341, Math Homework 3
Name:................................. Number:................................... 1. Prove that two noncoplanar lines exist(there is no plane to contain both of them). (Hint: Use the axioms AI1 - AI5 only!) ) 2. If two lines 1 and 2 intersect, there there is a unique plane to contain them. (Hint: This statement has two parts: existence and uniqueness which can be proved using the axioms AI1 - AI5.) 3. State and prove the Desargues theorem in 3-dimensional space. How can you obtain the same theorem in the plane?(Hint: See the class notes.) Find 4. the incidence matrix for all 5 Platonic solids. The matrix is defined by: a11 a12 a13 a21 a22 a23 , a31 a32 a33 a11 = the number of vertices, a22 = the number of edges, a33 = the number of faces, a12 = the number of points on each side, a21 = the valence of each vertex, a13 = the number of vertices on each face, a31 = the numbe...