MonographDOI
Geometric Transformations III: Affine and Projective Transformations
I. M. Yaglom,Abe Shenitzer +1 more
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TLDR
In this article, the authors present a series of geometric transformations of the plane, including congruencies and similarities investigated in the previous volumes of the Geometric Transformations I and II series.Abstract:
This book is the sequel to Geometric Transformations I and II, volumes 8 and 21 in this series, but can be studies independently. It is devoted to the treatment of affine and projective transformations of the plane these transformations include the congruencies and similarities investigated in the previous volumes. The simple text and the many problems are designed mainly to show how the principles of affine and projective geometry may be used to furnish relatively simple solutions of large classes of problems in elementary geometry, including some straight edge construction problems. In the Supplement, the reader is introduced to hyperbolic geometry. The latter part of the book consists of detailed solutions of the problems posed throughout the text.read more
Citations
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Journal ArticleDOI
Properties of normalized radial visualizations
TL;DR: This paper defines a class of normalized radial visualizations (NRVs) that includes the RadViz mapping onto the two-dimensional unit disk and shows that an NRV is the composition of a perspective and an affine transformation, which leads to a number of properties including line, point ordering and convexity invariance.
Journal ArticleDOI
The nine-point conic: a rediscovery and proof by computer
TL;DR: A heuristic description of the rediscovery with Sketchpad of a less well-known, but beautiful, generalization of the 9-point circle to a nine-point conic, as well as an associated generalisation of the Euler line is given in this article.
Book ChapterDOI
Elementary Geometry, Then and Now
TL;DR: The rapid rate of change in school curricula in all countries of the world, currently seeming to reach its maximum, would oblige us if the authors adopted that definition to accept the existence of indefinitely many elementary geometries.
Journal ArticleDOI
On the unification of hyperbolic and euclidean geometry
TL;DR: The polar decomposition of Mobius transformation of the complex open unit disc gives rise to the Mobius addition in the disc and, more generally, in the ball as discussed by the authors, a gyrogroup operation that plays a role analogous to the role that ordinary vector addition plays in the Euclidean geometry.
Journal ArticleDOI
The Centroid as a Nontrivial Area Bisecting Center of a Triangle
Allan Berele,Stefan Catoiu +1 more
TL;DR: In this article, a relatively new and little known subject, bisecting envelopes or deltoids, is introduced, and a simple proof to a classical theorem of convex geometry is given.