Commentary on the Torah, in five volumes. Translated by Rabbi Dr. C. B. Chavel, Shilo Publishing House, New-York. H. Roiter 1993: La mer d'airain du Roi Salomon et le nombre (PI), Kountrass 7, N 38, p. 10. N. Scherman, Rabbi 1980: Measurements from Sinai, an overview to Bircas HaChammah, Mesorah Publications, New-York. A. Steinsaltz 1976: The Essential Talmud, Basic Books, New-York. R. S. Westfall 1987: Never at Rest, Cambridge Univ. Press, Cambridge. Zuidhof 1982: King Solomon's molten sea and ( ), Biblical Archeologist, Summer 1982, 179-184. cm

Endnotes:...exegesis.

An earlier version has appeared in the Proceedings of the XVIIth Canadian Congress of History and Philosophy of Mathematics, Queen's University, Kingston, Ontario, May 27-29, 1991, pp. 93-101.

...rarely One of those rare cases is Isaac Newton's ``obsession with the [King Solomon's] temple's plan and dimensions...Being the man he was, he plunged into an extensive program of reading in Josephus, Philo, Maimonides, and the Talmud scholars'' [Westfall 1987, pp. 346-348]. Newton's inspirations were conjectured by Frank Manuel [Manuel 1974] in the following form:``The temple of Solomon was the most important embodiment of a future extramundane reality, a blueprint of heaven; to ascertain every last fact about it was one of the highest forms of knowledge, for here was the ultimate truth of God's kingdom expressed in physical terms'' (quoted in [Brooke 1988], p. 177.)

...Temple Built by the King Solomon, the ninth century BCE; the water of the tank was used by priests for ritual ablutions. ``The molten sea was a large, bronze water reservoir set on backs of twelve bronze oxen and placed in the court of Solomon's temple...The diameter was about 5 m (16 feet), the height about 2.5 m (8 feet), and the volume amounted to roughly 45,000 litres (12,000 U.S. gallons). There can be little doubt that it was one of the greatest engineering works ever undertaken in the Hebrew nation. Its size is comparable to some of the largest church bells cast in modern times'' [Zuidhof 1982, p. 179].

...not ``but several difficulties complicate the analysis of the design of the vessel, its dimensions and the volumetric capacity ...The sea apparently was not the typical straight-walled mathematical cylinder...a brim and a lily has outward curving petals...The biblical account mentions first the brim to brim diameter of ten cubits. A line streched across the top would easily have measured this...It is then



reasonable to conclude that the 30-cubit circumference was measured below the brim'' [loc.cit., pp. 179-181].

...want ``It has been suggested, perhaps by someone who believes that `God makes no mistakes', that `round' and `depth' are to be interpreted loosely, and that the tank was elliptical in shape'' [Almkvist, Berndt 1988, p. 599].

``Not all ancient societies were as accurate, however -- nearly 1500 years later the Hebrews were perhaps still content to use the value 3'' [Borwein, et al. 1989, p. 204].

...emphasize ``The inaccuracy of the biblical value of is, of course, no more than an amusing curiosity. Nevertheless, with the hindsight of what happened afterwards, it is interesting to note this little pebble on the road to the confrontation between science and religion'' [Beckmann 1971, p. 13-14].

...implicitly ``Also, the ratio between circumference and diameter ( ) of the circular vessel is not mentioned in the Bible...'' [Zuidhof 1982, p. 180]

...1984] Who attribute their exegesis to Rabbi Eliyahu of Vilna, alias Gaon-mi-Vilna, the famous Talmudic scholar of the late eighteenth century; unfortunately, the author was unsuccessful in locating the related reference to works of Gaon-mi-Vilna

...values Analogous numeric systems were used later, and, without doubt, following the Hebrew tradition, in the Arabic, Greek, and Cyrillic texts [Guitel 1975]

...RambamA Rabbinical authority, codifier, philosopher, and royal physician, Rabbi Moshe ben Maimon (1135-1204), known by his acronym, RAMBAM, and as Maimonides, was one of the most illustrious figures in Judaism of all time.

...Nachman A Rabbinical authority, codifier, philosopher, physician, and poet; born in 1195, died circa 1270; known by his acronym, RAMBAN, and as Nachmanides

...transmission A historian comments: Josephus, writing not long after 70 CE boasts of the existence of a longstanding fixed text of the Jewish Scriptures'' [Britannica 1985, vol.14, p. 760].

...ridicule



As an anonymous reviewer has written on the third draft of the present paper (which went in all through a dozen of drafts), ``Il n'auirait pas à adhérer à un acte de foi, comme celui décrit en p.2 ni comme en p.3-4:`(...) Ezra has faithfully reproduced these dimensions in his book' ''. The present author does not remember now what exactly has the reviewer referred to on the page 2 (nor was it clear to the author immediately after he has received the reviewer's text), but the author's statement about the ``faithfullness of Ezra'' has survived all changes (see the end of 4), to testify that no ``act of faith'' is needed to compare two verses and to conclude that the second one is a faithful copy of the first one.



Appendix DSource: http://www.1john57.com/1kings723.htm

THE HOLY BIBLE KNEW ABOUT THE CORRECT VALUE FOR PILONG BEFORE VIETE of 1593 A.D. DID!

by Don Hewey, email: [email protected] disclaimerCopyright © 1998-1999, "1john57.com" of KJV Apologetics. All rights reserved.

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NOTE: This outline will clearly illustrate the "inside" circumference of the molten sea solid brass tub) which is the non-brimmed portion of the molten sea. The confusion over 1 Kings 7:23 is that the reader automatically assumes that the thirty cubits stated in verse 23 is the corresponding circumference of the outer uttermost brimmed edge. It is not. For a complete discussion on the outer portion of the molten sea, please refer to this link here that gives the proof. outer circumference proof . The exact physical represention as it is written in verse 23 is physically impossible as one should immediately become suspicious of. But with further examination of this outline and also the "yfiles" link, the bible not only proves PI once, but twice! Amazing. Please refer to the molten sea diagram representation half way down this page for an illustration to this problem.

"1 Kings 7:[23] And he made a molten sea, ten cubits[#0520 ammah] from the one brim[#08193 saphah] to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about."

The mathematics in verse 23 is NOT in error. Why? Because of verse 26, ".....HAND BREADTH THICK..."

"1 Kings 7:[26] And it was an HAND BREADTH THICK[#02947 tephach], and the BRIM[#08193 saphah] thereof was wrought like the brim of a cup, withflowers of lilies: it contained two thousand baths." First, a cubit (strongs #0520 = 'ammah') is defined as approximately 18 in. For the sake of this illustration, 18 inches will be used.

The circumference of a circle is PI x d (diameter).

The rub with this verse 23 is that it does not state how thick the brim is! So here is the mathematics to prove that verse 26 is accurate ("...the hand breadth thick...").

PI = 3.14159 (approximately), the diameter must be solved to account for the width of the brim, so therefore we must solve for "d"......in doing this we get,

30 cubits = 30 x 18 inches = 540 inches it total circumference. 540 inches DIVIDED by PI = 171.8874 inches.

Now, since it is now known that DIAMETER is 171.8874, we must now subtract the different between the breadth thickness of EACH SIDE. In other words, when measuring the diameter of



an tank or container that has substantial thickness, the thickness must be accounted for TWICE. Once for the first edge, then ONCE MORE for the opposite edge. Therefore we get,

10 cubits = 180 inches - 171.8874 inches = 8.1126 inches.

Now divide 8.1126 by TWO, we get 4.0563 inches. NOW GET OUT A RULER AND MEASURE THE BREADTH OF YOUR HAND!!!!!

CUBIT = 0520 ammah {am-maw'}

prolonged from 0517; TWOT - 115c; n f

AV - cubit 242, measure 1, post 1, not translated 1; 245

1) cubit - a measure of distance (the forearm), roughly 18 in (.5m). There are several cubits used in the OT, the cubit of a man or common cubit (Dt 3.11), the egal cubit or cubit of the sanctuary (Eze 40.5) plus others. See a Bible Dictionary for a complete treatment

HAND BREADTH = 02947 tephach {tay'-fakh}

from 02946; TWOT - 818b; n m

AV - hand breath 3, coping 1; 4

1) span, width of the hand, hand breadth 1a) a unit of measurement, measurement of length 2) coping (an architectural term)

BRIM = 08193 saphah {saw-faw'} or (in dual and plural) sepheth {sef-eth'}

probably from 05595 or 08192 through the idea of termination (compare 05490); TWOT -2278a; n f

AV - lip 112, bank 10, brim 8, edge 8, language 7, speech 6, shore 6, brink 5, border 3, side 3, prating 2, vain 2, misc 4; 176

1) lip, language, speech, shore, bank, brink, brim, side, edge, border, binding 1a) lip (as body part) 1b) language 1c) edge, shore, bank (of cup, sea, river, etc)

[24] And under the brim of it round about there were knops compassing it, ten in a cubit, compassing the sea round about: the knops were cast in two rows, when it was cast. [25] It stood upon twelve oxen, three looking toward the north, and three looking toward the west, and three looking toward the south, and three looking toward the east: and the sea was set above upon them, and all their hinder parts were nward. [26] And it was an HAND BREADTH THICK, and the BRIM thereof was wrought like the brim of a cup, with flowers of lilies: it contained two thousand baths.



D2 = the measured diameter between the extreme OUTER points of the rim at the very top of the molten sea tub.

Table of computation of Pi from 2000 BC to now

Babylonians 2000? BC 3.125 = 3 + 1/8

Egyptians 2000? BC 3.16045

China 1200? BC 3

Holy Bible (1 Kings 7:23 and 26) 550 BC 3.1415926

Archimedes 250? BC 3.1418 (averaging technique)

Hon Han Shu 130 AD 3.1622 = square root of 10



Ptolemy 150 AD 3.14166

Chung Hing 250 AD 3.16227 = squareroot of 10

Wang Fau 250 AD 3.15555 = 142/45

Liu Hui 263 AD 3.14159

Siddhanta 380 AD 3.1416

Tsu Ch'ung Chi 480 AD 3.1415926

Aryabhata 499 AD 3.14156

Brahmagupta 640 AD 3.162277 = squareroot of 10

Al-Khowarizmi 800 AD 3.1416

Fibonacci 1220 AD 3.141818

Al-Kashi 1429 AD 3.1415929

Otho 1573 AD 3.1415929

Viete 1593 AD 3.1415926536 (ave.)

Romanus 1593 AD 3.1415926536 (ave.)

Van Ceulen 1596 AD 3.1415926536 (ave.)

Newton 1665 AD 3.1415926536 (ave.)

Sharp 1699 AD 3.1415926536 (ave.)

Graf Theoryhttp://www-groups.dcs.st-and.ac.uk/~history/Miscellaneous/other_links/Graf_theory

The brass tub in Solomon's temple was a thick-sided vessel, and the measurement of ten cubits referred to the outer diameter, while the measurement of thirty cubits referred to the inner circumference. The thickness of the annulus was recorded as a hand-breadth. If one considers a hand breadth to be 4 inches, and uses a figure of 17.75 for a cubit, the value of p in the equation:

((10 - 30/p)/2) 17.75 = 4

is p = 355/113 .

I don't think the Hebrews calculated the values recorded, merely observed them. The true value of would give slightly different values for a hand-breadth and a cubit. I think this fact is more interesting than the improper imputation of 3 as the 'Biblical' value of .

Comment by: Bob Graf, 29th October 1996.

We note that the value 355/113 as an approximation for was first noted by Zu Chongzhi (430-501 AD)



http://david.tribble.com/text/biblepi.htmPi and the Bible by David R. Tribble

Some mathematical comments are in order to add to the discussion of pi. If one takes a more analytical look at the Bible verses noted (II Chronicles 4:2-5 and I Kings 7:23-26), one will arrive at a ratio that is startlingly close to the real value of pi (3.14159+).

One fact that is overlooked in discussions of this sort is that the wall of the "sea" (bowl) was "one handbreadth" in thickness (I'm assuming that a handbreadth is about four inches and a cubit is about 18 inches, but more on this later). Taking the thickness of the walls into account, and assuming that the 10 cubit diameter was measured from the outside edge and that the 30 cubit circumference was measured along the inside edge, we compute pi thus:

Ci = 30 cubits inside circumference = 540 inches

Do = 10 cubits outside diameter = 180 inches

T = 4 inches wall thickness

given the following relationships:

Ci = pi × Di

Di = Do - 2 × T inside diameter

and substituting, we get:

Ci = pi' × (Do - 2 × T)

Ci pi' = ------------ described value of pi Do - 2 × T

540 inches = -------------------- 180 - 2 × 4 inches

= 3.139534+

The difference between the described value of pi (pi') and the actual value of pi is:

pi - pi' error = ---------- × 100% pi

3.141592+ - 3.139534+

= ----------------------- × 100% 3.141592+



= 0.0655%

This means that, given the assumptions above, the Biblical description of pi differs from the real value of pi by less than a fifteenth of a percent, or a measuring error of about a third of an inch. Not bad for measurements done by hand. This also agrees with the description of a "circular" bowl and not some other shape (such as a hexagon) that some scholars have postulated.

Now about that assumption I mentioned ealier. Although ancient standards of measure vary widely, a cubit is generally taken to be about 18 inches, although there are different types of cubits ("common" and "royal", varying from 17 to 22 inches). A handbreadth is taken to be about 3 inches, sometimes being defined as one-sixth of a cubit. However, if we assume that the Biblical account uses measurements rounded off to the nearest whole number (something the Hebrews did a lot), we can read "one handbreadth" as "one handbreadth, give or take a bit," making it completely reasonable to use a value of four inches. It is also reasonable for us to measure along the inside as well as the outside edges, since the verses don't explain how the measuring was done.

This same argument was made around AD 150 by the Hebrew Rabbi Nehemiah in his "Mishnat ha-Middot", the earliest known Hebrew geometry text. (See "A History of Pi" by Petr Beckmann, an entertaining story of the search for pi, for more details.)

Anyway, the bottom line in this whole discussion is that pi is a ratio between abstract geometric concepts, a purely mathematical idea not derived from any physical object or manifestation. As such, it is impervious to physical laws and, by the same token, legislative laws.



Appendix E

JokesThere are, of course, some “solutions” which were offered for

1 Kings 7:23 which will make you laugh.

π and G changing with time? Of course! Alan Sokal demonstrated that years ago in his ground-breaking essay, "Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity".

In mathematical terms, Derrida's observation relates to the invariance of the Einstein field equation Gμν = 8πTμν under nonlinear space-time diffeomorphisms (self-mappings of the space-time manifold which are infinitely differentiable but not necessarily analytic). The key point is that this invariance group "acts transitively": this means that any space-time point, if it exists at all, can be transformed into any other. In this way the infinite-dimensional invariance group erodes the distinction between observer and observed; the π of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone.

Posted by: Blake Stacey | August 14, 2006 10:12 AM

Source: http://scienceblogs.com/

Proof that a circle with a diameter of 10 cubits has a circumference of exactly 30 cubits

We start by defining a value x to simplify the math: Let x = 5π + 15Next, we write the formula for the circumference of a circle, plugging in the diameter of 10:

C = 10π

Add 30 to each side and substitute our handy value x: C + 30 = 10π + 30C + 30 = 2 (5π + 15)C + 30 = 2xMultiply each side by (C − 30): (C + 30) (C − 30) = 2x (C − 30)C2 − 900 = 2Cx − 60xAdd x2 to each side and rearrange the terms: C2 − 900 + x2 = 2Cx − 60x + x2



C2 − 2Cx + x2 = 900 − 60x + x2

Factor and simplify: (C − x)2 = (30 − x)2

(C − x) = (30 − x)C = 30QED!

PS: Just kidding!

But speaking of pi, here’s a formula I came up with a few years ago to make it easier to remember:

π = (12.3 + 4 + 5) / 6.78

Don’t believe this works? Try it!

Source: http://www.noble-minded.org

www.geocities.com/perianthium786


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