298 Index problem homogeneous, 177–181, 184, 186, 189, 190, 196, 198, 201, 224 isoperimetric, 212 Newton’s, 247, 250, 252, 254 parametric, 179, 184, 189, 190, 224 parametric Queen Dido, 186 Plateau’s, 16, 98 Queen Dido’s, 107, 120 soap-film, 14, 190 Zermelo’s navigation, 191, 194, 197, 211, 212 pseudosphere, 12 ray equation, 94 ray optics, 93, 101 refractive index, 93, 94 regular curve, 177 regular problem, 48 Riccati equation, 147, 169 rolling penny, 111 rotating hoop, 103 royal road, 255, 267–273 Scherk’s minimal surface, 25 slack variables, 136 sliding rod, 133 slope of the field, 256 soap film(s), 19, 63, 64 solid of revolution, 247, 251, 252 stationary point, 47 strain energy, 74, 76 strain energy density, 74 surface area, 4, 15, 17, 24, 98, 248 tautochrone, 4, 18, 19 tube trains, 5, 7, 19 variation, 33, 139 first, 36, 37, 41, 70, 71, 81, 97, 141, 151, 184, 193, 194, 199, 216, 217 fourth, 154 second, 36, 141–143, 148–150, 153, 154, 167, 168, 184, 190 strong, 34, 35, 141, 175, 176, 235, 237, 238, 241, 242, 247, 253 third, 154, 168 total, 36, 70, 77, 97, 140, 141, 199, 260–262 weak, 35, 69, 77, 96, 118, 140, 149, 172, 173, 175, 199, 235, 242 variational derivative, 30, 31, 45 Weierstrass E-function, 243 Weierstrass equation, 182, 184–186, 190 Weierstrass excess function, 243, 245, 246, 253, 262–266, 269
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