Hyperbolic Constructions using the Poincare Disk Model
... concurrency and label it the centroid. In this model, the centers will disappear as an artifact of the construction so move a vertex around and labe the vertex again so that it always appears. In Euclidean Geometry, the distance from the vertex to th ...
... concurrency and label it the centroid. In this model, the centers will disappear as an artifact of the construction so move a vertex around and labe the vertex again so that it always appears. In Euclidean Geometry, the distance from the vertex to th ...
Activity 2: Interior and central angles
... interior is contractible and whose boundary consists of finitely many line segments.” Recall our discussion concerning the role that definition can play. This is a general math definition. In the first edition of Discovering Geometry, a high school geometry text, the authors define a polygon as “ a ...
... interior is contractible and whose boundary consists of finitely many line segments.” Recall our discussion concerning the role that definition can play. This is a general math definition. In the first edition of Discovering Geometry, a high school geometry text, the authors define a polygon as “ a ...
Naming 2-D and 3-D Shapes
... Greek prefixes and numbers they represent. Encourage the students to make a connection between each Greek prefix and corresponding numbers. As each figure which the students built is named, have the students write the prefix and corresponding number into their math journal. Fill in the remaining num ...
... Greek prefixes and numbers they represent. Encourage the students to make a connection between each Greek prefix and corresponding numbers. As each figure which the students built is named, have the students write the prefix and corresponding number into their math journal. Fill in the remaining num ...
Activity 2: Interior and central angles
... interior is contractible and whose boundary consists of finitely many line segments.” Recall our discussion concerning the role that definition can play. This is a general math definition. In the first edition of Discovering Geometry, a high school geometry text, the authors define a polygon as “ a ...
... interior is contractible and whose boundary consists of finitely many line segments.” Recall our discussion concerning the role that definition can play. This is a general math definition. In the first edition of Discovering Geometry, a high school geometry text, the authors define a polygon as “ a ...
Investigating properties of shapes
... A square is a special case of a rectangle. An oblong is a rectangle that is not a square. A rhombus is a special case of a parallelogram. All polygons up to 20 sides have names, although many have alternatives based on either Latin or Greek. Splitting any polygon into triangles (by drawing all diago ...
... A square is a special case of a rectangle. An oblong is a rectangle that is not a square. A rhombus is a special case of a parallelogram. All polygons up to 20 sides have names, although many have alternatives based on either Latin or Greek. Splitting any polygon into triangles (by drawing all diago ...
Angles - loyolamath
... idea of a point in space. A point has no length, no width, and no height, but it does have location. We will represent a point by a dot, and we will label points with letters. A Point A ...
... idea of a point in space. A point has no length, no width, and no height, but it does have location. We will represent a point by a dot, and we will label points with letters. A Point A ...
List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.The Schläfli symbol describes every regular tessellation of an n-sphere, Euclidean and hyperbolic spaces. A Schläfli symbol describing an n-polytope equivalently describes a tessellation of a (n-1)-sphere. In addition, the symmetry of a regular polytope or tessellation is expressed as a Coxeter group, which Coxeter expressed identically to the Schläfli symbol, except delimiting by square brackets, a notation that is called Coxeter notation. Another related symbol is the Coxeter-Dynkin diagram which represents a symmetry group with no rings, and the represents regular polytope or tessellation with a ring on the first node. For example the cube has Schläfli symbol {4,3}, and with its octahedral symmetry, [4,3] or File:CDel node.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png, is represented by Coxeter diagram File:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png.The regular polytopes are grouped by dimension and subgrouped by convex, nonconvex and infinite forms. Nonconvex forms use the same vertices as the convex forms, but have intersecting facets. Infinite forms tessellate a one-lower-dimensional Euclidean space.Infinite forms can be extended to tessellate a hyperbolic space. Hyperbolic space is like normal space at a small scale, but parallel lines diverge at a distance. This allows vertex figures to have negative angle defects, like making a vertex with seven equilateral triangles and allowing it to lie flat. It cannot be done in a regular plane, but can be at the right scale of a hyperbolic plane.A more general definition of regular polytopes which do not have simple Schläfli symbols includes regular skew polytopes and regular skew apeirotopes with nonplanar facets or vertex figures.