Index 461 Gergonne, Joseph, 276 glide reflection, 442, 449 golden ratio, 224 constructing, 302 golden rectangle, 224 golden triangle, 225, 226 gravitational lensing, 12 great circle, 11, 34 great hyperbola, 37 greatest lower bound, 435 gremlin, 409, 412, 417 group, 373 half-plane closed, 77 is convex, 80 open, 77 Poincar´ 36 half-rotation, 85 height of a parallelogram, 209 of a trapezoid, 209 of a triangle, 208 height scaling theorem, 226 heptadecagon, 318 heptagon, 157, 319 Heron of Alexandria, 243 Heron’s formula, 243 hexagon, 157 constructing, 307 Hilbert’s axioms, 375–376 Hilbert’s betweenness axiom, 61, 375 Hilbert, David, 20, 375 hinge theorem, 117 HL congruence theorem, 121 horizontal line, 33 hyperbolic angle-sum theorem, 338 hyperbolic geometry, 11, 53, 123, 337–367 is consistent, 133 is not categorical, 339 postulates of, 123, 382 hyperbolic parallel postulate, 38, 337 hyperboloid model, 37, 41 hyperboloid, two-sheeted, 37 hypotenuse, 105 is the longest side, 116 hypothesis, 388, 406 if and only if, 392 if-then statement, 388 iff, 392 implication, 388 implicit universal quantifier, 397 implies (logical connective), 388 incenter, 265 incidence axioms, 25 in neutral geometry, 57 incidence geometry, 24–50 incidence theorems, 42–50 incircle, 265 for a triangle, 268 incircle theorem, 268 included angle, 104 included side, 104 inconsistent axiomatic system, 32 independence of a statement, 32 of axioms, 32, 139 of Euclid’s Postulate 5, 134 of the Euclidean parallel postulate, 133 of the neutral postulates, 139 indirect proof, 416 induction, mathematical, 420–422 injective function, 56, 429 inscribed angle in a circle, 257 inscribed angle theorem, 259 inscribed arc, 257 inscribed circle, 265 constructing, 305 for a triangle, 268 inscribed polygon, 262 is convex, 262 regular, 272 integer, 424, 433 intercepted arc, 257 interior of a circle, 248 of a convex polygon, 164, 171 of a polygon, 164, 167 of a ray, 71 of a segment, 65 of a simple polygonal region, 199 of an angle, 94, 95 of an arc, 254 vs. betweenness, 97 interior angle adjacent, 113 alternate, 150 formed by a transversal, 149 of a triangle, 113 of an asymptotic triangle, 351 remote, 113 interior angle measure, 159, 173
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