Geometry: Section 1.1 Name:
... Why must three letters be used to name these angles? Triangle: The union of three segments with common endpoints. The endpoints are called the vertices of the triangle. The segments are the sides of the triangle. We name a triangle by its three vertices. ∆ABC or ∆ACB or ∆CAB, etc. A ...
... Why must three letters be used to name these angles? Triangle: The union of three segments with common endpoints. The endpoints are called the vertices of the triangle. The segments are the sides of the triangle. We name a triangle by its three vertices. ∆ABC or ∆ACB or ∆CAB, etc. A ...
02 Spherical Geometry Basics
... We can rotate the sphere so that one of the points is the north pole. Then, as long as the other point is not the south pole, the shortest distance along the sphere is obvsiouly to go due south. We are, from now on, going to rule out pairs of antipodal points such as the north and south poles, becau ...
... We can rotate the sphere so that one of the points is the north pole. Then, as long as the other point is not the south pole, the shortest distance along the sphere is obvsiouly to go due south. We are, from now on, going to rule out pairs of antipodal points such as the north and south poles, becau ...
Girard`s Theorem: Triangles and
... this is a natural and elegant question to ask! The proof of Girard’s theorem is rather easy once we establish what we mean by ‘spherical triangle’ and how it relates to ‘lunes’. A spherical triangle is created by the pairwise intersections of three great circles. A great circle is the circle around ...
... this is a natural and elegant question to ask! The proof of Girard’s theorem is rather easy once we establish what we mean by ‘spherical triangle’ and how it relates to ‘lunes’. A spherical triangle is created by the pairwise intersections of three great circles. A great circle is the circle around ...
Geometry Vocabulary Graphic Organizer
... indefinitely. A transformation of a figure that creates a mirror image, “flips,” over a line. A line that acts as a mirror so that corresponding points are the same distance from the mirror. A transformation that turns a figure about a fixed point through a given angle and a given direction, such as ...
... indefinitely. A transformation of a figure that creates a mirror image, “flips,” over a line. A line that acts as a mirror so that corresponding points are the same distance from the mirror. A transformation that turns a figure about a fixed point through a given angle and a given direction, such as ...
1-2 Points, Lines and Planes
... directions; it has no thickness. Name a plane with a single capital letter, P, or name at least 3 non-collinear points in the plane. Points and lines in the same plane are ...
... directions; it has no thickness. Name a plane with a single capital letter, P, or name at least 3 non-collinear points in the plane. Points and lines in the same plane are ...
Problems for the exam
... 8. Is it possible to realize CP2 as a finite CW-complex with an even number of cells in every dimension? 9. Viewing S 1 ⊂ C2 as the unit complex numbers, define a continuous map φ : S1 × S1 → S1 × S1 by φ(ξ1 , ξ2 ) = (ξ1 , ξ1 ξ2 ). Is φ homotopic to the identity map? 10. Let ι : S 1 ,→ S 2 be the eq ...
... 8. Is it possible to realize CP2 as a finite CW-complex with an even number of cells in every dimension? 9. Viewing S 1 ⊂ C2 as the unit complex numbers, define a continuous map φ : S1 × S1 → S1 × S1 by φ(ξ1 , ξ2 ) = (ξ1 , ξ1 ξ2 ). Is φ homotopic to the identity map? 10. Let ι : S 1 ,→ S 2 be the eq ...
Practice
... 4. What are two other ways to name plane V? 5. Are points R, N, M, and X coplanar? 6. Name two rays shown in the figure. 7. Name the pair of opposite rays with endpoint N. 8. How many lines are shown in the drawing? ...
... 4. What are two other ways to name plane V? 5. Are points R, N, M, and X coplanar? 6. Name two rays shown in the figure. 7. Name the pair of opposite rays with endpoint N. 8. How many lines are shown in the drawing? ...
