History of Geometry

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

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

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!

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’

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

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

Euclid 323-283 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

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

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

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

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