MATH 338 - Timeline

Diophantus - wrote "Arithmetica" on Number Theory

Ptolemy - not general Ptolemy of Alexander the great - wrote "Almagest" --> The Great Book - we only have copies in Arabic - is about astronomy - used early version of trigonometry His universe was GEOCENTRIC and the orbits were CIRCLES

Copernicus - proposed HELIOCENTRISM - wasn'T listened to because still used circles

Alexander the Great - Conquered Egypt and Persia (TODAYS NORTHERN INDIA) - this brings math viz greek scholors to india Northern India was place for next couple of centuries where math was done

Bramagupta: Wrote book with ARITHMETIC RULES and had some MISTAKES Wrote formula for area of cyclic quadrilateral (quadrilaterals in circles): - where S = perimeter = a+b+c+d - A = sqrt((s-a)(s-b)(s-c)(s-d)) If d = 0 is area of triangle --> A = sqrt((s-a)(s-b)(s-c)) First to write quadratic formula

Mahavira: Wrote on combinatorics Found choose notation n = n!/m!(n-m)! m

Calif Mamur opened the HOUSE OF WISDOM: A research institute center of math for next 500 years In BAGDAD

Muhamed Al-Khuarizmi Wrote "Introduction to al-gebra w muqalaba" - where he established basic rules of algebra Also wrote book on Hindu arithmetic including what we today call "The division algorithm" Also found the quadratic equation

Abu Kamil: Did the arithmetic of SURDS *Greeks couldn'T do this because they saw rootes as LENGTHS

New event

The Museum - first director was Euclid - last director was Hypatia (she) was killed by christian mob

Hindu Mathematics Introduced: - place values - zero - negative numbers - surdes (roots)

Arabic mathematics: Around 700 the muslims CONQUERED EVERYTHING Many mathematicians fled to CONSTANTINOPLE (Bycantium, Istanbul) They REJECTED NEGATIVE NUMBERS