Geogirls and Geoguys
In History
Thales:
Thales was a salt and olive oil tycoon in Asia Minor from around 600 to 550 B.C. He was the first to lay down guidelines for the abstract development of geometry. In his travels, Thales came in contact with the stories of old mathematics and astronomy. In his retirement, he took them up as a hobby. He became famous because of his astronomical studies, mapping the stars and calculating the number of days in the year.
Pythagoras:
Pythagoras was one of Thales star students. He was encouraged to travel and increase his mathematical understanding. Around 540 B.C. he started a part religious, part mathematical cult that worshipped numbers and believed in reincarnation. Pythagoras is mostly remembered for the Pythagorean Theorem which proves that the square of the hypotenuse of a right triangle is the sum of the squares of the other two sides (the legs).
Plato:
Plato was also a philosopher and a mathematician. Plato was the one who insisted that geometric proofs be demonstrated with no aids other than a straightedge and a compass. He demanded accurate definitions, clearly stated assumptions, and logical deductive proof.
Archimedes:
Archimedes carried on all of Plato's work. He was a mathematician, a scientist, and also an engineer. He was most famous for his skill in making pulleys, pumps, and weapons to defend Syracuse from the Romans. With Newton and Gauss, he is ranked one of the three greatest mathematicians of all time. King Hieron of Syracuse asked Archimedes to find out if the royal goldsmith had put silver in his new gold crown, therefore cheating him. While taking his bath, Archimedes realized that if he weighed the crown in air and then while in water, he could compare the two weights to find the density of the medal from which the crown was made from. Since he was so excited, he rushed out of the bath and ran naked through the streets shouting, "Heureka! Heureka!" (I found it! I found it!).
Euclid
Euclid was the most famous of all the masters of geometry. He lived in about 300 B.C. Euclid began compiling the theorems of his predecessors. He organized all known geometric thoughts and rewrote the proofs into clear terms in a work called "The Elements."
Apollonius:
He studied with the successors of Euclid. Apollonius later was called "The Great Geometer" because he laid the foundations for a geometry of form and position, this was different than the work of Archimedes, which was based on measurement.
Hypatia:
The Greeks did their best to preserve Archimedes' tradition of creative inquiry in spite of many difficulties in the late Roman empire. Hypatia was among the last of the few Greek mathematicians during this time. She lectured at the University of Alexandria. Hypatia was killed around 400 B.C. More than 1000 years passed before geometry once again was a serious area of study.
Descartes:
Rene Descartes, a French aristocrat born in 1596, was one of the more recent mathematical giants. At the age of 22, after earning a law degree, he started to develop "analytic" geometry. Descartes looked for fundamental truths which could be used as basic axioms on which other proofs could grow. While watching a fly crawling on the ceiling, he discribed the insect's path in terms of its displacements along the perpendicular lines formed where the walls meet the cieling. This description was the begining of the idea of a pair of numbers determining the position of a point on a surface, one number as a distance measured vertically and the other number maesured horizontally. In Descartes' honor, the rectangular coordinate system is often called the "Cartesian Coordinate System." Descartes' method has been used to identify places on maps and atlases.
Euler:
Leonard Euler, an 18th century Swiss mathematician, developed the concept of network theory. Investigating the many sided objects known as polyhedra, which might be described as networks of points and lines in three dimensions, he discovered that no matter how many faces a polyhedra has, there is a predictable relationship among the number of points, edges, and sides. His study of networks led to the devolpment of the field of topology.
