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12 votes
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What theorem of Sophus Lie on the number of geometries is H. Poincaré referring to?

Poincare refers to the Lie's solution of the so-called problem of space, a.k.a. the Helmholtz , or Riemann-Helmholtz, or Helmholtz-Lie problem of space, which amounts to characterizing all manifolds (...
Conifold's user avatar
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6 votes
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Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?

From the Earliest Known Uses of Some of the Words of Mathematics site : PENCIL OF LINES. Desargues coined the term ordonnance de lignes, which is translated an order of lines or a pencil of lines [...
nwr's user avatar
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4 votes
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What motivated the development of the theory of perspective during the Renaissance?

There were of course philosophical and cultural reasons for the development of the (linear) perspective during the Renaissance. It cannot be considered simply a change of tastes of patrons of art or a ...
BakerStreet's user avatar
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4 votes

Who wrote "projective geometry" for the first time?

I looked in MathWords and found this PROJECTIVE GEOMETRY. In his account of the origins of projective geometry Katz (1993) mentions Pascal, Desargues and Monge before saying that J.-V.Poncelet ...
Gerald Edgar's user avatar
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4 votes

Who wrote "projective geometry" for the first time?

“The first known use of the expression 'projective geometry' only dates back to Olry Terquem (1859)” in the article Sur diverses géométries, Nouvelles Annales de Mathématiques, 18, 445–446, according ...
Viktor Blasjo's user avatar
3 votes

Who wrote "projective geometry" for the first time?

Actually Desargues used the term "project". The title of his fundamental work was "Brouillon d'un Project". Notice the unusual spelling (in modern French the word is spelled ...
Mikhail Katz's user avatar
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3 votes

What was the old system of using right circular cones to solve problems about circles in the plane?

Laguerre geometry is the geometry of Laguerre plane, and it was introduced by Laguerre, who defined it as the geometry of the oriented lines and circles in the real Euclidean plane (modern definition ...
Conifold's user avatar
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3 votes
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Did Einstein get inspired by projective geometry?

It is hard to prove that the answer is negative, but have this in mind: a friend who helped Einstein a lot (and who co-wrote two articles with him) while Einstein was trying to formulate the General ...
José Carlos Santos's user avatar
3 votes

Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?

This is a question about English terminology. As others on here have pointed out, the French terminology is different. The original meaning of the English word “pencil” is a fine brush; this is also ...
fdb's user avatar
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3 votes

Who wrote "projective geometry" for the first time?

In a series of six articles in the Athenaeum (1861) (pp. 446,509,549,617,652,727) on the history of perspective, Augustus De Morgan makes reference to "projective geometry": More than ...
Michael E2's user avatar
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2 votes

Which people are considered to be the founders of Projective Geometry?

While the wiki article mentions Desargues, it is inaccurate in that it implies that Desargues only had the notion of a point at infinity, whereas he went much further, including the line at infinity. ...
Mikhail Katz's user avatar
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