arithmetics in forestry

7/31/2019 Arithmetics in Forestry

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By

Jyothish J Ozhakkal

Roll No: 26 (FRO Trainee)

Arithmetics in Forestry


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Contents

Arithmetic operations

Powers & Roots

Ratio & Proportion

Simple Interest & Compound Interest

Logarithms


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Origin

From the Greek word arithmos - number

Arithmetic operations

Addition (+)

Subtraction ()

Multiplication ( or or *)

Division ( or /)
http://en.wikipedia.org/wiki/Numberhttp://en.wikipedia.org/wiki/Number


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x: base

n: either integer or fraction

Powers and Roots

n

x

...

8)givewillcubed2(since28

555

3/1

4

2

bbbbb


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Powers and RootsAlgebraic Rules for Powers

Rule for Multiplication:

Rule for Division:

Rule for Raising a Power to a Power:

Negative Exponents: A negative exponent indicatesthat the power is in the denominator:

Identity Rule: Any nonzero number raised to thepower of zero is equal to 1, (xnot zero).

mnmn xx

mnmn xxx

mnmn xxx

n

n

xx 1

10 x


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RatioProportion - Fraction .

1 to every 2 is a Ratio

1 out of 3 is a Proportion

One third is a Fraction

Ratios comparePART WITH

PART

Proportionscompare PARTWITH WHOLE

Fractionscompare PARTWITH WHOLE

using shorthand

such as 1/3

3 different ways to

say the same thing

3 different ways to

compare numbers


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Ratio, Proportion or Fraction?

two out of five

This is a proportion

two fifths

This is a fraction

four tenths

This is a fraction

four to every ten

This is a ratioten to every four

This is a ratiofour out of ten

This is a proportion4/10

This is a fraction


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Simple Interest

Principal: An amount of money borrowed orloaned.

Interest: A charge for the use of money, paid bythe borrower to the lender.

Simple Interest: Interest paid only to theprincipal

Interest = Principal Rate Time


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Compound Interest

F - future value

IfP represents the present value

rthe annual interest rate

tthe time in years

n the frequency of compounding

F = P( 1 + r/n)nt


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Continuous Compounded Interest

Compound just every hour, or every minute orevery second or for every millisecond!

The future value formula is:F = Pert.

The annual yield for continuouslycompounded interest:

y = er 1.

e =2.7182818


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Logarithms

102 = 10010 raised to the power 2 gives 100

Base

IndexPower

ExponentLogarithm

The power to which the base 10 must be raised to give 100 is 2

The logarithm to the base 10 of 100 is 2

Log10100 = 2

Number


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Logarithms

102 = 100Base

Logarithm

Log10100 = 2

Number

Logarithm

Number

Base

y = bxLogby = x

23 = 8 Log28 = 3

34

= 81 Log381 = 4Log525 =2 5

2 = 25

Log93 =1/2 9

1/2 = 3

logby = xis the inverse of

y = bx


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103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log4

16 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 =1/2 36

1/2 = 6

log12

1= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga

5 = b ab = 5

logpq = r pr = q

c = logab b = ac


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103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log4

16 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 =1/2 36

1/2 = 6

log12

1= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga

5 = b ab = 5

logpq = r pr = q

c = logab b = ac


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103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log4

16 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 =1/2 36

1/2 = 6

log12

1= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga

5 = b ab = 5

logpq = r pr = q

c = logab b = ac


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103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log4

16 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 =1/2 36

1/2 = 6

log12

1= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga

5 = b ab = 5

logpq = r pr = q

c = logab b = ac


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103 = 1000 log101000 = 3

24 = 16 log216 = 4

104 = 10,000 log1010000 = 4

32 = 9 log39 = 2

42 = 16 log4

16 = 2

10-2 = 0.01 log100.01 = -2

log464 = 3 43 = 64

log327 = 3 33 = 27

log366 =1/2 36

1/2 = 6

log12

1= 0 120 = 1

p = q2 logqp = 2

xy = 2 logx2 = y

pq = r logpr = q

logxy = z xz = y

loga

5 = b ab = 5

logpq = r pr = q

c = logab b = ac


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Laws of logarithms

Every number can be expressed in exponentialform every number can be expressed as a log

Let p = logax andq = logay

So x = apandy = aq

xy = ap+q

p + q = loga(xy)

p + q = logax + logay = loga(xy)

loga(xy) = logax + logay


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Laws of logarithms


Let p = logax andq = logay

So x = apandy = aq

xy = ap-q

p - q = loga(x/y)

p - q = logax - logay = loga(x/y)

loga(x/y) = logax - logay


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Laws of logarithms


Let p = logax andq = logax

So x = apandx = aq

x2 = ap+q

p + q = loga(x2)

p + q = logax + logax = loga(x2)

logaxn = nlogax

L f l i h


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Laws of logarithms


loga(x/y) = logax - logay

loga(xy) = logax + logay

logaxn = nlogax

am.an = am+n

am/an = am-n

(am)n = am.n

Ch f b


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Change of base property

Logax =Logbx

Logba


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Our final concern then is to

determine why logarithms like the

one below are undefined.

Can anyone give us

an explanation ?

2log ( 8)


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One easy explanation is to simply rewritethis logarithm in exponential form.Well then see why a negative value is not

permitted.

First, we write the problem with a variable.

2y

8 Now take it out of the logarithmic form

and write it in exponential form.

What power of 2 would gives us -8 ?

23

8 and 2 3

1

8

Hence expressions of this type are undefined.

2log ( 8) undefined WHY?

2log ( 8) y


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FOREST NURSERY

Seed Purity Percentage = Weight of Pure seed x100

Total weight of sample

Seed Moisture Percentage = Weight of moisture x100

Weight of moisture + dry matterweight

Quantity of seeds req. for raising plantation = A x DKgs

S x N x G x P x M

(A-area to be planted, D-density of plantation, S-survival %,N-no. of seeds per Kg, G-Germination %, P-purity of seed,


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PLANTATION FORESTRY

Method of calculating number of plants per hectare

Line method = 100 x 100 x Area in hectare

Line to line distance x plant to plant distance

Square method = 100 x 100 x Area in hectare

Square of the planting distance

Triangular method = 100 x 100 x 1.155 x Area in

hectareSquare of the planting distance(side of the

triangle)

Quincunx method = 100 x 100 x 2 x Area inhectare


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The Fibonacci NumbersThe number pattern that you have been using is known as the

Fibonacci sequence.

1 1

}+

2


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Fibonacci sequence.

1 1 2

}+

3


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Fibonacci sequence.

1 1 2 3

}+

5 8 13 21 34 55

These numbers can be seen in many natural situations


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Fibonaccis sequence in nature

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584

On many plants, the number of petals is aFibonacci number:

Buttercups have 5 petals; lilies and iris have 3petals; some delphiniums have 8; corn marigoldshave 13 petals; some asters have 21 whereas daisiescan be found with 34, 55 or even 89 petals.

13 petals: ragwort, corn marigold, cineraria, somedaisies21 petals: aster, black-eyed susan, chicory34 petals: plantain, pyrethrum55, 89 petals: michaelmas daisies, the asteraceaefamily.

Some species are very precise about the number ofpetals they have - eg buttercups, but others havepetals that are very near those above, with theaverage being a Fibonacci number.

Pairs
http://affiliates.allposters.com/link/redirect.asp?aid=910266&item=376240


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Pairs

1 pair

At the end of the first month there is still only one pair

Pairs


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Pairs

1 pair

1 pair

2 pairs

End first month only one pair

At the end of the second month the female produces anew pair, so now there are 2 pairs of rabbits

Pairs


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Pairs

1 pair

1 pair

2 pairs

3 pairs

End second month 2 pairs of rabbits

At the end of thethird month, theoriginal femaleproduces a second

pair, making 3 pairsin all in the field.


Pairs


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Pairs

1 pair

1 pair

2 pairs

3 pairsEnd third month3 pairs

5 pairs


End second month 2 pairs of rabbits

At the end of the fourth month, the first pair produces yet another new pair, and the femaleborn two months ago produces her first pair of rabbits also, making 5 pairs.


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1

1

2

3

5

8

13

21

34

55


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Fibonacci in Nature

The lengths of bones in a handare Fibonacci numbers.


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The Golden Ratio

The Golden (or Divine)Ratio has been talkedabout for thousands of

years.

People have shown thatall things of great beautyhave a ratio in theirdimensions of a number

around 1.618

1

1.618


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55+89 = 14434+55 = 89

21+34 = 55

13+21 = 34

8+13 = 21

5+8 = 13

3+5 = 8

2+3 = 5

1+2 = 3

1+1 = 2

ratio

1.6181.618

1.618

1.6191.615

1.625

1.61.666

1.5

The ratio of pairs of Fibonacci numbers gets closer to thegolden ratio


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The Golden Ratio

Leonardo da Vinci showedthat in a perfect man therewere lots of measurementsthat followed the GoldenRatio.


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arithmetics in forestry

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