Instructor:Hyperbolic Geometry Exercises Solutions
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 Four geodesics that don't cross.
 Four geodesics through the center.
 Three geodesics through point, parallel to given geodesic.
 Triangle with three 5° angles.
 90°5°5° triangle.
 Right angled pentagon.
 Fish in Circle Limit I alternate directions along geodesics, so that they are alternately head to head and tail to tail. In Circle Limit III, fish along the white lines all face the same direction, as if they could all be swimming forwards.
 He's talking about Circle Limit III. He needed to print each of four colors plus black. With black, because of the fourfold rotation symmetry, he only carved a block to print ¼ of the circle. With the colors, he could have carved half circle blocks but didn't  he used two quartercircle blocks for each color, each printing twice. So, (five colors) × (four impressions each) gives 20 impressions total.

 Sketch #45 (Angels and Devils): a) 8; b) 4; c) 45°45°90°; d) 180°; e) Euclidean
 Sphere with Angels and Devils: a) 6; b) 4; c) 60°60°90°; d) 210°; e) Spherical
 Circle Limit IV (Heaven and Hell): a) 8; b) 6; c) 45°45°60°; d) 150°; e) Hyperbolic
 Only b, c, and d, the Circle Limit artworks.
 a) {3,10}; b) All are 36°; c) 72°; d) <math>2\pi/5</math>; e) Draw {10,3}.
 a) {6,4}; b) All are 90°; c) 180°; d) <math>\pi</math>; e) Draw {4,6}.
 a) 180°; b)Largest area <math>\pi</math>, smallest area 0.
 Largest area </math>2\pi</math>, smallest area 0.
 a) 6, 12, 18, 24, 30, 6n; b) 5, 5, 1, 0, 0, 0; c) 7, 21, 63, 189, 567, <math>7\cdot 3^{n1}</math>