E
e(eccentricity of conic) 155
e(Euler’s number) 11,
152–154, 154, 173, 283,
300, 301, 314
earth 154–155, 166
eccentric 89
eccentricity 155, 161, 254,
373
echelon form 220
edge
on graph 233
of polyhedron 403
Egyptian fractions (unit
fractions) 155, 156, 192,
206
Egyptian mathematics
155–156, 423, 428, 497
Egyptian multiplication 155,
156
eigenvalue 156–157, 282
eigenvector (e-vector, latent
vector, characteristic vector,
proper vector) 156–157,
282
“Eine neue Bestimmung der
Moleküldimensionen”
(Einstein) 158
Einstein, Albert 157,
157–159, 227, 255, 398,
447, 496, 530
elasticity, mathematics of
227–228
“Élémens d’arithmétique
universelle” (Kramp) 187
elementary number theory
359–360
elementary operations 364
elementary row operation
220–222
Elemente der Mathematik
(Blatzer) 47
The Elements (Euclid) 1, 78,
159, 168–169, 171, 172,
183, 226, 238–239, 252,
253, 270
compass and straightedge
in 95
and foundations of
mathematics 200
perfect numbers in 389
Platonic solids in 396–397
Élements de géométrie
(Legendre) 308
Éléments de mathématiques
(Bourbaki) 50
Elements of Arithmetic (De
Morgan) 122
Elements of Geometry
(Menelaus) 336
Elements of Geometry
(Playfair) 377
elimination method. See
Gaussian elimination
Elizabethan multiplication
159–160, 160, 404
ell 309
ellipse 92–93, 93, 137, 155,
160, 160–161, 239
reflection property of 365
ellipsoid 161–162, 411
elliptic cone 411
elliptic cylinder 411
elliptic geometry. See spherical
geometry
elliptic paraboloid 374, 411
empty set (null set, Ø) 162,
257, 267, 460
Encyclopédie ou dictionnaire
raisonné des sciences, des
arts, et des métiers
(d’Alembert) 8
endpoints, of curve 114
enumerable. See denumerable
Enumeratio linearum tertii
ordinis (Newton) 353
envy-free fair division 188
epicycle 115
epicycloid 115
Epimenides 311
equality 162
equal sign (=) 442
equating coefficient 162, 380,
405
equating real and imaginary
parts 162–163
equation 163
equation of line 163–164
equiangular 164–165, 166,
506
equiangular polygon 402
equiangular transformation.
See conformal mapping
equidecomposable 165, 165
equidistant 76, 78, 165–166,
260
equilateral 164, 166, 285, 506
equilateral polygon 402
“Equilibrium Points in N-
person Games” (Nash) 347
equipotent (equipollent,
equinumerable) sets 60
equitangential curve. See
tractrix
equivalence 371
equivalent knots 295–296
equivalent sets 60
Eratosthenes 154, 166–167,
462, 510
Eratosthenes’ sieve 462–463
Erdös, Paul 167, 393
Erdös number 167
error 167–168, 197, 451, 457
error detection 461–462
error sum of squares 306
Essai sur une manière de
représenter les quantités
imaginaires dans les
constructions géometriques
(Argand) 25
Essay on Conic Sections
(Pascal) 382
“Essay on the Application of
Mathematical Analysis to the
Theory of Electricity and
Magnetism” (Green) 239
An Essay on the Principle of
Population (Malthus) 407
“An Essay Towards Solving a
Problem in the Doctrine of
Chances” (Bayes) 38
Euclid 1, 78, 168–169, 172,
183, 224, 226, 238–239,
252, 253, 265, 270, 314,
324, 410
and compass and
straightedge 95
definition of point 399
and formal logic 199, 250
and foundations of
mathematics 200
and fundamental theorem
of arithmetic 210
and perfect numbers 389
and Platonic solids
396–397
and pure mathematics 422
and Pythagorean triples
426
Euclidean algorithm 11, 82,
159, 169–170, 210, 237
Euclidean geometry 170, 409
axioms in 31
Hilbert on 250
vs. non-Euclidean geometry
294
and SAS rule 2
Euclidean space (Cartesian
space, n-space) 170
Euclides ab omni naevo
vindicatus (Saccheri) 455
Euclid of Megara
(philosopher) 168
Euclid’s postulates 6–7, 159,
170–171, 226, 255, 455, 474
See also parallel postulate
Euclid’s proof of the infinitude
of primes 159, 171–172,
238, 265, 410
Eudoxus 26, 57, 172–173
Euler, Leonhard 10, 107, 120,
140, 152, 161–163, 173,
173–174, 175, 180, 182,
185, 208, 284, 300, 431,
523–525, 529
and continued fractions 99
and continuously
compounded interest 276
and Fermat’s last theorem
190
and foundations of
mathematics 200
and geometry 6, 64, 80
and Goldbach’s conjecture
229–230
and graph theory 235–236
and number theory 13, 18,
187, 202, 247, 283, 349,
389, 426
and partition function 381
and pi (π) 393
and topology 500
and unit circle in
trigonometry 511
and zeta function 105,
447, 535–536
Euler circuit 233
Euler-Descartes formula. See
Euler’s theorem
Euler diagrams 26, 362
Eulerian circuit 235–236
Eulerian path 235
Euler line 80, 174, 174–175,
354, 507
Euler’s brick 174
Euler’s constant 174, 175,
175, 247, 283, 461
Euler’s formula 85–86, 122,
152, 163, 174, 175–176,
182, 185, 209, 236, 314
and logarithms 320
Euler’s polygon division
problem, Catalan numbers
and 65
Euler’s polynomial 174
Euler squares 303
Euler’s theorem (Euler-
Descartes formula) 80, 174,
176–177, 177, 233,
278–279, 358, 404, 472
Euler totient function 174
e-vector. See eigenvector
even functions 177, 490
even numbers 177–178
event 178, 413, 417
exa- (10
18
) 465
excircle 261, 354
excluded middle, law of 304
Exercitatio geometrica (D.
Gregory) 240
Exercitationes geometricae sex
(Cavalieri) 67
exhaustive subsets 371
existential quantifier (“there
exists”) 430–431
expanding brackets 9, 131,
162, 179, 179, 404, 431
and binomial theorem 45
and distributive property
143
and Elizabethan
multiplication 160
expected value (mean, expecta-
tion, µ) 179–180, 334
exponent 180–181, 263, 366,
475
exponential function
152–153, 181, 181–182
exponential inequalities 268
exponential notation. See
scientific notation
exponential series 182
exponential time 405
expression 182
exterior angle 182, 182–183,
504, 504
exterior-angle theorem 182,
183, 183, 377
Index 557