4 papers
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…
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…
Constructive Projective Geometry
Mark Mandelkern
Of the great theories of classical mathematics, projective geometry, with its powerful concepts of symmetry and duality, has been exceptional in continuing to intrigue investigator…