The Pascal Mysticum Demystified

@article{Conway2012ThePM,
  title={The Pascal Mysticum Demystified},
  author={John H. Conway and Alexander J. E. Ryba},
  journal={The Mathematical Intelligencer},
  year={2012},
  volume={34},
  pages={4-8}
}
  • J. Conway, A. Ryba
  • Published 1 August 2012
  • Philosophy
  • The Mathematical Intelligencer
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
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
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
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
...
...