MYSTERIES OF THE EQUILATERAL TRIANGLE - HIKARI Ltd

Biographical Vignettes 165
that a skilled artisan should always remove the scaffolding after a masterpiece
is finished. His personal diaries contain several important mathematical discoveries,
such as non-Euclidean geometry, that he had made years or decades
before his contemporaries published them. He died, aged 77, in Göttingen in
the Kingdom of Hanover. His brain was preserved and was studied by Rudolf
Wagner who found highly developed convolutions present, perhaps accounting
for his titanic intellect. His body is interred in the Albanifriedhof cemetery
[304, p. 59] and, in 1995, the present author made a pilgrimage there and
was only too glad to remove the soda pop cans littering this holy shrine of
Mathematics! Source material for Gauss is available in [23, 42, 221, 287, 297].
Vignette 21 (Jakob Steiner: 1796-1863).
Jacob Steiner, considered by many to have been the greatest pure geometer
since Apollonius of Perga, was born in the village of Utzenstorf just north of
Bern, Switzerland [144]. At age 18, he left home to attend J. H. Pestalozzi’s
school at Yverdon where the educational methods were child-centered and
based upon individual learner differences, sense perception and the student’s
self-activity. In 1818, he went to Heidelberg where he attended lectures on combinatorial
analysis, differential and integral calculus and algebra, and earned
his living giving private Mathematics lessons. In 1821, he traveled to Berlin
where he first supported himself through private tutoring before obtaining a
license to teach Mathematics at a Gymnasium. In 1834, he was appointed
Extraordinary Professor of Mathematics at the University of Berlin, a post
he held until his death. In Berlin, he made the acquaintance of Niels Abel,
Carl Jacobi and August Crelle. Steiner became an early contributor to Crelle’s
Jounal, which was the first journal entirely devoted to Mathematics. In 1826,
the premier issue contained a long paper by Steiner (the first of 62 which were
to appear in Crelle’s Journal) that introduced the power of a point with respect
to a circle, the points of similitude of circles and his principle of inversion.
This paper also considers the problem: What is the maximum number of parts
into which a space can be divided by n planes? (Answer: n3 +5n+6.)
In 1832,
6
Steiner published his first book, Systematische Entwicklung der Abhangigkeit
geometrischer Gestalten voneinander, where he gives explicit expression to his
approach to Mathematics: “The present work is an attempt to discover the
organism through which the most varied spatial phenomena are linked with
one another. There exist a limited number of very simple fundamental relationships
that together constitute the schema by means of which the remaining
theorems can be developed logically and without difficulty. Through the proper
adoption of the few basic relations one becomes master of the entire field.”. He
was one of the greatest contributors to projective geometry (Steiner surface
and Steiner Theorem). Then, there is the beautiful Poncelet-Steiner Theorem
which shows that only one given circle and a straightedge are required