The History of Mathematics

1. The History of Mathematics By: Molly Hanson

2. Noted Mathematicians • Archimedes • Euclid • Sir Isaac Newton • Pythagoras • Blaise Pascal • Aryabhatta • Ramanujam

3. Archimedes He is often considered to be the greatest mathematician of ancient times. He performed geometric proofs using Euclid’s geometric formulism. He excelled at computing volumes and areas using the method of exhaustion. Archimedes discovered how to calculate the volume of a sphere. It is two-thirds the volume of the smallest cylinder that can contain it. He was so proud of this discovery that he requested that a figure of a sphere and a cylinder be engraved in his tombstone.

4. Euclid • He wrote thirteen books called “Euclid’s Elements”. They covered the subjects of: • Plane Geometry • Number Theory • Eudoxe’s theory of irrational numbers • Solid Geometry • Properties of five regular polyhedrons The “Father of Geometry”

5. Sir Isaac Newton *Sir Isaac Newton developed simple methods for: -finding areas -lengths of curves -maxima and minima -He created the basis for elementary and integral calculus. -He also came up with the idea that the integration of a function is the opposite procedure of its differentiation. He is credited with the development of a potent problem solving and analysis tool in pure mathematics and physics.

6. Pythagoras • He observed mathematics, music and astronomy and concluded that “all things were numbers”. • He is credited with the Pythagorean Theorem. • He came up with the idea that vibrating strings make harmonious tones if the ratios of the length of the strings are whole numbers. • His followers, Pythagoreans, discovered that the diagonal of a square was not an integral multiple of its side. This discovery led to proof of the existence of irrational numbers.

7. *Later in his life, he became involved in gambling and found a sudden interest in probability. Blaise Pascal1623-1662 • He is best known for his triangle, which is rightly called Pascal’s Triangle. Pascal’s Triangle is a triangular expression of binomial coefficients. • In 1645 he invented the first calculating machine which had the ability to calculate computations. * When studying the mathematics of fluid at rest, or hydrostatics, his work led to the invention of the syringe and the hydraulic press.

8. Aryabhatta 476-550 A.D. • He found the approximate value of Pi • He also discovered that Pi is irrational • He was ahead of his time. • He mentions the formula to calculate the value of a triangle, which wasn’t discovered until much later. • He was also already aware that the earth spins on an axis. • He could explain the planets movements.

9. Ramanujam Ramanujam was one of India’s greatest mathematicians. -He did work with Elliptic Functions, continued fractions, and infinite series. -He taught himself how to do mathematics using a book called; Synopsis of elementary results in pure mathematics.

10. Mathematics and the World What areas of the world made contributions and what were they?

11. Mesopotamia • The Sumerians, the oldest of the Mesopotamian civilizations, developed a complex system of metrology. There is also evidence of them writing multiplication tables using geometry and division. • Clay tablets found from this civilization also include quadratic and cubic equations and the calculation of regular reciprocal pairs. The earliest math.

12. Egypt • Rhind Papyrus • It is an instruction manual used by students in arithmetic and geometry. • Moscow Papyrus • This contains story problems used to make mathematics entertaining

13. Greek and Hellenistic • Development of deductive reasoning rather than inductive. • Use of logic to derive conclusions, and the use of mathematics to prove these conclusions. • Greece gave us many great mathematicians • Pythagoras • Thales • Eudoxus • Aristotle • Archimedes • The mathematician Thales of Greece is credited as the first to use geometry to calculate the height of the pyramids and the distance of ships from the shore.

14. China • The use of “Rod Numerals” allowed for the use of very large numbers on the Chinese abacus. The Nine Chapters on Mathematical Art is a writing from the Han Dynasty that consists of 246 word problems dealing with agriculture, business, employment of geometry, figure height spans and dimension ratios for Chinese pagoda towers,, engineering, surveying, and includes material on right triangles and values of Pi

15. India The Sulba Sutras The Surya Siddhanta This writing gives us sin, cosine and inverse sin. The Decimal Place System first appears in the Aryabhatiya • These religious books give simple rules for building altars of various shapes • It also gives methods for constructing a circle with approximately the same area of a given square, which can bring us close to finding the value of Pi

16. Islamic World • The Islamic world came up with new methods for solving equations. • The Islamic world also gives us the first known proof. • The tangent function was developed my the Muslims. • Khwarizmi is called “The Father of Algebra” • He was the first to teach Algebra in elementary form • He also developed the idea of cancellation of like terms on opposite sides of the equation.