Journal ArticleDOI
A Car Crash Solved—with a Swiss Army Knife
TLDR
In this article, the authors apply Eves's theorem to accident scene reconstruction, to the circular products in the theorems of Ceva and Menelaus, and to perspective illustrations of the geometric mean.Abstract:
Though not well known, Eves�s theorem is a fundamental result of projective geometry�a tool as versatile as a Swiss Army knife. Named for the late Howard W. Eves (1911�2004), the theorem establishes a class of numerical projective invariants, of which the famous cross ratio is a special case. We illustrate the versatility of Eves�s theorem by applying it to accident scene reconstruction, to the circular products in the theorems of Ceva and Menelaus, and to perspective illustrations of the geometric mean. In addition, we show that the theorem is illustrated by everyday photographs of buildings and other common objects.read more
Citations
More filters
Journal ArticleDOI
Weighted Projective Spaces and a Generalization of Eves' Theorem
TL;DR: A generalization of Eves’ theorem, which applies to a larger class of configurations and gives an invariant with values in a weighted projective space and shows how the complex version of the invariant can be determined from classically known ratios of products of determinants.
Journal ArticleDOI
The Image of a Square
TL;DR: Every quadrangle is the perspective image of a square, illustrated by using perspective art techniques and by analogy to the visualization of conic sections.
Posted Content
Weighted Projective Spaces and a Generalization of Eves' Theorem
TL;DR: For a certain class of configurations of points in space, Eves' Theorem gives a ratio of products of distances that is invariant under projective transformations, generalizing the cross-ratio for four points on a line.
References
More filters
Book
Viewpoints: Mathematical Perspective and Fractal Geometry in Art
Marc Frantz,Annalisa Crannell +1 more
TL;DR: In this paper, the authors introduce the concept of Perspective and Space Coordinates and propose a perspective game based on the number of points and views in one-point and three-point perspective games.
Journal ArticleDOI
Means Appearing in Geometric Figures
TL;DR: A list of several means of a pair of positive numbers, a and b, can be found in this paper, where the authors show that there are many other means of two given positive numbers.
Journal ArticleDOI
Isomorphism Invariants for Projective Configurations
TL;DR: An isomorphism invariant is an expression defined for a configuration in the projective plane, which takes the same value for all isomorphic configurations as mentioned in this paper, and is defined as a general method (Nehring sequences) for constructing such invariants.