Ahlfors, Lars Valerian, 169–170, 230
Albers, Josef, 67
Alberti, Leon Battista, 41–42, 81
Aleksandrov, Pavel Sergeevich, 170–172
Alexander, James W., 172–173
algebraic geometry, 79–81, 115, 184, 186, 187, 202, 203, 206–207, 217, 222, 233–234, 235
algebraic notation, 74
angle-angle-angle (AAA) theorem, 62–63
angle-side-angle (ASA) theorem, 62
Anthemius, 71
Appollonius, 32–33, 38, 40, 41, 43–45, 49, 69–70, 73, 75, 116–119, 127, 148, 228
Archimedes, 28, 29, 32, 38, 40, 41, 47, 50, 65, 71, 76, 118, 119, 127–128, 130, 138, 141, 148
Archimedes screw, 119
astronomy, 22, 33–34, 40, 49, 76, 136, 137, 142, 145, 148, 162, 200, 205, 213
Atiyah, Sir Michael Francis, 173–174
Barrow, Isaac, 77
Beltrami, Eugenio, 56, 96, 97, 174–175, 199, 220
Betti, Enrico, 175–176, 213, 218
Bill, Max, 67
Bolyai, János, 54, 56, 57, 61, 94, 176–177, 198, 211
Brahe, Tycho, 36
Brianchon, Charles-Julien, 177–178
Bridge of Asses, 29–30, 62, 66
Brouwer, Luitzen Egbertus Jan, 97, 171, 178–180
Brownian motion, 236–237
Brunelleschi, Filippo, 41–42, 81
calculus, 43, 46, 47, 50, 55, 68, 85–86, 160, 174, 176
integral, 77, 124, 154, 161, 200
Cartesian geometry, 45–46
Cartesian plane, 179
Cavalieri, Bonaventura, 46–47, 77, 154–155, 167
Ceva, Giovanni, 155–156
Chasles, Michel, 51, 149, 166, 180–181
Chern, Shiing-Shen, 181–182
Chinese postman problem, 114
Clairaut, Alexis, 78
Clifford, William Kingdon, 182–184
conic sections, 22, 32, 39, 44–45, 49–50, 69–73, 84–85, 127, 145, 157, 178
curvature of curves, 85, 87–89
curvature of solids, 85, 89–91
Dantzig, George, 114
Dehn, Max, 68
Deligne, Pierre René, 184–185, 187, 222, 235
Democritus, 30
Desargues, Girard, 43–45, 51–52, 54, 71, 81, 82, 83, 156–158
Descartes, René, 43, 45–46, 50, 70, 73, 76, 86, 125, 135, 149, 157, 158–160, 168
De Witt, Johan, 75
differential geometry, 85–92, 94–95, 115–116, 166, 175, 237
Diocles, 71
Donaldson, Simon Kirwan, 185–186, 214
doubling the cube, 22, 26, 27, 45, 66, 70–71, 126, 139, 141, 143, 144, 148
Drinfeld, Vladimir Gershonovich, 186–187
Dudeney, 113
Einstein, Albert, 58, 182, 203, 214, 215, 217, 220
Enlightenment, 52
Eratosthenes, 27, 36, 70, 119, 128–129, 139, 144, 148
Euclid
fifth postulate, 52, 54, 57, 60–61, 93–94, 198
five postulates/axioms, 60–61, 131
Eudoxus, 29, 32, 69, 124, 133, 134, 137–139, 153
Euler, Leonhard, 77–78, 88, 89–90, 103, 108, 112, 160–163
Euler characteristic, 103
exhaustion, method of, 29, 31, 46, 65, 134, 138
Fermat, Pierre de, 43, 47–49, 76, 81, 125, 135, 149, 157
fractals, 192, 195, 200–202, 225, 236
Galileo Galilei, 50, 71, 125, 154, 155, 169
Gauss, Carl Friedrich, 53–54, 61, 66, 85, 90–91, 107, 175, 177, 189, 198, 199, 205, 219, 227
Gauss’s theorem, 91
geodesy/geodesics, 55, 56, 58, 85, 92, 97, 180
geometrical calculus, 46–49
graph theory, 108–114
Great Compilation, 33
Gregory, James, 77
Grothendieck, Alexandre, 80, 173, 184, 187–188, 207, 222, 233
Guthrie, Francis, 114
Hamilton, William Rowan, 78, 110, 183
Hausdorff space, 102
Heawood, Percy, 114
Herman, Jakob, 77–78
Hernon, 139–142
Hilbert, David, 57, 60, 61, 96, 188–191, 195, 203, 216, 219, 221, 227, 234
Hilbert space, 191
Hippocrates, 27, 28, 29, 71, 126, 130, 141, 142–143, 144
homeomorphism, 100–101, 103, 104, 105
hydrostatistics, 119, 120, 123
hyperbolic geometry, 93, 94, 96–97, 107
incommensurability, 24, 138, 150, 153
infinity
Islam/Islamic, 38–40, 67, 74, 116, 118, 125, 135
Jones, Vaughan, 107
Julia, Gaston Maurice, 192–193
Kepler, Johannes, 35–36, 46–49, 71, 125, 134, 135, 139
Klein, Felix, 97, 175, 193–195, 200, 211, 219, 227
Klein bottle, 114
Kodaira Kunihiko, 197–198
Königsberg bridge problem, 108, 112
Kuiper, Nicolaas, 96
Kuratowski, Kazimierz, 113
Lagrange, Joseph-Louis, 78, 163, 165, 166
Lambert, Johann Heinrich, 53, 54
Leibniz, Gottfried, 77, 87–88, 158
LeWitt, Sol, 67
Lindemann, Ferdinand von, 26
linear perspective, 41–43
linear programming, 114
Lobachevsky, Nikolay Ivanovich, 54, 56, 57–58, 61, 94, 175, 177, 182, 184, 198–200, 211
Mandelbrot, Benoit, 200–202, 236
manifolds, 104, 105, 173, 174, 176, 179, 183, 186, 197, 202, 208–210, 213, 219, 225, 229, 230
Menaechmus, 32, 69, 117, 138, 143–144
Mercator, Gerardus, 42–43
Milnor, John Willard, 202–203
Minding, Ferdinand, 92
Minding’s theorem, 91
Minkowski, Hermann, 189, 203–204, 237
Möbius, August Ferdinand, 204–206
Monge, Gaspard, 51, 78, 90, 163–167, 178
Mori Shigefumi, 206–207
Mumford, David Bryant, 207–208
Newton, Isaac, 49–50, 58, 75, 77, 78, 85, 88, 135, 149, 212, 214
Nicole, François, 78
Novikov, Sergey Petrovich, 208–209
Pappus, 83, 116, 117, 127–128, 129, 134, 141, 147–149
parabola, applications of, 71–73
parallelism, 31, 40, 43–44, 51–52, 61, 62, 82, 92, 93–94, 145, 176, 177, 198–199
Pascal, Blaise, 43, 45, 52, 81, 83–84, 158, 178
Perelman, Grigori, 105, 209–210, 214, 230
π, value of, 25–26, 29, 65, 124
Plato, 27, 29, 30, 33, 34, 69, 70–71, 126, 130, 137, 142, 143, 150, 153
Platonic solids, 31, 34–36, 68, 118, 130, 134, 140, 153
Poincaré, Henri, 97, 104, 112, 176, 190, 191, 195, 210–216, 225, 230
Poncelet, Jean-Victor, 82, 51–52, 149, 158, 166, 216–217
Proclus, 29–30, 118, 129–130, 133, 134, 141, 143, 144
proportional segments theorem, 82
psuedosphere, 96
Ptolemy I, 22, 33–34, 38, 40, 41, 42, 94, 118, 130, 139, 141, 147
Pythagorean theorem, 24–25, 31, 55, 60, 64, 66, 131, 132, 150
quantum field theory, 107
relativity, 58, 182, 202–203, 214, 217, 220, 231, 232
Renaissance, 41, 43, 76, 81, 115, 116, 125, 132, 135, 139
Rhind papyrus, 26
Riemann, Bernhard, 55, 58, 95, 175, 176, 182, 184, 189, 195, 200, 213, 217–221
Riemann sphere, 95
right angle, constructing, 23–24
Roberval, Gilles Personne de, 43, 77, 167–168
Saccheri, Girolamo, 52–53, 54, 56
Serre, Jean-Pierre, 188, 221–223
side-angle-side (SAS) theorem, 62
side-side-side (SSS) theorem, 62
Sierpiński, Wacław, 223–225
similarity, theorem of, 66, 82
spherical geometry, 53, 54–55, 92, 93, 94–95
squaring the circle, 22, 26, 28–29, 30, 66, 143
Staudt, Karl Georg Christian von, 52, 226–227, 228
Steiner, Jakob, 51–52, 180, 227–228
Stirling, James, 77
strake, 86–91
Sylvester, James, 113
Tait, Peter Guthrie, 107
Thales, 24, 29–30, 31, 65, 151–153
Thom, René Frédéric, 228–229
Thomson, William, 107
three and more dimensions, 68–69, 77–79, 98–100, 104, 105, 134, 166, 171, 173, 175, 176, 185–186, 204, 209–210, 213–214, 220, 225–226, 228, 229, 230, 232
Thurston, William Paul, 96, 104–105, 107, 229–230
topology, 79, 97–114, 116, 170–171, 172–175, 176, 178–179, 185, 188, 202–203, 204–205, 206, 208, 210, 213, 219, 221–222, 223–224, 225–226, 228–230, 231–232, 233, 235
traveling salesman problem, 114
trisecting the angle, 22, 26, 27–28, 45, 66, 144
Van Schooten, Frans, 75
Veblen, Oswald, 231–232
vector, 78–79
vector spaces, 104
Viète, François, 74–75
Voevodsky, Vladimir, 233–234
Von Koch, Niels Fabian Helge, 195–196
Wantzel, Pierre Laurent, 26
Weil, André, 184, 188, 234–235
Werner, Wendelin, 236–237
Wiles, Andrew, 81
Witten, Edward, 107
Yau, Shing-Tung, 237