Jakob Steiner, a Swiss mathematician born in 1796, aimed to renovate traditional geometry methods. He successfully achieved this goal during his lifetime, reaching the age of 67. Steiner primarily used “Pure Geometry” to accomplish his missions. He stated that calculating replaces thinking while geometry stimulates it. Through his contributions, Jakob revolutionized the traditional approaches to solving geometric problems. One of his significant mathematical accomplishments was uncovering the circumscribed and inscribed circles of a triangle.
Jakob made significant contributions to classic geometry and Projective geometry. One of his achievements was proving that Wallace lines of a triangle lie in a 3 pointed hypocycloid. Additionally, he formulated the formula for partitioning of space by planes. Three of his most notable theorems are the Poncelet-Steiner Theorem, Double-Element Theorem, and the Isoperimetric Theorem. His first major theorem stated that lengths constructible with straightedge and compass can also be constructed with straightedge alone, provided that the picture plane contains the center and circumference of some circle.
His second theorem, Double element theorem states that 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 is the Isoperimetric Theorem, which states that among all planar shapes with the same perimeter, the circle has the largest area; and equivalently, 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, often regarded as the foremost pure geometer, is frequently associated with the renowned Apollonius of Perga. In one of his writings, Jakob expressed his belief that despite their vast and rich content, music, mathematics, and chess hold no practical value. He deemed them metaphysically insignifiacnt and lacking responsibility. Moreover, he believed that they fail to establish a connection with the external world and rely solely on their own internal realm. Jakob referred to this phenomenon as the enchanting quality possessed by these subjects.
