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October 31, 2023

Events

Diophantus
- wrote "Arithmetica" on Number TheoryPtolemy
- 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 CIRCLESCopernicus
- proposed HELIOCENTRISM
- wasn'T listened to because still used circlesAlexander 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 doneBramagupta:
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 formulaMahavira:
Wrote on combinatorics
Found choose notation
n = n!/m!(n-m)!
mCalif Mamur opened the HOUSE OF WISDOM:
A research institute center of math for next 500 years
In BAGDADMuhamed 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 equationAbu Kamil:
Did the arithmetic of SURDS
*Greeks couldn'T do this because they saw rootes as LENGTHSNew
eventPeriods

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