Logical Reasoning IfThen download[10].
... Contrapositive - In a plane, if two lines are not parallel and intersect another line, then they are not perpendicular to the intersected line. True Converse - If a quadrilateral is a rectangle then it is a square. False Inverse - If a quadrilateral is not a square then it is not a rectangle. False ...
... Contrapositive - In a plane, if two lines are not parallel and intersect another line, then they are not perpendicular to the intersected line. True Converse - If a quadrilateral is a rectangle then it is a square. False Inverse - If a quadrilateral is not a square then it is not a rectangle. False ...
Chapter 6 Halving segments
... First we describe the construction, then we verify its correctness, and finally we count the middle-level vertices. The construction We construct an infinite sequence L0 , L1 , L2 , . . . of sets of non-vertical lines in the plane in general position. Every line in every Lm , m ≥ 0, is of one of two ...
... First we describe the construction, then we verify its correctness, and finally we count the middle-level vertices. The construction We construct an infinite sequence L0 , L1 , L2 , . . . of sets of non-vertical lines in the plane in general position. Every line in every Lm , m ≥ 0, is of one of two ...
Poincare disc model of Hyperbolic Geometry.
... 7. Use the properties of logarithms to prove that the following three properties of distance are satisfied in the Poincaré model. (a) Dist(A, B) = Dist(B, A). (b) Dist(A, B) ≥ 0. (c) Dist(A, B) = 0 if and only if A = B. Note: The triangle inequality also holds, but you do not need to prove it. ...
... 7. Use the properties of logarithms to prove that the following three properties of distance are satisfied in the Poincaré model. (a) Dist(A, B) = Dist(B, A). (b) Dist(A, B) ≥ 0. (c) Dist(A, B) = 0 if and only if A = B. Note: The triangle inequality also holds, but you do not need to prove it. ...