Index

Abbott, Edwin A., 354

addition, 33, 35–36

Algarotti, Francesco, 113

algebra: and Fermat’s Last Theorem, 128–32

and geometry and trigonometry, 98, 195–98, 248–50

history of, 52–54, 299

and infinite series, 208–10

in mathematical problems, 63–68, 73, 77–83, 111–12

matrix, 173–75

notation 208

as a practical tool, 217–19, 299

rules of, 123–24. See also equations: cubic; equations: quadratic

Analyst, The, 72

angles, 87

arithmetic: and geometric progressions, 11–14

history of, 179–80, 298–99

and large numbers, 8–9

learning, 33–38, 38–40, 41–43, 44–46, 46–48, 48–50, 50–51, 253–55, 275–77, 280–81

and logarithms, 201–3

with Napier’s rods, 158–61

in number tricks and puzzles, 2–4, 10–14

origin of, 179–80

in practical use, 231–32, 233–36, 237–41, 241–44, 250–52

problems, 69–71, 71–72, 74–76

status of, 291

arithmetic progressions, 111

astronomy, 168–72, 255–58, 292–93, 308–9, 329–31, 343–46, 348–51. See also celestial mechanics

Athenian Mercury, The, 109

Australia, 308–9

Baker, Humfrey, 2, 246

Banson, William, 46

Barnes, William, 309

barometer, 66, 68, 237

Barrow, Isaac, 247–48

Boyer, Carl, 204–5

Boy’s Own Magazine, The, 71

bubbles, soap, 148–49

calculus, 177–78. See also integration

Cantor, Georg, 134–39

Carroll, Lewis, 261, 326

cars, 241–42

Cavendish, Margaret, 327

celestial mechanics, 113–15, 173–75, 182–84, 187, 338

Child, Lydia Marie, 69

circle principle. See yenri

Combe, William, 343

combinations, 75–76, 77–79, 81–83, 139–44

comets, 255–58

compass rose, 153–54

computers, 173–75, 282–89

Cortés, Martín, 153

cosine. See trigonometry: definitions

Dee, John, 293

Despiau, L., 17–18

Digges, Leonard, 217

division, 39–40

Domett, Alfred, 346

Dooley, Willliam H., 237

Dudeney, Henry Ernest, 20

Duffet-Smith, Peter, 172–73

Eicholz, Robert E., 277

Einstein, Albert, 120–22

engineering, 231–32, 233–36

equations: cubic, 57–61

Diophantine, 77, 80–81, 128–32

quadratic, 55–56

Euclid, Elements, 248–50, 259–61, 300–301, 310–11

Euler, Leonhard, 205–10, 250

Evans, Augusta Jane, 347

Fale, Thomas, 155

Fenn, Joseph, 52

Fermat’s Last Theorem, 128–32

Feynman, Richard P., 318

four-color problem, 116–18

fourth dimension, 355–58

fractions, 41–43, 44–46

decimal, 44–46

reducing, 42–43

Frere, John, 340

Fun, 352

games: card, 29–31, 253–54

dice, 19–20

mathematical, 27–31, 261–65

number, 2–4, 53–55, 69–71

Gardner, Alan Clive, 103–4

Gascoigne, Serafim, 282

gauging, 220–24

geometry: definitions, 85–87

difficulty and danger of, 331, 332–35

Euclidean, 91–94, 248–50, 359–60

learning, 336–39

methods, 88–91

nature of, 259–61, 292, 299

problems, 5–6, 9, 63–68, 72, 73, 78–79, 194–98, 270–73

solid, 220–24

spherical, 100–103

spherical, definitions, 100–101

turtle, 282–89

in use, 153–54, 155–57, 336–39

Glanvill, Joseph, 296–97

Gossuin of Metz, 291

Gould, Lucius D., 233

graphs, 304–7

great circle. See geometry: spherical, definitions

group theory, 150–51

Gulliver, Captain, 332

Hammond, Allen L., 322

Hardy, G. H., 210–15

Hatton, Edward, 44

Heath, Thomas L., 188

Heather, J. F., 164–65

heuristics, 270–73

Hirschberg, Arthur, 74

humor, mathematical, 109, 340–42, 352–54, 359–60

Hunt, William, 220–21

Hutton, Charles, 179

Huxley, Thomas Henry, 314–15

infinity, 133–39

integration, 211–12

Kanigel, Robert, 210

Kepler, Johannes, 182–84

Kepler’s Laws, 113–15

Keyser, Cassius Jackson, 315

Khurgin, Iakov Isaevich, 144

Kirkby, John, 335

Kôwa, Seki, 191–98

Ladies’ Diary, The, 63

Leybourne, William, 9

lines, 85–87

Littlewood, J. E., 211, 214–15

Lodge, Oliver, 120

logic, 261–65, 317

LOGO, 282–89

lotteries, 18–19

Love, John, 224–25

Lovechild, Mrs., 252–53

Margolis, Louis, 241

Masterson, Thomas, 38

materials, strength of, 233–36

mathematical Olympiads, 77

mathematical sciences, 291–93

mathematicians, working methods of, 139–44, 198–200, 324–25, 361–65

mathematics: dangers of, 333–35, 343–46, 360

difficulty of, 321, 346–47

education, 32–61, 84–107, 245–89, 335–40

in fiction, 326–65

history of, 52–54, 176–215, 302–3

nature of, 294–96, 310–13, 314–15, 316–18, 324–25

philosophy of, 109–10, 260–61

and physics, 319–22, 361–65

uses of, 216–44, 268–69, 300–301, 302–3, 310–13

mazes, 118–20

measuring, 9, 16, 165–68, 225–27

measuring problems, 15–16

Mikami, Yoshio, 190–91

minimal surfaces, 148–49

“Monster” group, 150–51

multiplication, 38–39, 161

music, 292, 140

Napier’s bones, 158–61

Napier’s rules, 104–7

navigation, 153–54, 227–30

New Math, 274–77, 278–81

Newton, Isaac, 113–15, 177–78, 185–88, 201–4

biography of, 185–88

Newton’s law of gravitation, 114–15, 320–21

nocturnal, 168–72

Noether, Emmy, 198–200

Northrop, Eugene P., 123

NRICH, 27

numbers: binary, 31

complex, 60–61

large, 10–14

notation, 180–82

problems, 75–76

perfect, 110

real, 125–27, 137–39

number theory, 110, 339–40

O’Daffer, Phares G., 277

optics, 162–64

Ozanam, Jacques, 15

paradoxes, 123–27

Partridge, Seth, 157

Patoun, Archibald, 227–28

Pedoe, Dan, 133

physics, 66, 120–22, 147–48

Playfair, William, 304

points 85–86

pole. See geometry: spherical, definitions

Pólya, George, 270

precession, 173–75

pressure, 237–41

printing, 242–24

probability, 18–20, 125–27

problems, mathematical, 63–83, 352

proof, 270–73

proportions, 300–301

Pythagoras, 188–90, 359–60

Pythagoras’ theorem, 88, 91–94, 97, 359

history of, 93–94, 188–90

proof of, 91–93

Pythagorean numbers, 128–32

Rademacher, Hans, 127–28

Ramanujan, Srinivasa, 210–15

Recorde, Robert, 33, 85

Relativity, 120–22

Robinson, Horatio Nelson, 99

Robinson, Kim Stanley, 360–61

Rouse Ball, W. W., 116

route problems, 20–26, 143

Rudd, Thomas, 87

rule of signs, 106–7

rule of three, 48–50, 50–51, 74

Rumker, Charles Stargard, 307–8

saddle points, 144–48

Sault, Richard, 302

scales (for measuring), 165–68

Scarburgh, Edmund, 91, 300

Searle, Ronald, 359

secant. See trigonometry: definitions

series, infinite, 212–13

sets, 278–81

infinite, 133–39

Sharp, Evelyn, 274

Shaw, George Bernard, 200–201

Sidgwick, Mrs. Henry, 266

sine. See trigonometry: definitions

Slade, Samuel, 241

Small, Robert, 182

Smith, David Eugene, 190–91

sound, speed of, 16–17, 252

spherical triangle. See geometry: spherical, definitions

square roots, 46–48

squares, 88

star clock. See nocturnal

statistics, 304–7

steam engines, 231–2

Stein, Sherman K., 139

subtraction, 36–38

sums, infinite, 208–10

sundials, 8, 155–57, 336–38

surveying, 225–27

Sylvester, J. J. 314, 352–34

tangent. See trigonometry: definitions

Tapp, John, 41

telescopes, 6–7, 162–64, 329–31, 350–51

reflecting 163–64

refracting 162–63

Templeton, William, 230–31

Thompson, J. E., 56–57

Thompson, Thomas Perronet, 259

Thompson, Wardhaugh, 48

Toeplitz, Otto, 127–28

trigonometry, 64–65, 72, 73, 88–91, 97–99, 225–27, 228–30

definitions, 95–97

spherical, 104–7

van der Waerden, B. L., 198

van Etten, Henry, 4–5

velocity, 250–52

verse, 50–51, 340–41, 343–46, 346–47, 352–54

Voltaire, 177

Wells, Edward, 94

Wells, H. G., 326–27

Whitwell, Catherine Vale, 255

Willans, Geoffrey, 359

Withy, Nathan, 50

work and power, 241–42

Worthington, Hugh, 97

Worvill, Roy, 168

yenri, 191–98