The Art and Craft of Problem Solving

366 INDEX

tournament, 95, 102
transformation, 123, 124
transformations, 257, 296-3 14
and Felix Klein, 257, 298
and Henri Poincare, 257
composition, 298, 302, 304, 313
homothety, 305-307
and concurrence, 306
inversion, 307-3 11
algorithm for, 307, 313
rigid motions, 298-305
glide reflection, 301
reflection, 301
rotations, 302-305
translations, 298
shearing, 27 1
transversal,260
trapezoid, 279
triangle inequality, 51, 260
triangle( s)
circumcenter, 266
exterior angle measure, 261

incenter, 266

inscribed in circle, 266

isosceles, 262

medial, 269

orthocenter, 267

sum of interior angles, 26 1

triangles

congruent, 259

similar, see similar triangles

triangulation, 48, 55, 217

trigonometry, 280

TS, 40

twin prime, 234

Two Men of Tibet problem, 116-1 18

UCLA, 339

USAMO, see American mathematical

contests

Vadala, Derek, 20

Vandermonde convolution formula, 206

vectors, 298- 301

and complex numbers, 121, 122, 128

and lattice points, 53

and triangle inequality, 51

as motions, 298

basis, 34

dot product, 301

vertex of graph, see graph theory

vertical angles, 260

Vietnam, 8

Visual Complex Analysis, 120

W^5 ,40

weights, method of, 294

well-ordering principle, 74, 102

Wilf, Herbert, 138

Wilson's theorem, 68, 252

WLOG, 41

yoga, 23

Zen in the Art of Archery, 23

zeta function, 162, 163, 349, 354