Like other areas of mathematics, geometry is a continually growing and evolving field. Even in the six years since the first edition of the Facts On File Geometry Handbook, developments in geometry have been considerable. This revised edition highlights these new developments while also correcting and expanding on the material in the first edition. Much new material has been added in this edition, including: · more than 300 new glossary terms · 12 new biographies · 34 new events in the chronology · more than 150 new resources in the recommended readings, including more than 50 books published since the year 2000, 20 books giving the historical background of geometry, and new and updated Web resources · additional tables and theorem
[...]... obvious or conventional choice canonical parallel projection A parallel projection with the image plane equal to the xy-plane in three-dimensional coordinate space and having direction of projection parallel to the z-axis canonical perspective projection A perspective projection with the image plane equal to the xy-plane in three-dimensional coordinate space and with center of projection on the z-axis... give the rules governing the behavior of the undefined terms Definitions give the theory new concepts and terms based on the undefined terms and previously defined terms Theorems are statements giving properties of and relationships among the terms of the theory and proofs validate the theorems by logical arguments based on the axioms and previously established theorems All modern mathematical theories... with three points on each line and three lines passing through each point Brianchon point (1) The point of concurrency of the three diagonals connecting opposite vertices of a hexagon circumscribed about a circle or other conic section. (2) For the inconic of a triangle, the point of concurrency of the lines connecting a vertex of the triangle with point of tangency of the conic with the opposite side... rays with a common endpoint The two rays are called the sides of the angle and their common endpoint is called the vertex of the angle The interior of an angle is one of the two regions in the plane determined by the two rays that form the angle The measure of an angle is determined by that part of a circle that one ray sweeps out as it moves through the interior of the angle to reach the other ray Often,... endpoints at the bottom of the other braid braid index For a knot, the least number of strands in a braid that can be transformed into the knot by joining endpoints at the top of the braid to corresponding endpoints at the bottom of the braid branch An edge of a graph Bravais lattice A three-dimensional lattice There are 14 different Bravais lattices Brianchon-Pascal configuration A configuration of nine... congruent angles angle of a polygon The interior angle formed by two adjacent sides of a polygon angle of depression For a viewer looking at an object below the horizon, the angle between a ray from the viewpoint to the horizon and a ray from the viewpoint to the object viewed angle of elevation For a viewer looking at an object above the horizon, the angle between a ray from the viewpoint to the. .. angles of one triangle are congruent to two angles of another triangle, the two triangles are similar, and the ratio of proportionality is equal to the ratio of the given sides, which are adjacent to the second of the given angles of the triangles angle between two curves The angle formed by a tangent line to one of the curves and a tangent line to the other curve at a point of intersection of the two... tetrahedron 8-cell See hypercube 16-cell four-dimensional polytope with eight vertices and 16 A cells, each a tetrahedron 24-cell four-dimensional polytope with 24 vertices and 24 A cells, each an octahedron 120-cell four-dimensional polytope with 600 vertices and 120 A cells, each a dodecahedron 600-cell four-dimensional polytope with 120 vertices and 600 A cells, each a tetrahedron cell-regular ... arcwise connected glossary arbelos A concave region bounded by three semicircles, the smaller two of which are contained in the largest The diameters of the two smaller semicircles lie on the diameter of the largest semicircle and the sum of the two smaller diameters is equal to the larger diameter arc (1) The portion between two points on a curve or between two points on the circumference of a circle. ... sight The smallest angle, with vertex at the viewer’s eye, that completely includes an object being observed angle preserving See conformal angle sum The sum of the measures of the interior angles of a polygon angle-regular polygon A polygon with all angles congruent to one another For example, a rectangle and a square are both angle-regular angle-side-angle If two angles of one triangle are congruent . class="bi x0 y0 w1 h0" alt="" THE FACTS ON FILE GEOMETRY HANDBOOK Revised Edition CATHERINE A. GORINI, Ph.D. Maharishi University of Management, Fairfield, Iowa The Facts On File Geometry Handbook, . polygon are adjacent if they share a common side, two sides of a polygon are adjacent if they share a common vertex, and two faces of a polyhedron are adjacent if GLOSSARY AA – adjacent GLOSSARY. example, a rectangle and a square are both angle-regular. angle-side-angle If two angles of one triangle are congruent to the angles of another triangle, the triangles are similar and the ratio