2:00 Judith de Klerk Judith de Klerk Sydney, Melbourne, Brisbane, Perth and associated companies around the world Judith de Klerk passed away during the production of this fourth edition of her dictionary She was committed to updating the dictionary and ensuring it was perfect although she was quite ill She was assisted in all her endeavours by her husband, Louis de Klerk, who continued Judith’s work Pearson Education Australia A division of Pearson Australia Group Pty Ltd Level 9, Queens Road Melbourne 3004 Australia www.pearsoned.com.au/schools Offices in Sydney, Brisbane and Perth, and associated companies throughout the world Copyright © Pearson Education Australia (a division of Pearson Australia Group Pty Ltd) 2007 First published 1983 Reprinted 1984, 1985, 1986, 1988, 1989 (Twice) Second edition 1990 Third edition 1999 Fourth edition 2007 All rights reserved Except under the conditions described in the Copyright Act 1968 of Australia and subsequent amendments, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner Designed by Ben Galpin Typeset by Miriam Steenhauer & Eugenio Fazio Cover design by Ben Galpin Cover illustrations by Ben Galpin & Boris Silvestri Edited by Sally Green Prepress work by The Type Factory Produced by Pearson Education Australia Printed in Malaysia National Library of Australia Cataloguing-in-Publication data De Klerk, Judith Illustrated maths dictionary for Australian schools 4th ed ISBN 9780 7339 8661 Every effort has been made to trace and acknowledge copyright However, should any infringement have occurred, the publishers tender their apologies and invite copyright owners to contact them Contents A–Z Useful information 146 Units of measurement 146 A list of symbols 147 Roman numerals 148 Parts of a circle 148 Metric relationships 149 Formulae 150 More formulae 151 Large numbers 152 Letters used in mathematics 152 Decimal system prefixes 153 Numerical prefixes 153 Other prefixes 154 The multiplication square 154 Greek alphabet 155 Conversion tables: metric and imperial 156 Computing terms 158 v Introduction The language of mathematics often confuses children and it is sometimes difficult for teachers to explain the meaning of mathematical terms simply but accurately The fourth edition of this Illustrated Maths Dictionary offers an up-to-date dictionary of maths terms with the addition of a section explaining commonly used computer terms that have mathematical connotations The definitions are written in simple language that children can understand, yet are clear, precise and concise The terms are supported by hundreds of examples and illustrations This is essentially a dictionary for students, but I hope that teachers, parents and tertiary students will also find it helpful Judith de Klerk abscissa abacus A Usually a board with spikes or a frame with wires on which discs, beads or counters are placed Used for counting and calculating 1000 100 10 Examples a (i) In formulas, the letter A stands for area Example Area of a triangle abbreviation A shortened form of writing words and phrases When writing shortened forms of words, we usually put full stops after the letters b×h A= h Example b Victoria: Vic (ii) A, and other letters, are used to name points, lines, angles and corners (vertices) of polygons and solids Note: cm (centimetre) is a symbol We not write full stops after symbols Examples Examples m A A point A mm kg mL m2 cm3 See symbol B A line AB abscissa O B angle D AOB C G H A cm B E F polygon ABCD D A solid C B See angle name, area, formula, line, point, vertex The horizontal coordinate, or x-coordinate, of a point in a two-dimensional system of Cartesian coordinates is sometimes called the abscissa See axis, coordinates, ordinate accurate A accurate AD Exact, correct, right, without error Note: Measurements are not exact We usually measure to the nearest unit, therefore our answers are only approximate For example, if we say something is 30 cm long, we mean nearer to 30 cm than to either 31 cm or 29 cm See approximately (Anno Domini) Meaning: In the year of our Lord After the birth of Christ Example The eruption of Mount Vesuvius in AD 79 destroyed Pompeii See BC, CE add acute Join two or more numbers or quantities together Sharp Sharply pointed (i) Acute angle Example A sharply pointed angle with size less than a right angle (< 90°) + Examples 90º A right angle 22º O B = + = The apples were added together See addition, quantity acute angle 51º addend 45º Any number which is to be added Example 81º + = → In + = 8, and are addends, is the sum A triangle with all three inside angles being acute C acute triangle A → addend addend sum See angle, right angle (ii) Acute triangle Example → acute angle B See equilateral triangle, obtuse triangle, rightangled triangle, scalene triangle algebra addition adjacent (symbol: +) Positioned next to each other, having a common point or side (i) Joining the values of two or more numbers together A Example + = 10 (ii) On the number line my room –2 –1 3 your bathroom 2+3 =5 My room is adjacent to your bathroom (i) (iii) Addition of fractions Adjacent sides Example C + = +12 = 17 20 20 (iv) Addition of integers A +5 + –7 = –2 (v) Addition of algebraic terms 2a + 3b + 5a = 7a + 3b See algebraic expression, fraction, integers, number line B In this triangle, side AB is adjacent to side AC because they have a common vertex A (ii) Adjacent angles Two angles positioned in the same plane that have a common side and a common vertex Example A addition property of zero B When zero is added to any number, the sum is the same as the number Examples O 4+0=4 + 12 = 12 See sum, zero →to ЄBOC because they have ЄAOB is adjacent a common ray OB See plane, vertex additive inverse When we add a number and its inverse, the answer is zero Example + –8 = → → number inverse See inverse, zero C algebra Part of mathematics that studies number systems and number properties See algebraic expression, coefficient, numeral, pronumeral, symbol, variable algebraic expression A algebraic expression align In algebra we use numerals, symbols and letters called variables or pronumerals, and combinations of both They stand for the unknown values Lay, place in a straight line Example C Examples + =2 5–x a+b+c x – 2xy + y See coefficient, numeral, pronumeral, symbol, value, variable A D B E F Points A, B, D and E are aligned; points C and F are not See line alternate angles See parallel lines algorithm (algorism) altitude A rule for solving a problem in a certain number of steps Every step is clearly described Height How high something is above the surface of the Earth, sea level or horizon Altitude is the length of perpendicular height from base to vertex Example Use blocks to find how many × is Step Example Lay down one lot of four blocks vertex Step Put down the second and third lots of four altitude horizon base Step Exchange 10 units for one ten (long) The altitude of this aeroplane is 9000 metres See height, perpendicular, surface a.m (ante meridiem) Step Write down your answer × = 12 See multibase arithmetic blocks (MAB) The time from immediately after midnight until immediately before midday The term a.m is used only with 12-hour time 147 Useful Information A list of symbols Symbol Meaning Example ϩ addition sign, add, plus 2+1=3 Ϫ subtraction sign, subtract, take away, minus 7–6=1 ϫ multiplication sign, multiply by, times 3×3=9 division sign, divide by ÷ = 4.5 is equal to, equals 2+2=1+3 is not equal to is approximately equal to 302 ഠ 300 Յ is less than or equal to x Յ 12 Ն is greater than or equal to 5Նy Ͼ is greater than Ͼ 6.9 Ͻ is less than 2Ͻ4 is not less than is not greater than 3.3 c cent(s) 50c $ dollar(s) $1.20 decimal point (on the line) 5.24 % per cent, out of 100 50% ° degree Celsius, degree (angle measure) °C ' minutes (angle measure) 5° 35' feet (imperial system) 1' ഠ 30 cm " seconds (angle measure) 12°05'24" " inch inches (imperial system) 12" = 1' Єٙ angle Є AOB Ϭ ͤෆ ϭ Ӏഠϴ ' foot 5 35 °C triangle parallel lines, is parallel to 3.4 90° BOC ABC AB CD line segments of the same length right angle, 90° is perpendicular to, at 90° h b square root π ϵХ b = ±2 cube root pi, π ഠ 3.14 C = 2πr is congruent to h 27 = ABC ϵ DEF 148 Useful Information Roman numerals Thousands Hundreds Tens Units M C X I MM CC XX II MMM CCC XXX III CD XL IV D L V DC LX VI DCC LXX VII DCCC LXXX VIII CM XC IX Example MM = MMV II VII cir c Parts of a circle nce fere um quadrant segment chord sector diameter radius centre centre arc e rcl semici concentric circles area of a circle annulus 149 Useful Information Metric relationships Length Area Volume Capacity cm cm cm cm2 cm cm cm 10 mm cm2 100 mm2 cm3 1000 mm3 mL One cm cube (cubic centimetre) has a capacity of millilitre 10 cm 1000 1L 900 10 cm 10 cm 800 700 0.75 L 600 10 cm2 500 0.5 L 400 300 10 cm 200 ml 0.25 L 100 10 cm 10 cm 100 mm 100 cm2 10 000 mm2 1000 cm3 000 000 mm3 1L One 10 cm cube (1000 cm3) has a capacity of litre 1m 1m m2 1m 1m 1m 100 cm m2 10 000 cm2 m3 000 000 cm3 1m kL One cubic metre has a capacity of kilolitre These drums each hold kilolitre 150 Useful Information Formulae Plane shapes Diagram Area Perimeter A = πr C = 2πr = πd A = a2 P = 4a A = ab P = (a + b) C circle r d a square a a rectangle b b kite trapezium a h b a parallelogram h b A= ab A= a+b ×h P=a+b+c+d A = ah P = (a + b) A = ah P = 4a A = bh P=a+b+c a h rhombus a a h triangle b c 151 Useful Information More formulae Solids Diagram a cube Volume Surface area V = a3 S = 6a2 V = l wh S = 2(l w + hl + hw) a a h cuboid w l h pyramid V= base × h r h cylinder h cone V = πr 2h V= πr 2h V= πr 3 S = area of base + × Area of S = × πr + 2πrh = 2πr (r + h) r r sphere Pythagoras’ theorem a c b c2 = a2 + b2 a = c2 + b2 b = c2 − b2 c = c2 + b2 S = 4πr Useful Information 152 Large numbers million 1000 × 1000 106 billion 1000 millions 109 trillion 1000 billions 1012 quadrillion million billions 1015 Letters used in mathematics in sets I N Q R W integers natural numbers rational numbers real numbers whole numbers in geometry a, b, c, d, … A, B, C, D, … A b C d h l O P r s S, SA V w sides of polygons lengths of intervals names of lines points, vertices area of polygons base of polygons circumference of a circle diameter of a circle height length origin, centre of a circle perimeter radius of a circle side surface area volume of solids width 153 Useful Information Decimal system prefixes Prefix pico Symbol p nano n micro μ milli centi deci Value Value in words Example Meaning –12 one trillionth of pF picofarad –9 one thousand millionth of ns nanosecond –6 one millionth of μs microsecond –3 one thousandth of mg milligram –2 one hundredth of cm centimetre –1 one tenth of dB decibel 10 10 10 m 10 c 10 d 10 unit deca da 101 10 times hecto h 102 100 times hL hectolitre k 1000 times kg kilogram million times ML megalitre thousand million times GB gigabyte kilo mega giga 10 M 10 G 10 not commonly used in Australia Numerical prefixes Prefix Meaning Example mono monorail bi bicycle, binary tri tricycle, triangle tetra tetrahedron, tetrapack quad quadrilateral, quads penta, quin pentagon hexa hexagon hepta, septi heptagon octa octagon nona, non nonagon deca 10 decagon, decahedron undeca 11 undecagon dodeca 12 dodecagon, dodecahedron icosa 20 icosahedron hect 100 hectare kilo 1000 kilogram mega 000 000 megalitre, megawatt giga 1000 million gigabyte 154 Useful Information Other prefixes Prefix Meaning Example anti opposite, against anti clockwise circum around circumference co together cointerior, coordinate geo earth geometry hemi half hemisphere macro very big macrocosmos micro very small microbe multi many, much multibase blocks peri around perimeter poly many polygon semi half semicircle sub below, under subset trans across, beyond, over transversal uni one, having one unit The multiplication square × 10 1 10 2 10 12 14 16 18 20 3 12 15 18 21 24 27 30 4 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100 155 Useful Information Greek alphabet The letters of the Greek alphabet are used as symbols for angles, mathematical operations, etc Examples C γ α , β , γ , δ, … ␲ … Σ sum ϱ infinity A Handwritten β α Capital Lower case Pronunciation A α alpha B β beta Γ γ gamma Δ δ delta E ε epsilon Z ζ zeta H η eta Θ θ theta I ι iota K κ kappa Λ λ lambda M μ mu N ν nu Ξ ξ xi O ο omicron Π π pi P ρ rho Σ σ sigma T τ tau Y υ upsilon Φ φ phi X χ chi Ψ ψ psi Ω ω omega B 156 Useful Information Conversion tables: metric and imperial length Metric Imperial mm 0.03937 in cm 10 mm 0.3937 in 1m 100 cm 1.0936 yd km 1000 m 0.6214 mile Imperial Metric in 2.54 cm ft 12 in 0.3048 m yd ft 0.9144 m mile 1760 yd 1.6093 km nautical mile 2025.4 yd 1.853 km area Metric Imperial cm 100 mm 0.155 in2 m2 10 000 cm2 1.1960 yd2 10 000 m2 2.4711 acres km2 100 0.3861 mile2 Imperial Metric 6.4516 cm2 in ft2 144 in2 0.0929 m2 yd2 ft2 0.8361 m2 acre 4840 yd2 4046.9 m2 mile2 640 acres 2.59 km2 157 Useful Information mass Metric Imperial mg 0.0154 grain 1g 1000 mg 0.0353 oz kg 1000 g 2.2046 lb 1t 1000 kg 0.9842 ton Imperial Metric oz 437.5 grain 28.35 g lb 16 oz 0.4536 kg stone 14 lb 6.3503 kg hundredweight (cwt) 112 lb 50.802 kg long ton 20 cwt 1.016 t temperature volume Metric Imperial cm3 0.0610 in3 dm3 (decimetre) 1000 cm3 0.0353 ft3 m3 1000 dm3 1.3080 yd3 1L dm3 1.76 pt (pint) hL (hectolitre) 100 L 21.997 gal Imperial Metric in3 16.387 cm3 1728 in3 C = (Fahrenheit – 32) 40 100 30 0.0283 m3 pt 20 fl oz 0.5683L gal pt 4.5461L 90 80 20 28.413 mL 110 70 60 10 50 40 -10 -18 32 20 10 Fahrenheit fl oz (fluid ounce) To convert from Fahrenheit to Celsius: Celsius ft3 to convert from Celsius to Fahrenheit: F = × Celsius + 32 Useful Information 158 Computing terms bit CPU The smallest representation of computer storage A bit can be either a (off ) or (on) A bit represents the electrical state of a circuit on a motherboard (i.e on or off ) See byte (Central Processing Unit) The central part of the computer which controls all of the processing of data It is situated on the motherboard of a computer system and its speed is measured in hertz See hertz, kilohertz, megahertz, gigahertz Boolean function Mathematical logic used for searching computer databases Common Boolean functions include AND, OR and NOT Example Database Search: first name = ‘John’ AND age = ‘20’ This will only return all people with the first name of John who are aged 20 Database Search: first name = ‘John’ OR age = ‘20’ This will return all people with the first name of John and all people who are aged 20 Database Search: first name = ‘John’ NOT age = ‘20’ This will return all people with the first name of John who are not 20 years old byte A measurement of computer-based storage and also representation of computer data byte = bits Example 10011101 = byte (computer-based storage) 10011101 = 157 (computer data) See bit, kilobyte flowchart A method of describing an algorithm using symbols Symbols used: Terminal – to begin and end the flowchart Process – an action or step Decision – alternate options or pathways Flowline – used to connect symbols together and to describe the path of the algorithm See algorithm gigabyte (Gb) A measurement of computer-based storage gigabyte = 1024 megabytes See bit, byte, kilobyte, megabyte, terabyte gigahertz (GHz) One billion cycles or electrical pulses per second of a computer CPU GHz = 1000 MHz = 000 000 Kz = 1000 000 000 Hz See CPU, hertz, kilohertz, megahertz 159 Useful Information hertz kilohertz (Hz) (KHz) A measurement of clock speed of a computer CPU It is also used to measure sound frequencies for hearing aids and radio transmission hertz = cycle or electrical pulse of a CPU per second See CPU, megahertz, gigahertz One thousand cycles or electrical pulses per second of a computer CPU KHz = 1000 Hz See CPU, hertz, gigahertz megabyte (Mb) hexadecimal Containing 16 parts or digits It is a base 16 number system that is made up of 16 digits The digits represented by this number system are to and then A to F This number system is used primarily by computer systems, particularly by the programming languages that control computer hardware It is also the number system used to represent colours on web pages Example A measurement of computer-based storage megabyte = 1024 kilobytes See bit, byte, kilobyte, gigabyte megahertz (MHz) One million cycles or electrical pulses per second of a computer CPU MHz = 1000 KHz = 000 000 Hz See CPU, hertz, kilohertz Digits represented: 0, 1, 2, 3, 4, 5, 6, 7, 8, A = 10 octal F = 15 Containing parts or digits It is a base number system that is made up of digits The digits represented by this number system are to This number system is used primarily by computer systems, particularly by certain programming languages See binary, decimal, octal Example B = 11 C = 12 D = 13 E = 14 Digits represented: 0, 1, 2, 3, 4, 5, 6, kilobyte (Kb) A measurement of computer-based storage kilobyte = 1024 bytes See bit, byte, megabyte See binary, decimal, hexadecimal Useful Information RAM (Random Access Memory) The primary memory of a computer system When a computer system is turned off, all contents in RAM are lost The capacity of RAM is measured in bytes See byte, kilobyte, megabyte, gigabyte, terabyte resolution A measurement of the quality of a digital image It is calculated by multiplying the number of dots (pixels) horizontally of the image by the number of dots (pixels) vertically of the image Example Resolution of an image with 1024 horizontal pixels by 768 vertical pixels: Resolution = 1024 × 768 = 786 432 pixels 000 000 pixels = megapixel terabyte (Tb) A measurement of computer-based storage terabyte = 1024 gigabytes See bit, byte, kilobyte, megabyte, gigabyte 160 ... mathematical terms simply but accurately The fourth edition of this Illustrated Maths Dictionary offers an up-to-date dictionary of maths terms with the addition of a section explaining commonly used... Malaysia National Library of Australia Cataloguing-in-Publication data De Klerk, Judith Illustrated maths dictionary for Australian schools 4th ed ISBN 9780 7339 8661 Every effort has been made... de Klerk passed away during the production of this fourth edition of her dictionary She was committed to updating the dictionary and ensuring it was perfect although she was quite ill She was