Ovals in ﬁnite projective planes
A projective plane exists whenever q is a prime power. If q ≡ 1 or 2 (mod 4) and q is not the sum of two integer squares, there is no projective plane of order q (Bruck, Ryser, 1949). There is no…
Danzer's configuration revisited
We revisit the configuration of Danzer DCD(4), a great inspiration for our work. This configuration of type (35_4) falls into an infinite series of geometric point-line configurations DCD(n). Each…
Absolute Projectivities in Pascal's Multimysticum
The Pascal Multimysticum is a system of points and lines constructed with a straight edge starting from six points on a conic. We show that the system contains 150 infinite ranges (and 150 infinite…
Degenerations of Pascal lines
- MathematicsBeiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
A BSTRACT : Let K denote a nonsingular conic in the complex projective plane. Pascal’s theorem says that, given six distinct points A, B, C, D, E, F on K , the three intersection points AE ∩ BF, AD ∩…
John Horton Conway. 26 December 1937—11 April 2020
- MathematicsBIOGRAPHICAL MEMOIRS OF FELLOWS OF THE ROYAL SOCIETY
John Conway was without doubt one of the most celebrated British mathematicians of the last half century. He first gained international recognition in 1968 when he constructed the automorphism group…
Ten Points on a Cubic
In 1639 the 16-year old Blaise Pascal found a way to determine if 6 points lie on a conic using a straightedge. We develop a method that uses a straightedge to check whether 10 points lie on a plane…
Pascal’s Hexagram and Desargues Configurations
- MathematicsMathematica Pannonica
This paper solves an enumerative problem which arises naturally in the context of Pascal’s hexagram. We prove that a general Desargues configuration in the plane is associated to six conical…
A Hyperbolic Proof of Pascal’s Theorem
We provide a simple proof of Pascal's Theorem on cyclic hexagons, as well as a generalization by M\"obius, using hyperbolic geometry.
Desargues theorem, its configurations, and the solution to a long-standing enumeration problem
We solve a long-standing problem by enumerating the number of non-degenerate Desargues configurations. We extend the result to the more difficult case involving Desargues blockline structures in…
Desargues, Pascal and Kirkman
- HistoryThe Mathematical Gazette
SHOWING 1-8 OF 8 REFERENCES
Note sur quelques théorèmes de la géometrie de position. (Suite du Mémoire tome 31, p. 213, tome 34, p. 270 et tome 38 p. 97 de ce Journal).
Note relative à la sixième section du „Mémoire sur quelques théorèmes de la géomètrie de position.“ Tome 38 page 98.
Über ein neues Princip der Geometrie und den Gebrauch allgemeiner Symbole und unbestimmter Coefficienten.