Important Grecians

Question 1

Thales

Answer 1

Introduced “proof” to mathematics, unknowingly transforming mathematics into one separate from the empirical, real world.

Question 2

Pythagoras

Answer 2

Believed the world is made of numbers. Also created the pythagorean theorem.

Question 3

Fermat (not a Grecian, he’s from 1660)

Answer 3

Huge contributor to mathematics! Attempted to find a way to build large primes.

Question 4

Plato and Aristotle

Answer 4

Went against Thales; argued that in order to use proofs, one must start with unprovable truths. (falls under Epistemology)

Question 5

Plato and Aristotle: their contrary views?

Answer 5

Plato: that mathematical objects exist in a higher dimension and we can only see their shadow. (Think plate- eehee.)

Aristotle: Believed that mathematical objects are merely abstractions. Take the idea of a line in the sand, and subtract the sand, as well as the width.

Question 6

Euclid

Answer 6

Wrote the Elements of Mathematics! Built upon Thales’ idea of proofs, started with five un-provable truths.

Question 7

What are the five axioms in the Element of Mathematics?

Answer 7

1: Two points determine a line.
2: A line segment may be extended indefinitely.
3: Line segments can be used to create circles.
4: All right angles are equal.
5: Parallel Postulate. If lines never meet, they are parallel.

Question 8

Apollonius

Answer 8

Wrote a book called “conic sections”

think of circles and lines in “pollo”

Question 9

Pappus

Answer 9

Contributed a little to the subject of conic sections. Found the directrix of an ellipse, and created the idea of eccentricity: PF/PD = epsilon.

Question 10

Archimedes

Answer 10

Pioneered “geometric calculus”.
(Did an integral in polar coordinates years before calculus was invented.)
Also found the surface areas and volumes of spheres, conics, shells, and so on.

He also put all of this into his book, “The Sand Reckoner”
Died at the hand of some unknown Roman soldier who tried to get him to bow to a statue.

Question 11

Eudoxus

Answer 11

Did limits without limits! Thought of finding a circle area by approximating it as a many-sided polygon.
(notice the x in his name and think limits)

Question 12

Ptolemy

Answer 12

Did trigonometry without functions! Put it all into a book, called “The Almagest”. He was an astronomer, so when you think astronomy, think trigonometry.

Question 13

Diophantus

Answer 13

Diophantine equations!
Whole numbers such that, say, x^2 + 3y = 13.
Wrote Arithmetica
NOTE: Fermat’s Last Theorem was scrawled in the margins of his copy of Arithmetica.

Question 14

Hypatia

Answer 14

Last head of the Museum in Alexandria.
Killed by an angry Christian mob.
Her death was the End of Greek Mathematics.