Solution to Week 4 Exercise 1
... Case 2: T with angles 0, α, β. Drop a perpendicular from the ideal vertex to the opposite side, apply Case 1 to the two resulting triangles, and add, to get Area(T ) = π − (α + β). Case 3: Given a triangle with non-zero angles α, β, γ at vertices A, B, C, arrange it in the upper halfplane with the s ...
... Case 2: T with angles 0, α, β. Drop a perpendicular from the ideal vertex to the opposite side, apply Case 1 to the two resulting triangles, and add, to get Area(T ) = π − (α + β). Case 3: Given a triangle with non-zero angles α, β, γ at vertices A, B, C, arrange it in the upper halfplane with the s ...
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 ...
2D and 3D Design Notes
... b) Using Symmetry and Some Trig to Construct the Rhombicuboctahedron and the Rhombi Truncated Cuboctahedron c) Using Truncation to Construct The Truncated Icosahedron, The Truncated Dodecahedron and The Icosadocecahedron e) Using Symmetry and Some Trig to Construct the Rhombicosadodecahedron and the ...
... b) Using Symmetry and Some Trig to Construct the Rhombicuboctahedron and the Rhombi Truncated Cuboctahedron c) Using Truncation to Construct The Truncated Icosahedron, The Truncated Dodecahedron and The Icosadocecahedron e) Using Symmetry and Some Trig to Construct the Rhombicosadodecahedron and the ...
Math Voc. P-Sp
... which rectangles are used to surround a figure or parts of a figure. All the area is calculated in either area of rectangles or of triangular halves of rectangular regions. ...
... which rectangles are used to surround a figure or parts of a figure. All the area is calculated in either area of rectangles or of triangular halves of rectangular regions. ...
Matching Geometry - Vocabulary for Fall Midterm Vocab
... line that contains a side contains interior points. A circle that touches each side of the polygon at exactly one point ...
... line that contains a side contains interior points. A circle that touches each side of the polygon at exactly one point ...
The measure of angle C is 83˚, the measure of angle DBA is 138
... Reminder: You may not use the calculator in your cell phone during the exam. Bring a separate calculator! No protractors will be needed or allowed for this exam. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice som ...
... Reminder: You may not use the calculator in your cell phone during the exam. Bring a separate calculator! No protractors will be needed or allowed for this exam. Note: This is NOT a practice exam. It is a collection of problems to help you review some of the material for the exam and to practice som ...
Export To Word
... Item Type(s): This benchmark will be assessed using: MC , FR item(s) Clarification : Students will determine the measures of interior and exterior angles of polygons. Content Limits : All angle measurements will be in degrees. Stimulus Attributes : Items may be set in either real-world or mathematic ...
... Item Type(s): This benchmark will be assessed using: MC , FR item(s) Clarification : Students will determine the measures of interior and exterior angles of polygons. Content Limits : All angle measurements will be in degrees. Stimulus Attributes : Items may be set in either real-world or mathematic ...
Algebra/Geometry Institute Summer 2006
... triangle on the second sheet. Trace the triangle so that the two copies of the triangle are now on one of the patty papers. Step 3 Continue tracing the triangles in this manner filing the paper with tessellations of equilateral triangles. What is the measure of each angle of an equilateral triangle? ...
... triangle on the second sheet. Trace the triangle so that the two copies of the triangle are now on one of the patty papers. Step 3 Continue tracing the triangles in this manner filing the paper with tessellations of equilateral triangles. What is the measure of each angle of an equilateral triangle? ...
0035_hsm11gmtr_0904.indd
... 11. Make a Conjecture What is the relationship between the number of sides of a ...
... 11. Make a Conjecture What is the relationship between the number of sides of a ...
Final Exam info
... How much time? 75 minutes long How many points? 150 (16.5% of final grade) Format? 100 Multiple Choice questions worth 1.5 pt each and one page of extra credit Can I use a calculator? Yes! Don’t forget one because the math department will not loan out calculators on the day of the exam, and you may ...
... How much time? 75 minutes long How many points? 150 (16.5% of final grade) Format? 100 Multiple Choice questions worth 1.5 pt each and one page of extra credit Can I use a calculator? Yes! Don’t forget one because the math department will not loan out calculators on the day of the exam, and you may ...
Practice Test Ch 1
... ___________Geometric figures contained on the same flat surface ___________No interior points connected by a segment crosses the edge of this type of polygon ___________Set all of points ___________A line in one direction and an endpoint on the other ___________The length between two points ________ ...
... ___________Geometric figures contained on the same flat surface ___________No interior points connected by a segment crosses the edge of this type of polygon ___________Set all of points ___________A line in one direction and an endpoint on the other ___________The length between two points ________ ...
course notes
... it has a diagonal. (This may seem utterly trivial, but actually takes a little bit of work to prove. In fact it fails to hold for polyhedra in 3-space.) The addition of the diagonal breaks the polygon into two polygons, of say m 1 and m2 vertices, such that m1 + m2 = n + 2 (since both share the vert ...
... it has a diagonal. (This may seem utterly trivial, but actually takes a little bit of work to prove. In fact it fails to hold for polyhedra in 3-space.) The addition of the diagonal breaks the polygon into two polygons, of say m 1 and m2 vertices, such that m1 + m2 = n + 2 (since both share the vert ...
2_M2306_Hist_chapter2
... 2.2 The Regular Polyhedra Definition A polyhedron which is bounded by a number of congruent polygonal faces, so that the same number of faces meet at each vertex, and in each face all the sides and angles are equal (i.e. faces are regular polygons) is called the regular polyhedron Regular polygon: ...
... 2.2 The Regular Polyhedra Definition A polyhedron which is bounded by a number of congruent polygonal faces, so that the same number of faces meet at each vertex, and in each face all the sides and angles are equal (i.e. faces are regular polygons) is called the regular polyhedron Regular polygon: ...
Geometry Unit 1 Posttest Review
... 13) Polygon ABCD is transformed to create polygon A’B’C’D’. What transformation took place? ...
... 13) Polygon ABCD is transformed to create polygon A’B’C’D’. What transformation took place? ...
17.4 Connectivity - University of Cambridge
... The vertex space V of a graph of order n is the n-dimensional space over GF(2) whose coordinates are labelled by the vertices. The scalar field GF(2) is just the set {0, 1} with arithmetic performed (mod 2); this makes life very easy as every vector is just a 0-1 vector and corresponds in a natural ...
... The vertex space V of a graph of order n is the n-dimensional space over GF(2) whose coordinates are labelled by the vertices. The scalar field GF(2) is just the set {0, 1} with arithmetic performed (mod 2); this makes life very easy as every vector is just a 0-1 vector and corresponds in a natural ...
Unwrapped Standard 6
... Identify faces, edges, vertices, and nets. Identifying the Big Ideas from Unwrapped Standards: 1. All shapes are made up of lines, angles, and rays. 2. Two-dimensional figures remain congruent when translations, rotations, and reflections occur. 3. Two and three-dimensional figures are different but ...
... Identify faces, edges, vertices, and nets. Identifying the Big Ideas from Unwrapped Standards: 1. All shapes are made up of lines, angles, and rays. 2. Two-dimensional figures remain congruent when translations, rotations, and reflections occur. 3. Two and three-dimensional figures are different but ...
Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an edge with two bounding vertices. For a real polytope it is not possible to have a third vertex associated with an edge because one of them would then lie between the other two. On the complex line, which may be represented as an Argand diagram, points are not ordered and there is no idea of ""between"", so more than two vertex points may be associated with a given edge. Also, a real polygon has just two sides at each vertex, such that the boundary forms a closed loop. A real polyhedron has two faces at each edge such that the boundary forms a closed surface. A polychoron has two cells at each wall, and so on. These loops and surfaces have no analogy in complex spaces, for example a set of complex lines and points may form a closed chain of connections, but this chain does not bound a polygon. Thus, more than two elements meeting in one place may be allowed.Since bounding does not occur, we cannot think of a complex edge as a line segment, but as the whole line. Similarly, we cannot think of a bounded polygonal face but must accept the whole plane.Thus, a complex polytope may be understood as an arrangement of connected points, lines, planes and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Likewise, each line must contain multiple points, each plane multiple lines, and so on.