1. History of Geometry

2. Thales of Miletus 620-546 BCE (Greek)
Thales Primary Principle – water is the basis for everything
Believed that the earth was thin, round, and floated on water
Predicted the solar eclipse in 585 BCE

3. Thales of Miletus 620-546 BCE (Greek)
Attributed to 5 of Euclid’s properties although he didn’t formally prove any of them
diameter bisects the circle
base angles of an isosceles triangle are congruent
proved triangles are congruent through ASA, SSS, AAS, SAS
the angle in a semicircle is a right angle
2 intersecting lines create congruent vertical angles

4. Pythagoras of Samos 570-495 BCE (Born in Italy; Considered Greek)
Pythagorean Theorem was named after him although he didn’t discover it - his school was the first to prove it
His school was more of a cult because they isolated themselves and believed that Pythagoras and numbers were deity
Pythagoreans made many contributions to philosophy, mathematics, and religion
No direct proof that he did any mathematics!

5. Hippocrates of Chios 470-410 BCE (Greek)
Wrote the Elements which was the basis for Euclid
First to organize a basic geometry text book
Lune of Hippocrates – which is where he was tried “squaring the circle”
Found a way of duplicating the cube, which is constructing cube roots, and he developed a technique of ‘reduction’

6. Socrates 470-399 BCE Plato’s teacher
Socratic method- a form of discussion between individuals that promotes critical thinking
Known as one of the founders of Western Philosophy

7. Plato 428-347 BCE (Greek) Socrates’s student and Aristotle’s teacher
Founded the Academy of Athens, the first higher learning institution in the western world
Named platonic solids - regular, convex polyhedrons with congruent faces of regular polygons
tetrahedron, hexahedron, octahedron, dodecahedron, icosahedron

8. Euclid BCE (Greek)
Organized the Elements, which is the most influential works of mathematics
Known as the ‘Father of Geometry’
Worked with perspective, conic sections, spherical geometry, number theory, and rigor
His book is still used today to teach geometry

9. Archimedes of Syracuse 287-212 BCE (Greek – Italy)
Considered to be one of the greatest mathematicians of all time
Used displacement to determine volume of an object (a crown)
Had numerous inventions, such as the Archimedes screw, Archimedes claw, heat ray, and block and tackle pulley system
Used infinitesimals which later became integral calculus
Discovered an accurate approximation of pi and the square root of 3
Discovered that a sphere is 2/3 of the volume and surface area of the circumscribed cylinder

10. Eratosthenes 276-195 BCE Proved the world was round using proportions
Accurately measured the circumference of the earth
Calculated the tilt of the earth, the distance from the earth to the sun, and invented the idea of leap day
Sieve of Eratosthenes was a systematic way of finding prime numbers

11. Apollonius of Perga 262-190 BCE (Greek – Now Turkey)
Known for his writings about conics
Named the hyperbola, parabola, and ellipse
Did work with analytic geometry
Wrote commentaries about how to improve Euclid’s Elements

12. Hipparchius of Nicaea 190-120 BCE (Greek – Now Turkey)
Founder of trigonometry
First to accurately model the movement of the sun and moon
Made a large celestial globe that accurately depicts constellations
First to come up with trigonometry tables
Used trigonometry and astronomy to accurately predict lunar eclipses
Most famous for his precision of equinoxes