The History of Mathematics By: Molly Hanson

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

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.

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”

Sir Isaac Newton *Sir Isaac Newton developed simple methods for: -finding areas -lengths of curves -maxima and minima He is credited with the development of a potent problem solving and analysis tool in pure mathematics and physics. -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.

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.

Blaise Pascal 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. *Later in his life, he became involved in gambling and found a sudden interest in probability.

Aryabhatta 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.

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.

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

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.

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

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.

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

India The Sulba Sutras 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 The Surya Siddhanta This writing gives us sin, cosine and inverse sin. The Decimal Place System first appears in the Aryabhatiya

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.