Poincaré’s Proof of Poincaré’s Last Geometric Theorem

When William Wynne Willson died in the summer of 2010 he left behind an incomplete text covering a number of geometrical topics, including the so-called ‘Simson line’. Geoff Wain, who was completing and editing the text with a view to possible publication, sent me a copy. One chapter, entitled ‘Whose line is it anyway?’ contains the following paragraph.‘In 1799 the Scottish mathematician William Wallace … published a geometric theorem. Nowadays this result is known as ‘Simson's line’. It is not clear why it should have this name as Robert Simson, another Scottish mathematician, had died aged 80 in 1768, the year in which Wallace was born. Although Simson published a considerable body of mathematical writings … there seems to be no trace of this theorem among them.

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Combining Clifford Algebraic Computing and Term-Rewriting for Geometric Theorem Proving

Fundamenta Informaticae ◽

10.3233/fi-1999-391205 ◽

1999 ◽

Vol 39 (1,2) ◽

pp. 85-104 ◽

Cited By ~ 1

Author(s):

Stéphane Fèvre ◽

Dongming Wang

Keyword(s):

Theorem Proving ◽

Term Rewriting ◽

Geometric Theorem ◽

Algebraic Computing

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A simple proof for the matrix-geometric theorem

Applied Stochastic Models and Data Analysis ◽

10.1002/asm.3150080105 ◽

1992 ◽

Vol 8 (1) ◽

pp. 25-29 ◽

Cited By ~ 5

Author(s):

Guy Latouche

Keyword(s):

Simple Proof ◽

Geometric Theorem ◽

The Matrix

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A Porism Concerning Cyclic Quadrilaterals

Geometry ◽

10.1155/2013/483727 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5

Author(s):

Jerzy Kocik

Keyword(s):

Infinite Number ◽

Geometric Theorem

We present a geometric theorem on a porism about cyclic quadrilaterals, namely, the existence of an infinite number of cyclic quadrilaterals through four fixed collinear points once one exists. Also, a technique of proving such properties with the use of pseudounitary traceless matrices is presented. A similar property holds for general quadrics as well as for the circle.

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