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Special cases are right triangles (p q 2). Uniform solutions are constructed by a single generator point with 7 positions within the fundamental triangle, the 3 corners, along the 3 edges, and the triangle interior. All vertices exist at the generator, or a reflected copy of it. Edges exist between a generator point and its image across a mirror.
This list of triangle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or in triangular arrays such as Pascal's triangle or triangular matrices, or concretely in physical space.
Example of a void pantograph pattern before (left) and after (right) the document has been photocopied. In security printing, void pantograph refers to a method of making copy-evident and tamper-resistant patterns in the background of a document. Normally these are invisible to the eye, but become obvious when the document is photocopied.
Drafting pantograph in use Pantograph used for scaling a picture. The red shape is traced and enlarged. Pantograph 3d rendering. A pantograph (from Greek παντ- ' all, every ' and γραφ- ' to write ', from their original use for copying writing) is a mechanical linkage connected in a manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical ...
Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...
The concept of a triangulation may also be generalized somewhat to subdivisions into shapes related to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles—polygons that, like triangles, have exactly three convex vertices. As in point set triangulations ...
The Encyclopedia of Triangle Centers (ETC) is an online list of thousands of points or "centers" associated with the geometry of a triangle. This resource is hosted at the University of Evansville . It started from a list of 400 triangle centers published in the 1998 book Triangle Centers and Central Triangles by Professor Clark Kimberling .
Given a triangulation T P of P, one defines the graph G(T P) as the graph whose vertex set are the triangles of T P, two vertices (triangles) being adjacent if and only if they share a diagonal. It is easy to observe that G ( T P ) is a tree with maximum degree 3.