12 citations · 27 across the 7 of their papers we have counts for
7 papers
A Constructive Real Projective Plane
Mark Mandelkern
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates…
Convexity and Osculation in Normed Spaces
Mark Mandelkern
Constructive properties of uniform convexity, strict convexity, near convexity, and metric convexity in real normed linear spaces are considered. Examples show that certain classic…
Constructive Mathematics
Mark Mandelkern
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the…
The altitudes of a triangle
Mark Mandelkern
A long-standing, unanswered question regarding Euclid's Elements concerns the absence of a theorem for the concurrence of the altitudes of a triangle, and the possible reasons for…
Constructive Coordinatization of Desarguesian Planes
Mark Mandelkern
A classical theory of Desarguesian geometry, originating with D. Hilbert in his 1899 treatise, Grundlagen der Geometrie, leads from axioms to the construction of a division ring fr…
A constructive version of the Sylvester-Gallai Theorem
Mark Mandelkern
The Sylvester-Gallai Theorem, stated as a problem by J. J. Sylvester in 1893, asserts that for any finite, noncollinear set of points on a plane, there exists a line passing throug…