Borovik A. Shadows of the Truth: Metamathematics of Elementary Mathematics
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Index 275
constrained, 36
Ore, Oystein, 137
Oskay, Windell H., x, 87
Osserman, Robert, 222
Owl (Otus Persapiens), xi
pairing
of vector spaces, 8, 9
paradox
Zeno’s, 199
parallelepi p ed, 93
partition, 2
Pascal, Blaise, 171, 213
Patten, Teresa, x, 16 9
Pease, Alis on, x
pendulum, 41
permittivity, 11
permutation, 210
Perry, John, 146
Petrie, Karen, x
Pflügel, Eckhard, x
physics, 174, 182
π, 173
Piaget, Jean, 190
Pierce, David, x, 3, 53, 55, 79, 80,
82, 83, 126
Pitman, Sir James, 16
Plato, vii, 83
point
limit, 100
pointing, 127
pole, 220
Pólya, George, 28
polymorphism, 77
polynomial, 111
Laurent, 7, 10
Pons Asinorum, 215
Pormpuraaw, 218
Porter, Richard, x, 202
precalculus, 104
Preece, Donald A., x, 124
preoder, 88
price
shadow, 38
probability, 170
Problem
Lagrange Interpolation, 141
problem
scaling, 28
word, 14
procedure
decision, 99
product
cartesian, 67
dot, 8
inner, 8
scalar, 8, 9
tensor, 9, 219
progression
geometric, 199
projection
stereographic, 152, 153
prompt, 76
protractor, 1 72
Putinar, Mihai, x, 175
quadril lion, 125
quintillion, 125
quotient, 7
partial, 5
quotition, 2
Radzivilovsky, Vladimir, 126, 127
Ramachandran, Vilayanur, 44, 163
Reisch, Gregorius, 24
relation
equivalence, 67
remainder, 5, 137
Reni, Guido, iv, ix, 96
representative
coset, 115
Riepe, Thomas, x
ring
graded, 7
Laurent polynomial, 11
Noeterian, 128
unit of, 160
Robert, Alain M., 100
Roberts, Roy Stewart, x, 47, 48 , 97,
124
Robinson, Abraham, 99, 101
Ross, Frederick, x, 101
rounding, 76
row, 10
RSA, 162
ruler, 172, 175
Saint-Exupéry, Antoine de, v
Salinger, Jerome David, 199
scaling, 27, 2 8
Seban, Jane-Lola, x
section, 220
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ALEXANDRE V. BOROVIK
276 Index
semantics, 135
Sen, Ashna, x
St. Sergius of Radonezh, 195
series
Laurent, 7
set
directed, 88
empty, 84
set theory
internal, 100
sextillion, 125
Shackell, John R., x, 191
sharing, 1–3
sheaf, 220
Shen, Alexander, x
Shepherd, Simon J., x, 85
signified, 128
signifier, 128
Silagadze, Zu rab, 200
Sloman, Aaron, x
Souza, Kevin, x
space
dual, 219
finite dimensional vector, 219
vector, 219
speed
relative, 39
square
completion of the square, 184
perfect, 119
squil lion, 196
Stephenson, Christopher, x, 201
STICKLE BRICKS, 209, 210
Stokes, Sir George, 31
structure
o-minimal, 99
substitution
universal trigonometric, 153
subtraction, 3, 63, 69, 72
as ‘change giving’, 3
repeated, 12
supertask, 200
surface
orientable, 222
regualr, 222
Sutrop, Urmas, 221
Swan, Jerry, x, 209
Swanljung, Johan, x, 170
Swift, Tim, x, 15–17
symbol
minus, 63, 64
opposite, 64
symmetry
formal, 215
rotational, 208
system
direct, 88
table
multiplica tion, 4, 209
Taimina, Daina, 126
Tarski, Alfred, 12, 99
Tenejapan Tzeltal, 222
tensor, 8
Theorem
Binomial, 81
Chinese Remainder, 137, 142
Fermat’s Little, 81
Lagrange’s, 55
Pythagoras, 27, 28
Pythagorean, 38, 39
Stokes, 31
theorem
Euler’s, 55
theory
category, 8, 16, 44
model, 103
relativity, 1 86
representation, 17
Thompson, D’Arcy, 30, 39
tiling
Penrose, 208
time, 11
Tomczak, M atthias, 24
topolgy
set-theoretical, 103
topology, 101
algebraic, 71
transformation
didactic, 96 , 102, 103
linear, 219
transpose, 219
transposition didactique, 97
tree, 198
triangle, 29
isosceles, 215
trillion, 125
Trimble, Todd, 131
Tropashko, Vadim, x, 153, 167
Trubachov, Anatoly Mikhailovich,
32
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ALEXANDRE V. BOROVIK
Index 277
tuple
unordered, 72
turbulence, 11, 3 5
Tyrrell, Malcolm, 209
Tzeltal, 217, 218, 222
unit, 73, 120
of measurement, artificial, 20
dimensionless, 23
fundamental, 12
Planck’s, 12
Utyuzhnikov, Sergei, x
value
intermediate, 99
van Gogh, Vincent, 35
vector, 8
velocity, 11
Verbovskiy, Viktor, x, 192
Verne, Jules Gabriel, 19
Viéte, François, 7
viscosity, 31
visualization, 187
vizuali sation, 93
vortex, 34
Vygotsky, Lev Semenovich, 123
Wagner, Roy, x, 23
Walker, Peter, 155
wave number, 33
Weierstrass, Karl, 98
Wells, David, x
Wigner, Eugene P., 91
Wolfart, Jürgen, x, 123
work, 8
writing
mirror, 214
Wyles, Dean, x, 210
Zagier, Don, 54
Zaturska, Maria, x, 216
Zeno, 199
zero, 220
zero divisor, 116
zillion, 196
Zoellner, Logan, x, 114
SHADOWS OF THE TRUTH VER. 0.813 23-DEC-2010/7:19
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ALEXANDRE V. BOROVIK