The Oxford Mathematics Study Dictionary

148 Pages·2016·5.17 MB·English

by  Tapson Frank.

MATHEMATICS
3.1415926535 8979323846 2643383279 5028841971 6939937510
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8214808651 3282306647 0938446095 5058223172 5359408128
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7245870066 0631558817 4881520920 9628292540 9171536436
7892590360 0113305305 4882046652 1384146951 9415116094
3305727036 5759591953 0921861173 8193261179 3105118548
0744623799 6274956735 1885752724 8912279381 8301194912
9833673362 4406566430 8602139494 6395224737 1907021798
6094370277 0539217176 2931767523 8467481846 7669405132
0005681271 4526356082 7785771342 7577896091 7363717872
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5187072113 4999999837 2978049951 0597317328 1609631859
5024459455 3469083026 4252230825 3344685035 2619311881
7101000313 7838752886 5875332083 8142061717 7669147303
5982534904 2875546873 1159562863 8823537875 9375195778
1857780532 1712268066 1300192787 6611195909 2164201989
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0353018529 6899577362 2599413891 2497217752 8347913151
5574857242 4541506959 5082953311 6861727855 8890750983
8175463746 4939319z55 0604009277 0167113900 9848824012
8583616035 6370766010 4710181942 9555961989 4676783744
9448255379 7747268471 0404753464 6208046684 2590694912
9331367702 8989152104 7521620569 6602405803 8150193511
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1613611573 5255213347 5741849468 4385233239 0739414333
4547762416 8625189835 6948556209 9219222184 2725502542
5688767179 0494601653 4668049886 2723279178 6085784383
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4962524517 4939965143 1429809190 6592509372 2169646151
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6868386894 2774155991 8559252459 5395943104 9972524680
8459872736 4469584865 3836736222 6260991246 0805124388
4390451244 1365497627 8079771569 1435997700 1296160894
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0168427394 5226746767 8895252138 5225499546 6672782398
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The
STUDY
DICTIONARY
Frank Tapson
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Introduction in
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How to use this book if iv
Wordfinder v
1
The Dictionary 1-128
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Oxford University Press
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Oxford is a trade mark of Oxford University Press
© Frank Tapson 1996
The moral right of the author has been asserted.
First published 1996
Reprint for this edition: 10 9 8 7 6 5 4 3 2 1 0 j
ISBN 0 19 914559 8 Hardback edition l
0 19 914551 2 Paperback edition

\
A CIP catalogue record for this book is available from the British Library.
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, without prior,
permission in writing from Oxford University Press. Within the UK, exception
are allowed in respect of any fair dealing for the purpose of research or private
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Patents Act, 1988, or in the case of reprographic reproduction in accordance with
the terms and licences issued by the Copyright Licensing Agency. Enquiries
concerning reproduction outside these terms and in other countries should be sent
to the Rights Dep"1ment, Oxford University Press, at the address above.
Typeset and illustrated by the author in association with Gecko Ltd, Bicester,
Oxon
Printed in Great Britain by BPC Wheatons Ltd, Exeter
Introduction
This dictionary is written mainly for students in the 11-16 age group, but
it should also be helpful to anyone seeking a basic knowledge of the
vocabulary of mathematics, and there are words from the fascinating
byways of mathematics that are outside the strict limits of a school
curriculum.
This is not a dictionary of etymology, grammar or English usage. So, for
instance, there is no attempt to list every possible noun, adjective or verb,
or to list all singular and plural forms—although there is a two-page spread
devoted to word origins and plurals on pp.124-5. The main purpose is to
provide headwords in the form in which they are most often met in
mathematics.
Any dictionary must use words to explain other words. There is no escape
from this, and all users are assumed to have a grasp of non-mathematical
English language. The real problem, which has been acknowledged since
the time of Euclid, is that of defining the most basic words such as ‘point’,
‘line’, ‘surface’, and so on. These words are defined in this dictionary, but
it has to be accepted that they are ‘intuitive ideas’ or ‘common notions’. No
matter where a start is made, understanding has to break in at some point.
Cross-referencing is always a problem yi a dictionary, which usually looks
at words in isolation. For that reason,this dictiopary is divided into a
number of themes, each contain J on two facing pages. This helps readers
to see how words relate to each other. It is mucl easier to read about the
: i
circle, for instance, than to look at a series of s'ejbarate entries on words
such as ‘circle’, ‘diameter’ and ‘radius’, with diagrams for some and not
for others and an inconsistent set of ‘see alsos’. In this way each two-page
opening gives the reader a good account of a particular mathematical topic.
There is a Wordfinder at the front to help in finding where a particular word
is to be found.
During the writing of this dictionary I have received much help and advice
from the staff of Oxford University Press and the Oxford Mathematics
Development Office in Taunton. This dictionary has benefited from that,
and I must express my gratitude for their assistance.
Frank Tapson
April 1996
iii
How to use this book
1. Look up the word in the Wordfinder at the front of the book. It looks
like this and will give you the page number(s) you need in the
Dictionary. Celsius scale 106
centi- 119
centigrade (angle) 13
Centigrade (temperature) 106
centre of rotation 110
centre of symmetry 102
Chord 22,39,44
circle 22
circumcircle (of a polygon) 72
circumcircle (of a triangle) 112 appears on Mu pages although
circumference 22,88 the meaning is the same -
entries in order of significance
2. Look up the page number(s). All the entries are in two-page spreads
organised by topic. Read the explanations which look like this:
using a word which is explained
elsewhere, often on the same page
rhombus A rhombus is a quadrilateral whose edges are
all the same length; and usually no vertex (=comer)
angle is a right angle. Its diagonals bisect each other
at right angles and both are also lines of symmetry.
words in italics are rot part of Ihe
explanation but give further information
Some words or phrases have the same meaning:
pnTrar = index
Sometimes one word can have two meanings which an. slightly different, «nd it is
shown like this:
to emphasise a par.icuitL word
circle A circle is either a closed curve ,
OR it is the shape
Area of circle = jt x Radius x Radius = nr2
3. Look at the diagrams (if there are any).
Wordfinder
A arc (in topology) 108
abacus 20 arc (of a circle) 22,38
abbreviations and mnemonics 2 arc (of a curve) 30
arccos 114
Abelian group 99,34
abscissa 28 Archimedean solids 74,34
Archimedes’ spiral 30,34
absolute difference 18
arcsin 114
absolute error 4
arctan 114
absolute value (of a vector) 120
are 116
abundant numbers 60
area 89
acceleration so
accuracy 4 area (of an ellipse) 26,39
acre 116 area (of a polygon) 72
acronym 2 area (of a sector) 22,38
acute angle 12 area (of a segment) 39
acute triangle 112 area (of a t,,angle) 38,112
area under a curve 105
addition (of number, ) 18
addition (of matrices) 57 area (units for) 116
Argand diagram 67,34
additive number systems 65
argument 52
adjacent angles 43
aggregate 18 arithmetic (basics) 14
arithmetic (commercial) 16
algebra (basics) 6
arithmetic (the four rules) 18
algebra (equations) 8
arithmetic mean 94
algebra (functions) 10
arithmetic progression 84
algebraic fractions 41
a./thmetic series 85
algorithm 104
alphametics 83 ajray 56
a,,owhead 80
alternate angles 43
associative 98
alternate segments 44
assumption 52
alternating series 85
asterithms 83
altitude (of a triangle) 112
astroid 32
altitude (of a pyramid) 78
asymmetric 103
amicable pair 60
asymptote 30
angle at the centre 44
atto- 119
angle in a segment 44
automoiphic numbeis 60
angle in a semicircle 44
average 94
angles 12
average speed 50
angle of depression 13
axes 28
angle of elevation 13
axiom 52
angle properties of circles 44
axis of rotation 103
angle sum of a polygon 72
annulus 22 axis of symmetry 103
anticlockwise 126 B
antiprism 78
AP 2,84 Babylonian number system 65
apex 78 back bearing 58
bar chart 92,122
approximation 4,122
barrel 117
APR 17, 2
v
Wordfinder
base (in number) 64 centre of symmetry 102
base (of an index) 62 centred-polygon numbers 70
base (of a cone) 24 certain 126
base (of a pyramid) 78 chain 116
base (of a triangle) 112 chance 76
BASIC 44 changing the subject 7
bearing 58 chord 22,39,44
biased 76 circle 22
bilateral symmetry 103 circle (formulas for) 38
billion 63 circle (from ellipse) 26
bimodal 91 circular cone 24
binary 64 circumcircle (of a polygon) 72
binary operation 98 circumcircle (of a triangle) 112
binomial 9 circumference 22,88
bisect 126 circumscribe 126
bit 48 circum-sphere 74
block graph 92 class 90
BODMAS 2 class interval 90
bounds ll class limits 90
box and whisker diagram 96 clockwise 126
boxplot 96 closed 98
brackets 101 closed curve 30
breadth 89 cm 2
bushel 116 Cocker 34
byte 48 codomain 10
c coefficient 6
collinear 42
C 66
column 56
C and C++ 48 column matrix 56
calculating aids 19 combination 63
calculator 49 combined events 77
capacity (or volume) 122 common factors 36
capacity (units for) 116 common fraction 40
cardinal numbers 67 common tangent 44
cardioid 32 commutative 98
Cartesian coordinates 28,34 commutative group 99
casting out 9’s 15 compass angles 58
catenary 30 complement (of a set) 86
Celsius scale 106 complement (of an angle) 12
centi- 119 complementary addition 19
centigrade (angle) 13 complementary angles 12,122
centigrade (temperature) 106 complex numbers 67
centilitres 116 composite number 36
centillion 63 compound events 77
centimetre 116 compound interest 16
central tendency 94 compound measures 51
centre 22 computer 48
centre of enlargement 111 concave polygon 72
centre of rotation 110 concentric circles 22
Wordfinder
conditional equation 7 curved surface of a cone 24
conditional probability 77 curved surface of a cylinder 24
cones, cylinders and spheres 24,39 curves 30
congruent (in number) 99 cusp 32
congruent (in shape) 43.123 cutting numbers 61
conic sections 26 cycles 60
conjecture 54. i23 cyclic quadrilateral 80
conjugate angles 12 cycloids 32
consecutive numbers 14 cylinder 24,39
constant 6
D
constant ..’ 50
constant term 7 data 90
continuous data 90 database 48
contrapositive 54 day 116
convention for letters 6,118 deca- 119
convergent series 85 decagon 70
converse 54 decametre 116
conversion factors 117 deceleration 50
conversion graph 107 deci- 119
conversion scale 107 decimal 64
convex polygon 72 decimal fraction 40
convex polyhedron 74 decimal places 5
coordinate pairs 3 decimal point 40
coordinate systems 28 decimetre 116
corollary 54 decomposition 18
correlation 92 deficient numbers 60
corresponding angles 43 degree 12
cos-1 114 decree of an expression 8
cosecant 114 degree o* a i. ,rm 8
cosine 114 deltahedron 74
cosine curve 115 deltoid 32
cosine rule 115,38 denaiy 64
cotangent 114 denominator 40
counter-example 52 denumerable 87
counting numbers 66 dependent events 77
counting on 18 dependent variable 11
cross-multiplication 104 depreciation 16
cross-section 78 depth 89
cu 2 determinant 57
cube (number) 15 deviation 95
cube (shape) 74 diagonal matrix 57
cube root 15 diagonal (of a shape) 88
cubic (graph) 47 diagonals (of a matrix) 56
cubic (units of volume) 116 diameter 22
cuboid 74 difference 18,126
cumulative frequency 92 difference of two squares 105
cumulative frequency diagram 92 digit 14
curve 126 digit sum 15
curve of pursuit 30 digital invariants 61
vii
Wordfinder
digital root 15 envelope 30
dimension 89 epicycloid 32
Diophantine equations 9,34 eponyms 34
direct common tangent 44 equal addition 18
direct isometry 111 equally likely 76
direct proof 53 equation 7
direct proportion 127 equations of uniform motion 51
directed numbers 66 equator 58
direction 58 equiangular polygon 72
directrix 26 equiangular spiral 30
discount 17 equilateral polygon 72
discrete data 90 equilateral triangle 112
disjoint 87 equivalent 127
disk or disc 123 equivalent fractions 41
dispersion 91 Eratosthenes’ sieve 34
displacement 50 error 4
dissections 82 estimation 4,122
distance-time graph 51 Euclidean geometry 42,34
distribution 91 Euler’s formula 108,34,3
distributive law 99 evaluate 127
divergent series 85 even numbers 14
dividend 19 even vertex 108
division 19 evens 77
division of fractions 3 event 76
divisor 19 exa- 119
dodecagon 72 exclusive 122
dodecahedron 74 expansion 9
domain 10 experimental probability 76
doubling sequence 84 explicit function il ~ \ -
dozen 63 exponent 62
dp or d.p. 2 exponential 47
expression 6
E
exterior vertex angle 72
e 3,101 extrapolation 47
Earth facts 119
F
eccentric circles 22
eccentricity 26 / 90
edge (in topology) 108 f(x) 10,101
edge (of a polyhedron) 74 F(x,y) ii
edge (of a shape) 88 face (in topology) 108
Egyptian number system 65 face (of a shape) 88
element (of an array) 56 face diagonal 88
element (of a set) 86 factorial 62
elimination 7 factors (in algebra) 9
ellipse 26,39 factors, multiples and primes 36
empty set 86 Fahrenheit scale lOo
ends (of a cylinder) 24 fair 76
enlargement 111 fallacy 55
enumerate 87 false 52
viii