Jakob Steiner

Topics: Geometry, Circle, Mathematics Pages: 2 (328 words) Published: March 17, 2013
Jacob Livingston
Mrs. Dabiesingh
Mathematician Essay
Jakob Steiner
Born 1796 in Switzerland this mathematician had hopes of renovating the classic methods of geometry. Living to the ripe old age of 67 he accomplished just that. He often succeeded in his quest using “Pure Geometry”. Jakob wrote "Calculating replaces thinking while geometry stimulates it." Jakob’s contributions to geometry renovated the classic ways of solving geometric problems.

One of Jakob’s greater mathematical achievements was the discovery of the circumscribed and inscribed circles of a triangle. Along with this achievement he also wrote many theorems used today in classic geometry as well as Projective geometry. Jakob proved that Wallace lines of a triangle lie in a 3 pointed hypocycloid. He also developed the formula for partitioning of space by planes. Perhaps his three greatest theorems were the Poncelet-Steiner Theorem, Double-Element Theorem, and the Isoperimetric Theorem.

Jakobs first great theorem stated that “lengths constructible with straightedge and compass can be constructed with straightedge alone as long as the picture plane contains the center and circumference of some circle”. His second theorem, Double element theorem stated “If in a projectivity between two pencils of lines through two points (centers), the line joining the centers corresponds to itself, and the pencils are perspective”. Jakobs final theorem was the Isoperimetric Theorem and it stated “Among all planar shapes with the same perimeter the circle has the largest area, is equivalent to, Among all planar shapes with the same area the circle has the shortest perimeter” (Dirichlet found a flaw in this theorem, but it was corrected by Weierstrass).

Jakob Steiner is often paired with the great Apollonius of Perga and considered the greatest pure geometers. Jakob once wrote “For all their wealth of content, music, mathematics, and chess are resplendently useless. They are metaphysically...
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