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THE UNIVERSAL BOOK OF MATHEMATICS

From Abracadabra to Zeno's Paradoxes


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Errata


Alphabetical List of Entries



abacus
Abbott, Edwin Abbott (1838-1926)
ABC conjecture
Abel, Niels Henrik (1802-1829)
Abelian group
abracadabra
abscissa
absolute
absolute value
absolute zero
abstract algebra
Abu’l Wafa (A.D. 940-998)
abundant number
Achilles and the Tortoise paradox. See Zeno's paradoxes
Ackermann function
acre
acute
adjacent
affine geometry
age puzzles and tricks
Agnesi, Maria Gaetana (1718-1799)
Ahmes papyrus. See Rhind papyrus
Ahrens, Wilhelm Ernst Martin Georg (1872-1927)
Alcuin (735-804)
aleph
Alexander’s horned sphere
algebra
algebraic curve
algebraic fallacies
algebraic geometry
algebraic number
algebraic number theory
algebraic topology
algorithm
algorithmic complexity
Alhambra
aliquot part
al-Khowarizmi (c.780-850)
Allais paradox
almost perfect number
alphamagic square
alphametic
Altekruse puzzle
alternate
altitude
ambiguous figure
ambiguous connectivity. See impossible figures
Ames room
amicable numbers
amplitude
anagram
anallagmatic curve
analysis
analytical geometry
analytical number theory
anamorphosis
angle
angle bisection. See bisecting an angle
angle trisection. See trisecting an angle
animals' mathematical ability
annulus
antigravity houses and hills
antimagic square
antiprism
aperiodic tiling
Apéry's constant
apex
apocalypse number. See beast number
Apollonius of Perga (c. 255-170 B.C.)
Apollonius problem
apothem
apotome
applied mathematics
Arabic numeral
arbelos
arc
arch
Archimedean dual. See Catalan solid
Archimedean solid
Archimedean spiral
Archimedean tessellation
Archimedes of Syracuse (c. 287-212 B.C.)
Archimedes's cattle problem
Archimedes's square. See loculus of Archimedes
area
area codes
Argand diagram
argument
Aristotle’s wheel
arithmetic
arithmetic mean
arithmetic sequence
Around the World game. See Icosian game
array
Arrow paradox
arrowhead. See dart
artificial intelligence (AI)
artificial life
associative
astroid
asymptote
Atiyah, Michael Francis (1929-)
Atomium, The
attractor
Aubel's theorem
autogram. See self-enumerating sentence
automorphic number
automorphism
Avagadro constant
average
axiom
axiom of choice
axis

Babbage, Charles (1791-1871)
Bachet de Méziriac, Claude-Gaspar (1581-1638)
backgammon
baker's dozen. See thirteen
Bakhshali manuscript
ball
Ball, Walter William Rouse (1850-1925)
Banach, Stefan (1892-1945)
Banach-Tarski paradox
Bang's theorem
Banker's rounding
Barbaro, Daniele (1513-1570)
barber paradox. See Russell paradox
Barbier’s theorem. See curve of constant width
Barlow, Peter (1776-1862)
Barnsley’s fern
base
basin of attraction
basis
Bayes, Thomas (1702-1761)
Bayesian inference
Bayes's theorem
Beal cipher
Beal's conjecture
beast number (666)
Beatty sequences
beauty and mathematics
Bell, Eric Temple (1883-1960)
bell curve
Bell number
Benford’s law
Benham’s disk
Bernoulli family
Bernouilli number
Berry’s paradox
Bertrand's box paradox
Bertand's postulate
Bessel, Friedrich Wilhelm (1784-1846)
beta function
Betti number
bicorn
bicuspid curve
Bieberbach conjecture
bifurcation
bilateral
bilateral diagram
billion. See large numbers
bimagic square
binary
binary operation
binomial
binomial coefficient
binomial theorem
Birkhoff, George David (1884-1944)
birthday paradox
birthday surprise
bisect
bisecting an angle
bishops problem
bistromathics
bit
blackjack
Blanche’s dissection
Bólyai, János (1802-1860)
book-stacking problem
Boole (Stott), Alicia (1860-1940)
Boole, George (1815-1864)
Boolean
Boolean algebra
Borel, Emile (1871-1956)
Borges, Jorge Luis (1899-1986)
Borromean rings
Borsuk-Ulam theorem
bottle sizes
boundary condition
boundary value problem
Bourbaki, Nicholas
brachistochrone problem
Brahmagupta (A.D. 598-after 665)
braid
Brianchon's theorem
bridges of Königsberg
Briggs, Henry (1556-1630)
Brocard problem
broken chessboard. See polyomino
Bronowski, Jacob (1908-1974)
Brouwer, Luitzen Egbertus Jan (1881-1966)
Brouwer fixed-point theorem
Brownian motion
Brun's constant. See twin primes
bubbles
buckyball
Buffon’s needle
bundle
Burali-Forti paradox
Buridan's ass
burr puzzle
butterfly effect
butterfly theorem
Byron, (Augusta) Ada (1815-1852)
byte

caduceus
Cage, John (1912-1992)
Caesar cipher
cake-cutting
Calabi-Yau space
calculus
calculus of variations
calendar curiosities
Caliban
Caliban puzzle
cannonball problem
canonical form
Cantor, Georg Ferdinand Ludwig Philipp (1845-1918)
Cantor dust
cap
Cardano, Girolamo (1501-1570)
Cardan's rings. See Chinese rings
cardinal number
cardioid
cards
Carmichael number
Carroll, Lewis (1832-1898)
Cartesian geometry. See analytical geometry
Cartesian coordinates
Cartesian oval
Cassinian ovals
casting out nines
Catalan number
Catalan solid
Catalan's conjecture
Catalan’s constant
catastrophe theory
Catch-22
category theory
catenary
catenoid
cathetus
Cauchy, Augustin Louis, baron (1789-1857)
causality
caustic
Cavalieri’s principle
Cayley, Arthur (1821-1895)
Cayley number. See octonion
Cayley's mousetrap
Cayley's sextic
ceiling
cell
cellular automaton
celt
center of perspective
centillion. See large numbers
central angle
centroid
century
Ceva, Giovanni (1647-1734)
chained arrow notation. See Conway's chained arrow notation
Chaitin, Gregory (1947-)
Chaitin’s constant
Champernowne's number
chance. See probability
change ringing
chaos
chaos tiles. See Penrose tiles
chaotic attractor
character theory
chess
Chinese cross. See burr puzzle
Chinese remainder theorem
Chinese rings
Chinese room
chiral
Chladni, Ernst Florens Friedrich (1756-1827)
chord
chromatic number
chronogram
Church, Alonzo (1903-1995)
Church-Turing thesis
cipher
circle
circle involute
circular cone
circular helix. See helix
circular prime
circumcenter
circumcircle
circumference
cissoid
classification
clelia
Clifford, William Kingdon (1845-1879)
clock puzzle
closed
cochleoid
code. See cipher
codimension
coding theory
codomain
coefficient
Coffin, Stewart T.
cohomology
coin paradox
coincidence
Collatz problem
combination
combinatorics
commensurable
common fraction
communication theory. See information theory
commutative
complement
complete
complete graph
complex adaptive system (CAS)
complex analysis
complex number
complex plane. See Argand diagram
complex system
complexity
complexity theory
composite number
compound polyhedron
compressible
computability theory
computable number
concave
conchoid
cone
conformal mapping
congruent
congruum problem
conic section
conical helix. See helix
conjecture
conjugate
connected
connected graph
connectionism
connectivity
consistency
constructible
continued fraction
continuity
continuum
continuum hypothesis
convergence
convex
Conway, John Horton (1937-)
Conway's chained-arrow notation
coordinate
coordinate geometry. See analytical geometry
coprime
cosine. See trigonometric function
countable set
counterfeit coin problem
covariance
Coxeter, Harold Scott MacDonald
cross
crunode
cryptarithm
cryptography
Császár polyhedron
cube
cubic curve
cubic equation
cubit
cuboctahedron
cuboid
Cullen number
Cutler, William ("Bill")
Cunningham chain
cup
curvature
curve
curve of constant width
cusp
cute number
cybernetics
cyclic number
cyclic polygon
cycloid
cylinder

d'Alembert, Jean Le Rond d' (1717-1783)
Dandelin spheres
dart
de l'Hopital, Guillaume Francis Antoine (1661-1704)
de l'Hoptal's cubic. See Tschirnhaus' cubic
de Malves's theorem
de Méré’s problem
de Moivre, Abraham (1667-1754)
de Moivre's theorem
de Morgan, Augustus (1806-1871)
decagon
decimal
decimal fraction
Dedekind, Julius Wilhelm Richard (1831-1916)
Dee, John (1527-1609)
deficient number. See abundant number
degree
degree of freedom
deletable prime. See truncatable prime
delta curve
deltahedron
deltoid
denominator
derivative
Desargues, Girard (1591-1661)
Descartes, René (1596-1650)
Descarte's circle theorem. See Soddy formula
determinant
deterministic system
devil’s curve
Dewdney, Alexander Keewatin
diagonal
diagonal matrix
diameter
dice
difference equation
differential
differential equation
differential geometry
differential topology
differentiation
digimetic
digit
digital root
digraph
dihedral angle
dimension
dinner party problem. See Ramsey theory
Diocles (c. 240-c. 180 B.C.)
Diophantine approximation
Diophantine equation
Diophantus of Alexandria (A.D. c.200-c.284)
Diophantus's riddle
Dirac, Paul Adrien Maurice (1902-1984)
Dirac string trick
direct proportion
directed graph
directrix
Dirichlet, Peter Gustav Lejeune (1805-1859)
Dirichlet's theorem
discontinuity
discrete
discriminant
disk
disme
dissection
dissipative system
distortion illusion
distributive
diverge
division
dodecagon
dodecahedron
Dodgson, Charles Lutwidge. See Carroll, Lewis
dollar
domain
domino
domino problem
dozen. See twelve
dragon curve
dual
Dudeney, Henry Ernest (1857-1930)
Dunsany, Lord Edward Plunkett (1878-1957)
Dupin cyclide
duplicating the cube
Dürer, Albrecht (1471-1528)
Dürer's shell curve
dynamical system
dynamics

e
Earthshapes
eccentricity. See conic section
economical number
Eddington number
edge
edge coloring theorem. See Tait's conjecture
edge of chaos
egg
Egyptian fraction
eigenvalue
eight
eight curve
Einstein problem
elementary function
eleven
ellipse
ellipsoid
elliptic curve
elliptic function
elliptical geometry
embedding
emergence
emirp
empty set
enantiomorph
enormous theorem
entropy
envelope
epicycloid
Epimenides paradox. See liar paradox
epitrochoid
EPORN
equichordal point
equilateral
equilibrium
equivalent numbers
Eratosthenes of Cyrene (c.276-194 B.C.)
Eratosthenes’s sieve. See sieve of Eratosthenes
Erdös, Paul (1913-1996)
ergodic
Escher, Maurits Cornelius (1898-1972)
escribed circle
Eternity puzzle
Euclid of Alexandria (c.330-270 B.C.)
Euclidean geometry
Euclidean space
Euclid’s postulates
Eudoxus of Cnidus (c.408-c.355 B.C.)
Euler, Leonhard (1707-1783)
Euler characteristic
Euler circuit
Euler line
Euler path
Euler square
Euler-Mascheroni constant
Euler's conjecture
Euler's constant. See Euler-Mascheroni constant
Euler's formula
Euler's formula for polyhedra
even function
evolute
excluded middle law
existence
exponent
exponential
extrapolate. See interpolate
extravagant number. See economical number

face
factor
factorial
factorion
Fadiman, Clifton (1904-1999)
Fagnano’s problem
fair division. See cake-cutting
Farey sequence
Fechner, Gustav Theodor (1801-1887)
Federo, E. S. (1853-1919)
feedback
Feigenbaum's constant
Fermat, Pierre de (1601-1665)
Fermat number
Fermat’s last theorem
Fermat’s little theorem
Fermat's spiral
Fibonacci (c.1175-1250)
Fibonacci sequence
field
Fields medal
Fifteen puzzle
figurate number
films and plays involving mathematics
finite
finite-state automaton
Fisher, Adrian Fitchneal
five
fixed-point attractor
Flatland: A Romance of Many Dimensions
flexagon
floor function
flower of life
fly between trains problem
focal chord
focal radius
focus
foliation
folium
formal system
formalism
Fortune’s conjecture
four
four coins problem
four fours problem
four knights puzzle
four-color map problem
Fourier, (Jean Baptiste) Joseph, Baron (1768-1830)
Fourier series
fourth dimension
fox and geese
fractal
fractal dimension
fraction
Fraser spiral
Fredholm, Erik Ivar (1866-1927)
Freemish crate. See impossible figure
Freeth's nephroid. See nephroid
Frege, Friedrich Ludwig Gottlob (1848-1925)
Frénicle de Bessy, Bernard (1602-1675)
frequency
friendly number. See amicable number
frogs and toads
frugal number. See economical number
frustum
function
fundamental group
fundamental theorem of algebra
fundamental theorem of arithmetic
fuzzy logic

Gabriel's horn
Galois, Évariste (1811-1832)
Galois theory
game
game theory
gamma. See Euler-Mascheroni constant
gamma function
Gardner, Martin (1914-)
gauge field
Gauss, Carl Friedrich (1777-1855)
Gaussian
Gelfond’s theorem
general relativity. See relativity theory
general topology. See point-set topology
genetic algorithm
genus
geoboard
geodesic
geometric mean
geometric sequence
geometry
geometry puzzles
Gergonne point
Germain, Sophie (1776-1831)
Get off the Earth
Gettier problem
Giant's Causeway
Gilbreath’s conjecture
glissette
gnomon magic square
Go
God
Gödel, Kurt (1906-1978)
Gödel’s incompleteness theorem
Goldbach conjecture
golden ratio (phi)
Golomb, Solomon W. (1932-)
golygon
googol
Gordian knot
graceful graph
gradient
Graham, Ronald L. (1936-)
Graham’s number
grandfather paradox
graph
graph theory
great circle
great monad
greatest common divisor
greatest lower bound
Green, George (1793-1841)
Green's theorem
Grelling's paradox
gross
group
Grundy’s game. See Nim
Guy, Richard Kenneth (1916-)

haberdasher’s puzzle
Hadwiger problem
hailstone sequence
hairy ball theorem
half-line
half-plane
halting problem
ham sandwich theorem
Hamilton, William Rowan (1805-1865)
Hamilton circuit
Hamilton path
Hankel matrix
happy number
Hardy, Godfrey Harold (1877-1947)
harmonic analysis
harmonic division
harmonic mean
harmonic sequence
Harshad number
hat problem
Hausdorff, Felix (1868-1942)
Hausdorff dimension
Heesch number
Hein, Piet (1905-1996)
helicoid
helix
Henon, Michele
Henstock integration. See integration
heptagon
Hermann grid illusion
Hermite, Charles (1822-1901)
Heron of Alexandria (c. A.D. 60)
Heron's formula
Herring illusion
heuristic argument
Hex
hexa-
higher dimensions
Hilbert, David (1862-1943)
Hilbert space
Hinton, Charles Howard (1853-1907)
Hippias of Elis (c. 5th century B.C.)
hippopede
Hi-Q. See peg solitaire
hnefa-tafl
Hoffmann, Louis "Professor" (1839-1919)
Hofstadter, Douglas R. (1945-)
Hofstadter's law
Hogben, Lancelot Thomas (1895-1975)
hole hole-in-a-postcard problem
hole-through-a-sphere problem
hole-through-the-Earth problem
holism
homeomorphic
homeomorphism
homology
homomorphism
homotopy
Hordern, L. Edward (d. 2000)
hundred
hundred fowls problem
Hunter, James Alston Hope
Huygens, Christiaan (1629-1695)
Hypatia of Alexandria (c. A.D. 370-417)
hyperbola
hyperbolic geometry
hyperbolic spiral
hyperboloid
hypercube
hyperellipse. See superellipse
hyperfactorial
hypergeometric function
hyperreal number
hypersphere
hypocycloid
hypoellipse. See superellipse
hypotenuse
hypothesis. See conjecture
hypotrochoid

i
i-ching
icosahedron
Icosian game
idempotent
identity
imaginary number
impossibilities in mathematics
impossible figure
impossible tribar. See Penrose triangle
impossible trident
incircle
incomputable number
induction
inequality
infinite dimensions
infinite series
infinitesimal
infinity
inflection
information theory
injection
inscribed angle
inscribed circle
instability
integer
integral
integral equation
integration
interesting numbers
international date line
interpolate
intersection
invariant
invariant theory
inverse
involute
irradiation illusion
irrational number
irreptile. See rep-tile
Ishango bone
isochrone
isogonal conjugate
isometry
isomorphism
isoperimetric inequality
isosceles
isotomic conjugate
isovolume problem
iterate
iteration
Jacobi, Karl Gustav Jacob (1804-1851)
Johnson solid
Johnson's theorem
Jordan, (Marie-Ennemond) Camille (1838-1922)
Jordan curve
Jordan matrix
Journal of Recreational Mathematics
Julia set
jump discontinuity

Kaczynski, Theodore John (1942-)
Kakeya needle problem
Kaluza-Klein theory
kampyle of Eudoxus
kappa curve
Kaprekar constant
Kaprekar number
Kasner, Edward (1876-1955)
Kepler, Johannes (1571-1630)
Kepler-Poinsot solids
Kepler's conjecture
Khayyam, Omar (1044-1123)
Khintchine's constant
kings problem
kinship puzzles
Kirkman, Thomas Penyngton (1806-1895)
kite
Klein, Christian Felix (1849-1925)
Klein bottle
knight's problem
knight's tour
knot
Knuth's up-arrow notation
Koch snowflake
Kolmogorov, Andrei Nikolaievich (1903-1987)
Königsberg bridge problem. See bridges of Königsberg
Kronecker, Leopold (1823-1891)
labyrinth. See maze
Lagrange, Joseph Louis (1736-1813)
lambda calculus
Lamé curve
lamination
Langley's adventitious angles
Langton’s ant
Laplace, Pierre Simon (1749-1827)
large numbers
lateral inhibition illusion. See Hermann grid illusion
Latin square
lattice
lattice path
lattice point
latus rectum
league
least common multiple
least upper bound
Lebesgue, Henri Leon (1875-1941)
Lebombo bone
left-right reversal. See mirror reversal problem
Leibniz, Gottfried Wilhelm (1646-1716)
Leibniz harmonic triangle
lemma
lemniscate
Leurechon, Jean (c.1591-1670)
liar paradox
Lie, Marius Sophus (1842-1899)
Lie algebra
Lie group
life, Conway’s game of
limaçon of Pascal
limerick
limit
limping triangle
line
linear
linear algebra
linear group
linear programming
linear system
Liouville number
Lissajous figure
lituus
Lobachevsky, Nikolai Ivanovich (1793-1856)
localized solution
loculus of Archimedes
locus
logarithm
logarithmic spiral
logic
logical depth
loop
Lorenz, Edward Norton (1917-)
Lorenz system
Lovelace, Lady. See Byron, Ada
loxodrome
Loyd, Sam (1841-1911)
lozenge
L-system
Lucas, (François) Edouard (Anatole) (1842-1891)
Lucas sequences
lucky number
Ludolph's number
lune
Lyapunov fractal

Maclaurin, Colin (1698-1746)
Maclaurin trisectrix
MacMahon, Percy Alexander (1854-1929)
MacMahon squares
Madachy, Joseph S.
magic cube
magic square
magic tour
main diagonal
major axis
Malfatti circles
mancala
Mandelbrot, Benoit B. (1924-)
Mandelbrot set
manifold
many worlds hypothesis
Markov chain
Martingale system
Mascheroni construction
matchstick puzzles
mathematical lifespan
mathematics
matrix
maximum
maze
mean
measure
measure theory
measuring and weighing puzzles
mechanical puzzles
medial triangle
median
Menaechmus (c.380-c.320 B.C.)
Menger sponge
Mersenne, Marin (1588-1648)
Mersenne number
Mersenne prime
method of exhaustion
metric
metric space
metrizable
Michell, John (1724-1793)
midpoint
mile
million
minimal prime
minimal surface
minimax theorem
minimum
Minkowski, Hermann (1864-1909)
Minkowski space
minor axis
mirror reversal problem
missing dollar problem
Mittag-Leffler, (Magnus) Gösta (1846-1927)
mixed strategy
Möbius band
mode
model of computation
model theory
modulo
Moiré pattern
Moivre, Abraham de. See de Moivre, Abraham
Monge, Gaspard (1746-1818)
monkeys and typewriters
monochromatic triangle
monomial
monotonic
monster curve. See Peano curve
monster group
monstrous moonshine conjecture
Monte Carlo method
Montucla, Jean Etienne (1725-1799)
Monty Hall problem
Morley’s miracle
mousetrap. See Cayley's mousetrap
moving sofa problem
Mrs. Perkins’ quilt
Müller-Lyer illusion
multigrade
multiple
Mydorge, Claude (1585-1647)
myriad

Nagel point
Napier, John (1550-1617)
Napoleon Bonaparte (1769-1821)
narcissistic number
Nash, John Forbes Jr. (1928-)
Nash equilibrium
natural number
Necker cube
negative base
negative numbers
Neile’s parabola
nephroid
net
neural network
Neusis construction
Newcomb’s paradox
Newton, Isaac (1642-1727)
Newton's method
Nim
nine
nine holes. See three men's morris
nine men's morris
nine rooms paradox
nine-point circle
Noether, Emmy (Amalie) (1882-1935)
non-Abelian
nonagon
nonconvex uniform polyhedron
non-Euclidean geometry
nonlinear system
nonstandard analysis
normal
normal number
nothing
noughts and crosses. See tic-tac-toe
NP-hard problem
nucleation
null hypothesis
null set. See empty set
number
number line
number system
number theory
numeral
numerator
numerical analysis

obelus
oblate spheroid
oblique
oblong
oblong number
obtuse
octa-
octagon
octahedron
octant
octonion
odd
officer problem. See thirty-six officers problem
omega. See Chaitin's constant
one
one-to-one
153
open
operator
optical illusion
Orbison’s illusion
orbit
order
ordered pair
ordinal number
ordinary differential equation
ordinate
origami
origin
orthic triangle
orthocenter
orthogonal
osculating
Oughtred, William (1574-1660)
oval
Ovid's game
Ozanam, Jacques (1640-1717)

Pacioli, Luca (1445-1517)
packing
Padovan sequence. See plastic number
palindrome
palindromic number
pandiagonal magic square
pandigital number
pandigital product
pangram
Pappus of Alexandria (lived c. A.D. 300)
parabola
parabloid
paradox
parallel postulate
parallelepiped
paralellogram
parameter
parity
Parrondo’s paradox
partial differential equation
partition number
Pascal, Blaise (1623-1662)
Pascal’s mystic hexagon
Pascal’s triangle
pathological curve
payoff
Peano, Guiseppe (1858-1932)
Peano curve
pearls of Sluze
pedal curve
pedal triangle
peg solitaire
Pell numbers
Pell equation
Penrose, Roger (1931-)
Penrose stairway
Penrose tiling
Penrose triangle
penta-
pentomino. See polyomino
Perelman, Yakov Isidorovitch (1882-1942)
perfect cube
perfect number
perfect power
perfect square
Perigal, Henry (1801-1898)
perimeter
period, of a decimal expansion
periodic
periodic attractor
periodic tiling
permutable prime
permutation
perpendicular
Perrin sequence
perturbation
phase space
phase transition
phi. See golden ratio
Phillips, Hubert (1891-1964)
phutball
pi
Pick's theorem
pitch drop experiment
pizza
place-value system
Planck time
plane
plane partition
plastic number
Plateau, Joseph Antoine Ferdinand (1801-1883)
Plateau curves
Plateau problem
Platonic solid
Platonism
pleated surface
Poggendorff illusion
Poincaré, (Jules) Henri (1854-1912)
Poincaré conjecture
Poincaré disk
Poinsot, Louis (1777-1859)
point-set topology
Poisson, Siméon Denis (1781-1840)
polar coordinates
Pólya’s conjecture
polychoron
polycube
polygon
polygonal number
polyhedron
polyiamond
polynomial
polyomino
polytope
Poncelot, Jean Victor (1788-1867)
Poncelot's theorem
pony puzzle
postage stamp problems
power
power law
power tower
powerful number
practical number
prime number
primitive root
primitive root of unity
primorial
Prince Rupert's problem
prism
prisoner's dilemma
probability theory
Proclus Diadochus (A.D. c. 410-485)
product
projective geometry
projective plane
pronic number
proof
proper divisor. See aliquot part
proportional
pseudoprime
pseudosphere
pure mathematics
pursuit curve
puzzle jug
puzzle rings
puzzle vessels
pyramid
pyramidal number
Pythagoras of Samos (c. 580-500 B.C.)
Pythagoras’s theorem
Pythagorean square puzzle
Pythagorean triangle
Pythagorean triplet

QED
quadrangle
quadrant
quadratic
quadratrix of Hippias
quadrature
quadric
quadrifolium. See rose curve
quadrilateral
quantum field theory
quantum mechanics
quartic
quartile
quasicrystal
quasiperiodic
quasi-regular polyhedron
quaternion
queens puzzle
quine
quintic
quotient

radian
radical
radical axis
radius
radix. See base
railroad problems. See shunting puzzles
Ramanujan, Srinivasa Aaiyangar (1887-1920)
Ramsey theory
random
random number
random walk
range
ranunculoid
ratio
rational number
raven paradox
ray
real number
realm
reciprocal
Recorde, Robert (c.1510-1558)
rectangle
rectangular coordinates. See Cartesian coordinates
rectangular hyperbola. See hyberola
recursion
recursive function
recursively enumerable set
reductio ad absurdum
reductionism
redundancy
reflection
reflex angle
reflexible
regular polygon
regular polyhedron
relativity theory
renormalization
repdigit
representation theory
rep-tile
rep-unit
Reuleaux polytope
Reuleaux triangle
Reutersvärd, Oscar (1915-)
Rhind papyrus
rhombus
Richard's paradox. See Berry's paradox
Riemann, (Georg Friedrich) Bernhard (1826-1866)
Riemann hypothesis
Riemann integral
Riemann sphere
Riemann surface
Riemann zeta function
Riemannian geometry. See elliptical geometry
right
ring
Rithmomachia
river-crossing problems
Robinson, Abraham (1918-1974)
Roman numerals
rooks problem
root
root of unity
rope around the Earth puzzle
Rosamund's bower
rose curve
rotation
rotor
roulette
round
round-off error
Rubik’s cube
Rucker, Rudy (1946-)
ruled surface
ruler-and-compass construction. See Mascheroni construction
Russell, Bertrand Arthur William (1872-1970)
Russell’s paradox
Russian multiplication

Saccheri, Giovanni Girolamo (1667-1733)
saddle
St. Ives problem
St. Petersburg paradox
salinon
Sallows, Lee C. F.
scalar
scalene triangle
schizophrenic number
Schläfli, Ludwig (1814-1895)
Schläfli symbol
Schoolgirls problem
Schröder’s reversible staircase
Schubert, Hermann (1848-1911)
Schuh, Frederick (1875-1966)
scintillating grid illusion. See Hermann grid illusion
score
search space
secant
secretary problem. See sultan's dowry
self-enumerating sentence
self-intersecting
self-organization
self-organized criticality
self-referential sentence
self-similarity
semigroup
semi-magic square
semi-regular polyhedron
Senet
sensitivity
sequence
series
serpentine
set
set of all sets. See Russell's paradox
set theory
seven
seventeen
sexagesimal
Shannon, Claude Elwood (1916-2001)
shell curve. See Dürer's shell curve
shuffle
shunting puzzles
Siegel’s paradox
Sierpinski, Waclaw Franciszek (1882-1969)
Sierpinski carpet
Sierpinski gasket
Sierpinski number
sieve of Eratosthenes
significant digits
similar
simple group
simplex
simply-connected
simulation
Singmaster, David
six
six circles theorem
sixty. See sexagesimal
skeletal division
Skewes' number
slide rule
sliding-piece puzzles
Slocum, Jerry
slope
Slothouber-Graatsma puzzle
Smith number
smooth
Smullyan, Raymond (1919-)
snow
snowball prime
snowflake curve. See Kock snowflake
Soddy circle
Soddy's formula
solidus
solitaire. See peg solitaire
soliton
soma cube
Sophie Germain prime
space
space-filling curve
spacetime
special function
special relativity. See relativity theory
spectrum
Sperner’s lemma
sphere
sphere packing. See packing, Kepler's conjecture, and cannonball problem
spherical geometry. See elliptical geometry
sphericon
spheroid
sphinx riddle
spider-and-fly problem
spinor
spiral
spirograph curve. See roulette
Sprage-Grundy theory
Sprouts
square
square free
square pyramid problem. See cannonball problem
square root of 2
squarefull number. See powerful number
squaring the circle
squaring the square
standard deviation
Stanhope, Earl
star of Lakshmi
state space. See phase space
statistical mechanics
statistics
Steiner, Jakob (1796-1863)
Steiner-Lehmus theorem
Steinhaus, Hugo (1887-1972)
stellation
Stewart, Ian (1945-)
Stewart toroid
stochastic
stochastic process
stomachion. See loculus of Archimedes
strange attractor. See chaotic attractor
strange loop
strategy
string
string puzzles
string theory
strobogrammatic prime
strophoid
subgroup
sublime number
substitution cipher
sultan’s dowry
supercomputer
superegg
superellipse
supersymmetry
supplementary angles
surface
surface of revolution
surreal number
swastika
syllogism
Sylvester, James Joseph (1814-1897)
Sylvester's problem of collinear points
symmedian
symmetric group
symmetry
symmetry group
system
Szilassi polyhedron

tachyon
TacTix
tafl game
Tait, Peter Guthrie (1831-1901)
Tait's conjecture
tally
tangent
tangle
tangled graph
tangloids
tangrams
Tarry, Gaston (1843-1913)
Tarski, Alfred (1902-1983)
Tartaglia, Niccoló Fontana (1499-1557)
tautochrone problem
tautology
ten
tensor
tessellation. See tiling
tesseract
tetrahedral number
tetrahedron
Tetris
tetromino. See polyomino
theorem
theory of everything
Thiery figure
thirteen
thirty colored cubes puzzle
thirty-six officers problem
Thompson, D’Arcy Wentworth (1860-1948)
thousand
three
three hat problem. See hat problem
three men's morris
three-body problem
Thue-Morse constant
tic-tac-toe
tie knots
tiling
time
time complexity
time dilation. See relativity theory
time travel
time-reversible
Tinner's rabbits
Tippee top
Titchener illusion
Toeplitz matrix
topological group
topological dimension
topological space
topology
torus
tour
tower of Brahma
tower of Hanoi
T-puzzle
trace
tractrix
transcendental number
transfinite number
transformation
translation
transpose
transposition cipher
transversal
trapezium
trapezoid
traveling salesman problem
tree
trefoil curve
triangle
Triangular Lodge
triangular number
triangulation
tribar illusion. See Penrose triangle
tricuspoid. See deltoid
trident of Newton trifolium. See rose curve
trigonometric function
trigonometry
trillion
trimorphic number. See automorphic number
trinomial
triomino
trisecting an angle
trisector theorem. See Morley's miracle
trisectrix
triskaidekaphobia. See thirteen
trochoid
truel
truncate
truncatable prime
Tschirnhaus's cubic
Turing, Alan Mathison (1912-1954)
Turing machine
Turing test
twelve
twenty
twin primes
twins paradox. See relativity theory
twisted cubic
two
two-dimensional worlds

Ulam, Stanislaw Marcin (1909-1984)
Ulam spiral
Ulam's conjecture. See Collatz problem
uncountable set
undulating number
unduloid
unexpected hanging
uniform polyhedron
unilluminable room problem
unimodal sequence
unimodular matrix
union
unique number
unit circle
unit cube
unit fraction
universal approximation
universal computer
universal library
universe of discourse
untouchable number
up-arrow notation. See Knuth's up-arrow notation
upside-down picture
Ussher, James (1581-1656)
utility function

vampire number
van der Pol, Balthazar (1889-1959)
vanishment puzzles
vector
vector space
Venn diagram
vertex
vertex figure
vertical-horizontal illusion
vesica piscis
Vickrey auction
vigesimal
vinculum
Viviani’s curve
Viviani's theorem
volume
volvox fractal
von Neumann, John (1903-1957)
von Neumann machine
Voronoi diagram
vulgar fraction. See common fraction

walking in the rain problem
Wallis, John (1616-1703)
Wallis formula. See pi
wallpaper group
wari. See mancala
Waring's conjecture
weak inequality
Weierstrass, Karl Wilhelm Theodor (1815-1897)
Weierstrass' nondifferentiable function
weighing puzzles. See measuring and weighing puzzles
weird number. See abundant number
Wessel, Caspar (1745-1818)
Weyl, Hermann Klaus Hugo (1885-1955)
wff
What color was the bear?
wheat and chessboard problem
wheel paradoxes
Whitney's umbrella
Wiener, Norbert (1894-1964)
Wiles, Andrew (1953-)
Wilson's theorem
winding number
wine
witch of Agnesi curve. See Agnesia, Maria Gaetana
word puzzles
word trivia
worldline
Wundt illusion
Wythoff’s game

x
x-axis
X-pentomino

yard
y-axis
ying-yang symbol. See great Monad

Zeller's formula
Zeno’s paradoxes
zero
zero divisors
zero of a function. See root
zero-sum game
zeta function
Zipf's law
Zöllner illusion
zombie
zone
zonohedron


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