section 8.1-8.3 - Fulton County Schools
... Dilation = A transformation that is not rigid. Preserves the shape of an object, but the size may vary. (Example: Your eyes will dilate to adjust to brightness). Dilations can be found on a coordinate plane by multiplying the x and y coordinates of a point by the same number n. D(x, y) = (nx, ny) Th ...
... Dilation = A transformation that is not rigid. Preserves the shape of an object, but the size may vary. (Example: Your eyes will dilate to adjust to brightness). Dilations can be found on a coordinate plane by multiplying the x and y coordinates of a point by the same number n. D(x, y) = (nx, ny) Th ...
Chapter 10: Polygons and Area
... Find the measure of one exterior angle of a regular heptagon. By Theorem 10–2, the sum of the measures of the exterior angles is 360. Since all exterior angles of a regular polygon have the same measure, divide this measure by the number of exterior angles, one at each vertex. 360 ←sum of exterior a ...
... Find the measure of one exterior angle of a regular heptagon. By Theorem 10–2, the sum of the measures of the exterior angles is 360. Since all exterior angles of a regular polygon have the same measure, divide this measure by the number of exterior angles, one at each vertex. 360 ←sum of exterior a ...
Solution Set 1 Problem 1 Let G be a connected graph with equally
... U has at least two vertices and therefore has a leaf `. The vertex ` must have bordered two leaves of T . Problem 4 Let T be a tree. (a) Show that it is possible to color the vertices of T black and white so that neighboring vertices have opposite colors. We work by induction on the number of verti ...
... U has at least two vertices and therefore has a leaf `. The vertex ` must have bordered two leaves of T . Problem 4 Let T be a tree. (a) Show that it is possible to color the vertices of T black and white so that neighboring vertices have opposite colors. We work by induction on the number of verti ...
Ab-initio construction of some crystalline 3D Euclidean networks
... E-mail address: [email protected] (S.T. Hyde). ...
... E-mail address: [email protected] (S.T. Hyde). ...
PP--Polygons-
... Polygon—Exterior Angle Sum The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. m<1+m<2+m<3+m<4+m<5 =360° ...
... Polygon—Exterior Angle Sum The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. m<1+m<2+m<3+m<4+m<5 =360° ...
Slide 1
... integer coordinates. Which of the following arguments correctly answers and justifies the question: "Is quadrilateral RSTU a regular quadrilateral?" A. Yes, it is a regular quadrilateral because all sides are the same length. B. Yes, it is a regular quadrilateral because the diagonals are perpendicu ...
... integer coordinates. Which of the following arguments correctly answers and justifies the question: "Is quadrilateral RSTU a regular quadrilateral?" A. Yes, it is a regular quadrilateral because all sides are the same length. B. Yes, it is a regular quadrilateral because the diagonals are perpendicu ...
Developing the teaching of Mathematics in primary
... before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on”. The NCETM fully endorses these principles, and will be developing further this progressi ...
... before any acceleration through new content in preparation for key stage 4. Those who are not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on”. The NCETM fully endorses these principles, and will be developing further this progressi ...
Revised Version 070419
... circumcenter for polygons can be facilitated by consideration of perpendicular bisectors. Every point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. This fact supports the conclusion that if the perpendicular bisectors of the sides of a polygon are conc ...
... circumcenter for polygons can be facilitated by consideration of perpendicular bisectors. Every point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment. This fact supports the conclusion that if the perpendicular bisectors of the sides of a polygon are conc ...
Section 9.1- Basic Notions
... • A polyhedron is a convex polyhedron if and only if the segment connecting any two points in the interior of the polyhedron is itself in the interior. • A concave polyhedron is a polyhedron that is not convex. • A regular polyhedron is a convex polyhedron whose faces are congruent regular polygonal ...
... • A polyhedron is a convex polyhedron if and only if the segment connecting any two points in the interior of the polyhedron is itself in the interior. • A concave polyhedron is a polyhedron that is not convex. • A regular polyhedron is a convex polyhedron whose faces are congruent regular polygonal ...
Polygon Angle Sum Conjectures
... discover a method for finding the sum of the angles in any convex n-gon, where n is the number of sides (or angles) of a given polygon. Step 1: Draw a series of convex n-gons, starting with n = 3 and ending with n = 6. ...
... discover a method for finding the sum of the angles in any convex n-gon, where n is the number of sides (or angles) of a given polygon. Step 1: Draw a series of convex n-gons, starting with n = 3 and ending with n = 6. ...
Analytical Calculation of Geodesic Lengths and Angle Measures on
... In art such as modular origami and architecture, regular and semi-regular polyhedra have been popular subjects [2][3]. These polyhedra have regular polygons as their faces and edges with the same length. Five Platonic solids and thirteen Archimedean solids in Figure 1 are convex regular and semi-reg ...
... In art such as modular origami and architecture, regular and semi-regular polyhedra have been popular subjects [2][3]. These polyhedra have regular polygons as their faces and edges with the same length. Five Platonic solids and thirteen Archimedean solids in Figure 1 are convex regular and semi-reg ...
The Definite Integral - USC Upstate: Faculty
... The mesh or norm of a partition is the length of its largest subinterval. The norm of a partition P is denoted by P. In other words, if P = {a = x0 < x1 < x2 < . . . < xn = b}, P = max { x k | k = 1, 2, . . . , n}. ...
... The mesh or norm of a partition is the length of its largest subinterval. The norm of a partition P is denoted by P. In other words, if P = {a = x0 < x1 < x2 < . . . < xn = b}, P = max { x k | k = 1, 2, . . . , n}. ...
Activity 8.6.2 Golden Triangles
... compass and straightedge alone. (Recall from Unit 3 that we are able construct regular polygons with 3, 4, and 6 sides using only Euclid’s tools. Now we may add the regular pentagon to the list.) ...
... compass and straightedge alone. (Recall from Unit 3 that we are able construct regular polygons with 3, 4, and 6 sides using only Euclid’s tools. Now we may add the regular pentagon to the list.) ...
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.