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Great Mathematicians

By: Vinnie Boettcher, Joe Burbach, Peter Dziewiontkoski,

and Jesse Lucas

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Johann Kepler 1571-1630

• Kepler was a German mathematician and astronomer who discovered that the Earth and planets travel around the sun in elliptical orbits

• Gave 3 fundamental laws of planetary motion

• Discovered 2 new polyhedra

• Studied orbit of Mars

• His father was a mercenary soldier and his mother the daughter of an innkeeper

• Father left when he was five, so he lived at his grandmother’s inn

• His mother charged with witchcraft

• “Some of what these pamphlets [of astrological forecasts] say will turn out to be true, but most of it time and experience will expose as empty and worthless. The latter part will be forgotten [literally: written on the winds] while the former will be carefully entered in people's memories, as is usual with the crowd”

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Leonhard Euler 1707 - 1783

• He went to the University of Basel at 14 to study the ministry

• In 1723 he completed his Master’s in philosophy

• 1727 won 2nd place in the Grand Prize of the Paris Academy

• 1727- 1730 served in the Russian Navy as a medical lt.

• In 1738 and 1740 Euler won the Grand Prize of the Paris Academy

• In 1744 he became the math director at the Berlin Academy

• 1744-1766 Euler wrote 380 articles, and wrote books on calculus and other math

• 1772 he wrote a 775 page work on the motion of the moon

• Throughout his life he introduced

• Beta, Gamma functions and integrating factors

“Now I will have less distraction.” after losing sight in one of his eyes

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Felix Klein1849-1925

• German Mathematician

• He was born on 25/4/1849 and delighted in pointing out that each of the day (52), month (22), and year (432) was the square of a prime.

• He is best known for his work in non-Euclidean geometry, for his work on the connections between geometry and group theory, and for results in function theory

• Attended the Gymnasium in Düsseldorf

• Was appointed professor at Erlangen, in Bavaria in southern Germany, in 1872

“Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry”

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Gottfried Wilhelm von Leibniz1646-1716

• German mathematician who developed the present day notation for the differential and integral calculus

• Attended the Nicolai School in Leipzig at age seven

• In 1661, at the age of fourteen, Leibniz entered the University of Leipzig.

• Work was to be published in 1666 as Dissertatio de arte combinatoria (Dissertation on the combinatorial art). In this work Leibniz aimed to reduce all reasoning and discovery to a combination of basic elements such as numbers, letters, sounds and colors.

“Nothing is more important than to see the sources of invention which are, in my opinion more interesting than the inventions themselves”

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Pierre de Fermat1601 - 1665

• 1629 he gave a copy of his restoration of Apollonius’s Plane loci to a mathmatician

• He went to Orleans to study law

• 1631 He became a civil lawyer and a government official in Toulouse

• Changed his name to Pierre de Fermat

• He worked on maxima, minima, and tangents

• He worked on spirals

• However, he is most known for his number theory, Fermat’s Last Theorem

“And perhaps, posterity will thank me for having shown it that the ancients did not know everything”

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Nikolai Ivanovich Lobachevsky 1792-1856

• Russian mathematician that studied non-Euclidean geometry

• Graduated from Gymnasium in 1807 and entered Kazan University as a free student.

• Lobachevsky received a Master's Degree in physics and mathematics in 1811.

• In 1814 he was appointed to a lectureship and in 1816 he became an extraordinary professor.

• In 1822 he was appointed as a full professor

• Taught a wide range of topics including mathematics, physics and astronomy.

“There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world”

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Marin Mersenne 1588-1648

• Born into a working class family in the small town of Oizé in the province of Maine.

• His first posting was in 1614 to the monastery in Nevers where he taught philosophy and theology to the younger members of the community.

• After Mersenne's death, letters in his cell were found from 78 different correspondents including Fermat, Huygens, Pell, Galileo and Torricelli.

• Mersenne's name is best remembered today for Mersenne primes

• [Animals] do not so much act as be put into action, and that objects make an impression on their senses such that it is necessary for them to follow it just as it is necessary for the wheels of a clock to follow the weights and the spring that pulls them.

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John Napier1550 - 1617

• Scottish scholar who is best known for his invention of logarithms

• Mathematical contributions include a mnemonic for formulas used in solving spherical triangles

• Constructed two formulas known as Napier's analogies

• His family had owned the Merchiston estate from the 1430s when one of his ancestors acquired the estate, becoming the first Napare of Merchiston

• Archibald Napier(father) was a justice-depute and was knighted in 1565

“Seeing there is nothing that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers ... I began therefore to consider in my mind by what certain and ready art I might remove those hindrances”

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0011 0010 1010 1101 0001 0100 1011• Isaac Newton was the greatest English mathematician of his generation

• Laid the foundation for differential and integral calculus

• Born in the manor house of Woolsthorpe, near Grantham in Lincolnshire

• Was Lucasian professor at Cambridge

• Upon the death of his stepfather in 1653, Newton lived in an extended family consisting of his mother, his grandmother, one half-brother, and two half-sisters

“To explain all nature is too difficult a task for any one man or even for any one age. `Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things.”

Sir Isaac Newton1643 - 1727

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Fibonacci of Pisa 1170 - 1250

• Lived mainly in North Africa during childhood

• Father was a diplomat

• Traveled a lot

• 1202 writes his famous book Liber abaci

• Wrote many books, however most are lost

• Known books include Flos (1220) and Liber quadratorum (1225)

• He also wrote a commentary on Euclid’s Elements

• Created a sequence of numbers which each number is the sum of the 2 preceding numbers

“And perhaps, posterity will thank me for having shown it that the ancients did not know everything”

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Blaise Pascal1623 - 1662

• Pascal was a French Mathematician and Philosopher

• Pascal made many accomplishments in conic sections and projective geometry

• He also laid the foundations for the theory of probability

• Pascal was one of four children and the only male. His father educated Blaise himself as a young child

“We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others”

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Srinivasa Ramanujan1887 - 1920

• He was one of India’s greatest Mathematicians

• He made substantial contributions to the analytical theory of numbers

• He also worked on elliptic functions, continued fractions, and infinite series

• He was elected to the Cambridge Philosophical Society and to the Royal Society of London

“An equation means nothing to me unless it expresses a thought of God”

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Evariste Galois1811 - 1832

• 1826 he was asked to repeat his year of school because of his grades

• 1827 he enrolled in 1st math course

• 1829 his 1st math paper was published on continued fractions

• His father committed suicide on July 2 1829

• Passed his Ecole Polytechnique on December 29 1829 after failing twice

• He worked on the elliptic functions and abelian integrals

• May 9, 1831 he was arrested for conspiracy to overthrow the government

• He was again arrested on July 14, 1831

• He was wounded in a duel and died from the wounds

“Unfortunately what is little recognized is that the most worthwhile…”

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GF Bernhard Riemann1826 - 1866

• Riemann was a German mathematician worked on ideas concerning geometry of space

– This had a profound effect on the development of modern theoretical physics.

• He also clarified the notion of integral

– Now called the Riemann integral

• He was the second of 6 children

• His father taught him until he was 10 years old when he went to school

“If only I had the theorems! Then I should find the proofs easily enough”

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Thales Of Miletus624 BC – 547 BC

• Thales was the first known Greek philosopher, scientist and mathematician

• He is credited with five theorems of elementary geometry.

• Although he worked in math and science, he was also an engineer

• He is believed to have been the teacher of Anaximander

• Thales believed that the Earth floats on water and all things come to be from water “I will be sufficiently rewarded if when telling

it to others you will not claim the discovery as your own, but will say it was mine”

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John Von Neumann1903 - 1957

• Von Neumann built a solid framework for quantum mechanics

• He also worked in game theory

– Now called von Neumann Algebras

• He also was one of the pioneers of computer science

• His father, Max Neumann, was a top banker

• Although the family as Jewish, Max did not observe the strict practices “In mathematics you don't understand things.

You just get used to them”

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Karl Friedrich Gauss1777 - 1855

• In 1792 he entered Brunswick Collegium Carolinum where he learned Bode’s law by himself

• 1798 he discovered the construction of a regular 17-gon by ruler and compasses

• Received Brunswick degree in 1799

• 1801 he published the book Disquisitiones Arthmeticae

• Within 3 years he lost his father, wife, and his 2nd son

• 1809 he published another book Theoria motus corporum coelestium in sectionibus conicis Solem ambientium, has differential equations, conic sections, and elliptic orbits

• He introduced the hypergeometric function

“Life stands before me like an eternal spring with new and brilliant clothes”

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Andrew Wiles1953 -

• He proved Fermat's Last Theorem in 1995

• His father, Maurice Frank Wiles, was the Regius Professor of Divinity at the University of Oxford

• At age 10, Wiles understood complex math theories and problems

• He studied at Oxford

• Wiles was awarded a Guggenheim Fellowship

• In 1994 Wiles was appointed Eugene Higgins Professor of Mathematics at Princeton

“...Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever”

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Zeno Of Elea490 BC - 425 BC

• Zeno was a Greek philosopher famous for proposing “paradoxes” which challenged mathematicians' view of the real world

• Zeno was a pupil and friend of the philosopher Parmenides

• Zeno is believed to have written one book on philosophy, however, it has not survived

• Most information on Zeno comes from Plato “Zeno's challenge to simple pluralism is

successful, in that he forces anti-Parmenideans to go beyond common sense”

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Maria Gaetana Agnesi1718 - 1799

• She was one of 21 Children

• She was an Italian Mathematician

• She published many books including:

– Propositiones Philosophicae

– Traité analytique des section coniques

– Instituzioni analitiche ad uso della gioventù italiana

– A book on calculus

• She also accepted the Chair of Mathematics at the University of Bologna

"It is marvelous to see a person of (Agnesi's) age so conversant with such abstract

subjects."---Author C. De Brosses

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Hypatia370 - 415

• First woman to make a substantial contribution to math

• Helped her father write his eleven part comentary on Ptolemy’s Alagest

• She also helped her father write a newer version of Euclid’s Elements

• She wrote documentaries on Diophantus’s Arithmetica

• Also Appolonius’s Conics

• Ptolemy’s astronomical writings, however, this is doubted

“Reserve your right to think, for even to think wrongly is better than not to think at all”

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Mohammed Al-Khowarizmi780 - 850

• He was an Iraqi Mathematician, Astronomer, and somewhat Philosopher

• He was a scholar at the House of Wisdom in Baghdad

• Translated Greek scientific manuscripts

• Gave us the word “algebra”

• Wrote a treatise on algebra, Hisab al-jabr w'al-muqabala, which is one of the most important books on algebra

• Wrote a treatise on astronomy

• Wrote a book about political history

“It is impossible to overstress the originality of the conception and style of al-Khwarizmi's algebra...”

---Rashed

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Charles Babbage1791 - 1871

• English

• He suffered illness while he was a child

• His father was wealthy and sent him to a private school

• He published Memoirs of the Analytical Society

• Translated La Croix’s Sur le calcul différentiel et intégral

• He published a book on calculus

• He tried to invent a engine that would compute mathematical tables

• Invented the concepts behind a modern day computer

• Perhaps it would be better for science, that all criticism should be avowed.

--Charles Babbage

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Bernoulli Family• A Swiss family that had 7 mathematicians in

it.– Daniel: 1700-1782– Jacob: 1654-1705– Jacob II: 1759-1789– Johann: 1667-1748– Johann II: 1710-1790– Johann III: 1744-1807– Nicolaus: 1687-1759– Nicolaus II: 1695-1726

• Achievements of them all Combined

• Found the Bernoulli principle which states an increase in speed results in a decrease in pressure

• First to use the word “integral”

• Studied the refraction of light

• Worked on probability and Heat of Light,

• Studied curves and equations

It would be better for the true physics if there were no mathematicians on earth.

--Daniel Bernoulli

Daniel Bernoulli

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Rene Descarte1596 - 1650

• Rene was a French philosopher

• He worked on La géométrie which includes his application of algebra to geometry from which we now have Cartesian geometry.

• His work had a great influence on both mathematicians and philosophers.

• As a child, he had some trouble in school, but Math always made sense to him

• Descartes' Meditations on First Philosophy, was published in 1641

“Of all things, good sense is the most fairly distributed: everyone thinks he is so well supplied with it that even those who are the hardest to satisfy in every other respect never desire more of it than they already have”

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Janos Boylai1802 - 1860

• Romanian Mathematician who’s father wanted him to be one

• Made his own definition of parallel

• Tried to develop all of mathematics on an axiom system—it failed

• Developed a geometric concept of complex numbers as ordered pairs of real numbers

• His work was published in an appendix in a textbook of his father’s work

• Only published a few pages of his work but there were more than 20,000 when he died that went unpublished

Mathematical discoveries, like springtime violets in the woods, have their season which no man can hasten or retard.

--Janos Bolyai

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George Boole1815 - 1864

• He was an Irish Mathematician

• He wrote a paper On a general method of analysis which used algebra to solve differential equations

• He was appointed to the chair of mathematics at Queens College

• He published many mathematical books

• He published An Investigation into the Laws of Thought, on Which are founded the Mathematical Theories of Logic and Probabilities

• Looked at logic in a new way using simple algebra

• Invented Boolean Algebra which is used in computers and circuits

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

--George Boole

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Brahma-gupta598 - 670

• He was an Indian Mathematician and Astronomer

• His father was Jisnugupta, who studied mathematics and astronomy

• Head of the foremost Ancient Indian Observatory

• Published Brahmasphutasiddhanta

• Was a work on math and astronomy

• Included longitude and latitude of planets, lunar and solar eclipses, rising and settings, lunar orbit, moons shadow, etc.

• Gave arithmetical rules on using positive and negative numbers

“As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them”

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QUIZClick to see the Answer

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1. Who created an algebra that is used in computers even today? (Hint: Truth Tables)

A. Boylai, Janos

B. Agnesi, Maria Gaetana

C.Boole, George

D.Kepler, John

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2. Which mathematician first used the word “algebra”?

A. Al-Khowarizmi, Mohammed 

B. Zeno Of Elea

C. Newton, Sir Isaac

D. Mohammed Al-Khowarizmi

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3. Who laid the foundations for the theory of probability?

A. Pascal, Blaise

B. Lobachevsky, Nikolai Ivanovich

C. Fermat, Pierre de

D. Babbage, Charles

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4. Who was the greatest English mathematician of his generation? (Hint: He worked better at knight)

A. Klein, Felix

B. Descarte, Rene

C. Newton, Sir Isaac

D. Thales Of Miletus

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5. Who discovered that the Earth and planets travel around the sun in elliptical orbits?

A. Kepler, Johann

B. Gauss, Karl Friedrich

C. Wiles, Andrew

D. Bernoulli Family

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6. Who constructed two formulas known as Napier's analogies? (Hint: Don’t think too hard about this)

A. Klein, Felix

B. Babbage, Charles

C. Napier, John

D. Newton, Sir Isaac

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7. Which mathematician tried to invent an engine that would compute mathematical tables?

A. Euler, Leonhard

B. Riemann, GF Bernhard

C. Leibniz, Gotfried Wilhelm

D. Babbage, Charles

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8. Who is the mathematician that gave arithmetical rules on positive and negative numbers?

A. Fermat, Pierre de

B. Brahma-gupta

C. Zeno Of Elea

D. Napier, John

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9. Who was a Russian mathematician that studied non-Euclidean geometry?

A. Lobachevsky, Nikolai Ivanovich

B. Klein, Felix

C. Bernoulli Family

D. Galois, Evariste

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10. What is the name of the family that had many mathematicians in it?

A. Descarte, Rene

B. Leibniz, Gotfried Wilhelm

C. Beroulli Family

D. Von Neumann, John

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11. Which mathematician was one of 21 children?

A. Klein, Felix

B. Agnesi, Maria Gaetana

C. Newton, Sir Isaac

D. Zeno Of Elea

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12. Who was the mathematician whose father wanted him to become one?

A. Gauss, Karl Friedrich

B. Pascal, Blaise

C. Descarte, Rene

D. Bolyai, Janos

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13. Who worked on non- Euclidian Geometry and had a Perfect Square Birthday?

A. Klein, Felix

B. Thales Of Miletus

C. Mersenne, Marin

D. Babbage, Charles

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14. Who developed the present day notation for the differential and integral calculus?

A. Hypatia

B. Brahma-gupta

C. Leibniz, Gotfried Wilhelm

D. Wiles, Andrew

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15. After whose death were 78 letters found in his cell?

A. Fibonacci of Pisa

B. Mersenne, Marin

C. Ramanujan, Srinivasa

D. Bernoulli Family

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16. What Indian scholar made substantial contributions to the analytical theory of numbers?

A. Al-Khowarizmi, Mohammed

B. Brahma-gupta

C. Hypatia

D. Ramanujan, Srinivasa

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17. Who worked on ideas concerning geometry of space?

A. Riemann, GF Bernhard

B. Gauss, Karl Friedrich

C. Boole, George

D. Euler, Leonhard

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18. Who was famous for proposing “paradoxes”?

A. Fibonacci of Pisa

B. Zeno Of Elea

C. Bolyai, Janos

D. Agnesi, Maria Gaetana

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19. Who understood complex math from a very young age?

A. Brahma-gupta

B. Galois, Evariste

C. Wiles, Andrew

D. Pascal, Blaise

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20. Who is credited with five theorems of elementary geometry?

A. Thales Of Miletus

B. Kepler, Johann

C. Descarte, Rene

D. Bernoulli Family

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21. Who built a solid framework for quantum mechanics?

A. Babbage, Charles

B. Hypatia

C. Gauss, Karl Friedrich

D. Von Neumann, John

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22. Who wrote 380 articles, and wrote books on calculus and other math?

A. Euler, Leonhard

B. Mersenne, Marin

C. Galois, Evariste

D. Wiles, Andrew

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23. Who worked on La géométrie?

A. Ramanujan, Srinivasa

B. Al-Khowarizmi, Mohammed

C. Zeno Of Elea

D. Descarte, Rene

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24. Who helped her father write a newer version of Euclid’s Elements?

A. Agnesi, Maria Gaetana

B. Hypatia

C. Pascal, Blaise

D. Brahma-gupta

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25. Who introduced the hyper geometric function?

A. Gauss, Karl Friedrich

B. Wiles, Andrew

C. Galois, Evariste

D. Riemann, GF Bernhard

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26. Who is most known for his number theory, Fermat’s Last Theorem? (Hint: … Really?)

A. Newton, Sir Isaac

B. Fermat, Pierre de

C. Bolyai, Janos

D. Lobachevsky, Nikolai Ivanovich

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27. Who had trouble in school as a young child?

A. Hypatia

B. Riemann, GF Bernhard

C. Boole, George

D. Galois, Evariste

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28. Who created a sequence of numbers which each number is the sum of the 2 preceding numbers?

A. Euler, Leonhard

B. Von Neumann, John

C. Fibonacci of Pisa

D. Babbage, Charles