1) Given 2 distiinct pints A, B sketch an incremental construction (copying the old picture and adding a new elememt at each step) and justify it. Of the fixed point F of the Euclidean rigid motion R_B,pi * T_AB. By definition F is a fixed point if R_B,pi *T_AB(F) =F. (Take the construction of a midpoint , as well as of straight and right angle for granted).

2) 4.a See file

4.b) Prove that there is a hyperbolic equilateral triangle with one of the angles alpha=30 degrees = pi/6. you may use your results from part 4.a (alonmg with a continuity argument)

3) let gamma be the bowed geodesic in the poincare upper half plane with the endpoints A=(3,0) and B=(5,0). let the circle centered at A and of euclidean radius 4. Finde the image of gamma under inversion with respect to C. Sketch gama, A, B,C AND I_c(gama),

Subject | Mathematics |

Due By (Pacific Time) | 05/23/2013 10:09 am |

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