Table Of ContentREVISED EDITION
DK LONDON
Project editor Vicky Richards
Art editor Chrissy Barnard Editor Rona Skene
Managing editor Francesca Baines Managing art editor Philip Letsu
Production editor Kavita Varma Production controller Samantha Cross
Jacket design development manager Sophia MTT
Publisher Andrew Macintyre Associate publishing director Liz Wheeler
Art director Karen Self Publishing director Jonathan Metcalf
DK DELHI
Senior art editor Mahua Sharma Editor Upamanyu Das
MATHs
Managing editor Kingshuk Ghoshal Managing art editor Sudakshina Basu
DTP designers Bimlesh Tiwary, Rakesh Kumar
Jacket designer Tanya Mehrotra
FIRST EDITION
Senior editor Francesca Baines Project editors Clare Hibbert, James Mitchem
Designer Hoa Luc Senior art editors Jim Green, Stefan Podhorodecki
Additional designers Dave Ball, Jeongeun Yule Park
Managing editor Linda Esposito Managing art editor Diane Peyton Jones
Category publisher Laura Buller
Production editor Victoria Khroundina Senior production controller Louise Minihane
Jacket editor Manisha Majithia Jacket designer Laura Brim
Picture researcher Nic Dean
DK picture librarian Romaine Werblow
Publishing director Jonathan Metcalf
Associate publishing director Liz Wheeler
Art director Phil Ormerod
This edition published in 2022
First published in Great Britain in 2012 by
Dorling Kindersley Limited,
DK, One Embassy Gardens, 8 Viaduct Gardens,
London, SW11 7BW
The authorised representative in the EEA is
Dorling Kindersley Verlag GmbH. Arnulfstr. 124,
80636 Munich, Germany
TThhiiss bbooookk iiss ffuullll ooff ppuuzzzzlleess aanndd
aaccttiivviittiieess ttoo bboooosstt yyoouurr bbrraaiinn Copyright © 2012, 2022 Dorling Kindersley Limited
A Penguin Random House Company
ppoowweerr.. TThhee aaccttiivviittiieess aarree aa lloott ooff
10 9 8 7 6 5 4 3 2 1
ffuunn,, bbuutt yyoouu sshhoouulldd aallwwaayyss cchheecckk 001– 324978–Jan/2022
wwiitthh aann aadduulltt bbeeffoorree yyoouu ddoo aannyy
All rights reserved. No part of this publication may
ooff tthheemm ssoo tthhaatt tthheeyy kknnooww wwhhaatt
be reproduced, stored in or introduced into a retrieval
yyoouu aarree ddooiinngg aanndd aarree ssuurree system, or transmitted, in any form, or by any means (electronic,
tthhaatt yyoouu aarree ssaaffee.. mechanical, photocopying, recording, or otherwise), without the
prior written permission of the copyright owner.
A CIP catalogue record for this book is available from the British Library.
ISBN: 978-0-2415-1524-2
Printed and bound in China
www.dk.com
This book was made with Forest
Stewardship Council ™ certified
paper – one small step in DK’s
commitment to a sustainable
future. For more information go to
www.dk.com/our-green-pledge
000022__000033__118822443388__IImmpprriinntt__ttiittllee..iinndddd 22 0022//0099//2211 66::3399 PPMM
REVISED EDITION
DK LONDON
Project editor Vicky Richards
Art editor Chrissy Barnard Editor Rona Skene
Managing editor Francesca Baines Managing art editor Philip Letsu
Production editor Kavita Varma Production controller Samantha Cross
Jacket design development manager Sophia MTT HOW TO BE A
Publisher Andrew Macintyre Associate publishing director Liz Wheeler
Art director Karen Self Publishing director Jonathan Metcalf
DK DELHI
Senior art editor Mahua Sharma Editor Upamanyu Das
MMAATTHHss
Managing editor Kingshuk Ghoshal Managing art editor Sudakshina Basu
DTP designers Bimlesh Tiwary, Rakesh Kumar
Jacket designer Tanya Mehrotra
FIRST EDITION
Senior editor Francesca Baines Project editors Clare Hibbert, James Mitchem
Designer Hoa Luc Senior art editors Jim Green, Stefan Podhorodecki
Additional designers Dave Ball, Jeongeun Yule Park
Managing editor Linda Esposito Managing art editor Diane Peyton Jones
Category publisher Laura Buller
Production editor Victoria Khroundina Senior production controller Louise Minihane
Jacket editor Manisha Majithia Jacket designer Laura Brim
Picture researcher Nic Dean
GENIUS
DK picture librarian Romaine Werblow
Publishing director Jonathan Metcalf
Associate publishing director Liz Wheeler
Art director Phil Ormerod
This edition published in 2022
First published in Great Britain in 2012 by
Dorling Kindersley Limited,
DK, One Embassy Gardens, 8 Viaduct Gardens,
London, SW11 7BW
The authorised representative in the EEA is
Dorling Kindersley Verlag GmbH. Arnulfstr. 124,
80636 Munich, Germany
TThhiiss bbooookk iiss ffuullll ooff ppuuzzzzlleess aanndd
aaccttiivviittiieess ttoo bboooosstt yyoouurr bbrraaiinn Copyright © 2012, 2022 Dorling Kindersley Limited
A Penguin Random House Company
ppoowweerr.. TThhee aaccttiivviittiieess aarree aa lloott ooff
10 9 8 7 6 5 4 3 2 1
ffuunn,, bbuutt yyoouu sshhoouulldd aallwwaayyss cchheecckk 001– 324978–Jan/2022
wwiitthh aann aadduulltt bbeeffoorree yyoouu ddoo aannyy
All rights reserved. No part of this publication may
ooff tthheemm ssoo tthhaatt tthheeyy kknnooww wwhhaatt
be reproduced, stored in or introduced into a retrieval
yyoouu aarree ddooiinngg aanndd aarree ssuurree system, or transmitted, in any form, or by any means (electronic,
tthhaatt yyoouu aarree ssaaffee.. mechanical, photocopying, recording, or otherwise), without the
prior written permission of the copyright owner.
A CIP catalogue record for this book is available from the British Library.
ISBN: 978-0-2415-1524-2
Printed and bound in China
www.dk.com Written by Dr Mike Goldsmith
This book was made with Forest Consultant Branka Surla
Stewardship Council ™ certified
paper – one small step in DK’s
commitment to a sustainable
future. For more information go to Illustrated by Seb Burnett
www.dk.com/our-green-pledge
000022__000033__118822443388__IImmpprriinntt__ttiittllee..iinndddd 22 0022//0099//2211 66::3399 PPMM 000022__000033__118822443388__IImmpprriinntt__ttiittllee..iinndddd 33 0022//0099//2211 66::3399 PPMM
CCOONNTTEENNTTSS
6 A world of maths
MMAATTHHSS BBRRAAIINN IINNVVEENNTTIINNGG NNUUMMBBEERRSS MMAAGGIICC NNUUMMBBEERRSS
26 Learning to count
10 Meet your brain 50 Seeing sequences
28 Number systems
12 Maths skills 52 Pascal’s triangle
30 Big zero
14 Learning maths 54 Magic squares
32 Pythagoras
16 Brain vs. machine 56 Missing numbers
34 Thinking outside the box
18 Problems with numbers 58 Karl Gauss
36 Number patterns
20 Early mathematicians 60 Infinity
38 Calculation tips
22 Seeing the solution 62 Numbers with meaning
40 Archimedes
64 Number tricks
42 Maths and measures
66 Puzzling primes
44 How big? How far?
46 The size of the problem
4
000044__000055__118822443388__CCOONNTTEENNTTSS..iinndddd 44 2277//0088//2211 66::0099 PPMM
CCOONNTTEENNTTSS
6 A world of maths
MMAATTHHSS BBRRAAIINN IINNVVEENNTTIINNGG NNUUMMBBEERRSS MMAAGGIICC NNUUMMBBEERRSS SSHHAAPPEESS AANNDD SSPPAACCEE AA WWOORRLLDD OOFF MMAATTHHSS
10 Meet your brain 26 Learning to count 50 Seeing sequences 70 Triangles 94 Interesting times 120 Glossary
12 Maths skills 28 Number systems 52 Pascal’s triangle 72 Shaping up 96 Mapping 122 Answers
14 Learning maths 30 Big zero 54 Magic squares 74 Shape shifting 98 Grace Hopper 126 Index
16 Brain vs. machine 32 Pythagoras 56 Missing numbers 76 Round and round 100 Probability 128 Acknowledgments
18 Problems with numbers 34 Thinking outside the box 58 Karl Gauss 78 The third dimension 102 Displaying data
20 Early mathematicians 36 Number patterns 60 Infinity 80 3-D shape puzzles 104 Logic puzzles and paradoxes
22 Seeing the solution 38 Calculation tips 62 Numbers with meaning 82 3-D fun 106 Breaking codes
40 Archimedes 64 Number tricks 84 Leonhard Euler 108 Codes and ciphers
42 Maths and measures 66 Puzzling primes 86 Amazing mazes 110 Alan Turing
44 How big? How far? 88 Optical illusions 112 Algebra
46 The size of the problem 90 Impossible shapes 114 Brainteasers
116 Secrets of the Universe TThhee bbooookk iiss ffuullll ooff
pprroobblleemmss aanndd ppuuzzzzlleess ffoorr
118 Katherine Johnson
yyoouu ttoo ssoollvvee.. TToo cchheecckk
tthhee aannsswweerrss ttuurrnn ttoo
ppaaggeess 112222––112255..
4 5
000044__000055__118822443388__CCOONNTTEENNTTSS..iinndddd 44 2277//0088//2211 66::0099 PPMM 000044__000055__118822443388__CCOONNTTEENNTTSS..iinndddd 55 2277//0088//2211 66::0099 PPMM
TThheerree’’ss aa hheeiigghhtt rreessttrriiccttiioonn
oonn tthhiiss rriiddee,, ssoonnnnyy.. TTrryy
II´´llll bbee iinn tthhiiss qquueeuuee ffoorr
ccoommiinngg bbaacckk nneexxtt yyeeaarr..
1100 mmiinnuutteess,, ssoo II sshhoouulldd ssttiillll
bbee iinn ttiimmee ttoo ccaattcchh tthhee nneexxtt
II wwoonnddeerr wwhhaatt wwoouulldd
bbuuss hhoommee..
hhaappppeenn iiff tthhee rriiddee ssppuunn
eevveenn ffaasstteerr??
PPeeooppllee aarree hhuunnggrryy
ttoonniigghhtt.. AAtt tthhiiss rraattee,, II’’llll
rruunn oouutt ooff hhoott ddooggss iinn
hhaallff aann hhoouurr..
SS cc Miiateeshcisnn tieccosn tttieeehesasetstrsts oe me t t–nbh etihiuextdie aloalenh rcd if vte.pleoeb rupsrn S it s f oadttangoimh rde eepsg r,tr mma oh acmeutkiaoneccr dia hleir isnu d esese,s, !
n
a
CC
j Yo aa
MMAA WWAAOOTTRRLLHHDD OOSSFF caacllloc bsuetalsa wc,t iaaooknurnedks ae ttt nodiam d baou oi eunc unstag tteurs ie.es mvQdlline uumccrgasy anuutth tt hlliitnsieaag ts,ott ,f rmiiomaook enn
m
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It is impossible to imagine our world without
maths. We use it, often without realizing, for PPaanneell ppuuzzzzllee
These shapes form a square panel, used
a whole range of activities – when we tell the
AA in one of the fairground stalls. However,
time, go shopping, catch a ball, or play a game. an extra shape has somehow got mixed
up with them. Can you work out which
This book is all about how to get your maths
piece does not belong?
brain buzzing, with lots of things to do, many of
BB
the big ideas explained, and stories about how
EE
great maths brains have changed our world. FF
CC
DD
6
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GGuullpp!! TThhee sslliiddee llooookkss
TThheerree’’ss aa hheeiigghhtt rreessttrriiccttiioonn
eevveenn sstteeeeppeerr ffrroomm tthhee ttoopp..
oonn tthhiiss rriiddee,, ssoonnnnyy.. TTrryy
II´´llll bbee iinn tthhiiss qquueeuuee ffoorr II wwoonnddeerr wwhhaatt ssppeeeedd II’’llll
ccoommiinngg bbaacckk nneexxtt yyeeaarr..
1100 mmiinnuutteess,, ssoo II sshhoouulldd ssttiillll bbee ggooiinngg wwhheenn II ggeett ttoo
bbee iinn ttiimmee ttoo ccaattcchh tthhee nneexxtt tthhee bboottttoomm??
II wwoonnddeerr wwhhaatt wwoouulldd LLooookk aatt mmee!! II’’mm
bbuuss hhoommee..
hhaappppeenn iiff tthhee rriiddee ssppuunn flflooaattiinngg iinn tthhee aaiirr aanndd
eevveenn ffaasstteerr?? II’’vvee ggoott ttwwoo ttoonngguueess!!
PPeeooppllee aarree hhuunnggrryy
ttoonniigghhtt.. AAtt tthhiiss rraattee,, II’’llll OOnnee iinn ffoouurr ppeeooppllee aarree II tthhiinnkk II’’vvee ggoott tthhee
rruunn oouutt ooff hhoott ddooggss iinn hhiittttiinngg aa ccooccoonnuutt.. GGrrrr!! II’’mm aannggllee jjuusstt rriigghhtt...... oonnee
hhaallff aann hhoouurr.. mmaakkiinngg aa lloossss.. mmoorree ggoo aanndd II’’llll wwiinn
aa pprriizzee..
MMAASS cc Mii ateeshcisnn tieccosn tttWWiAAeeehesasetstrsts oe me ta t–nbh netihiuextdie aloaOOlenh rcd if vte.pleoeb rupsrn S it s f oadttTTangoimh RRrde eepsg r,tr mma oh acmeutkiaoneccr dia LLhleir isnu d esese,s, ! HHDD OOSSFF ccaaaacclllllloocc bbssuueettaallssaa wwcc,,tt iiaaaaoooojjkknnuurrnneeddkkss aaee tttttt nnooYYddiiaammoo dd bbaaoouu ooii eeuunncc uuCCCCnnssttaagg tttteeuurrssaaaa iiee..eemmss mmvvQQddlllliiaannee uuuummttccccrrggaaiissyyoo aannuuuuttttnnhh tttt hh..lllliiiittnnssiieeaaaagg ttss,,ootttt ,,ff rrmmiiiioommaaooookk eennnn nuOreesftpewesed nuwa t cttioahnh o y vheasroesM s hloelv pahof e p nwoPPtu ahlywo saat isant o hanettrkknarueiinpndnttmase ggsieeb ns . cfoe sorrabfrpr nesmnn i phr b eassaae ttv htees.r ns, SS hhU aan sdppperaseescetussetna s.ahsnhi ienedYsn i ldoco anplfu dr sgut eendhsuisaei eshn egoatgfdw n po t tomeraroims lna ctkdyaak thnkynah seoir d g tonwa ogu amnc–br de oes.ua tt e
It is impossible to imagine our world without
maths. We use it, often without realizing, for PPaanneell ppuuzzzzllee PPrrooffiitt mmaarrggiinn AA ggaammee ooff cchhaannccee
These shapes form a square panel, used It costs £144 a day to run the dodgems, Everyone loves to try to knock down
a whole range of activities – when we tell the
AA in one of the fairground stalls. However, accounting for wages, electricity, a coconut – but what are your chances
time, go shopping, catch a ball, or play a game. an extra shape has somehow got mixed transport, and so on. There are of success? The stall owner needs to
up with them. Can you work out which 12 dodgem cars, and, on average, know so he can make sure he’s got
This book is all about how to get your maths
piece does not belong? 60 per cent of them are occupied each enough coconuts, and to work out how
brain buzzing, with lots of things to do, many of BB session. The ride is open for eight much to charge. He’s discovered that, on
hours a day, with four sessions an average, he has 90 customers a day, each
the big ideas explained, and stories about how
EE hour, and the fare is £2 per session. throwing three balls, and the total
great maths brains have changed our world. FF How much profit is the number of coconuts won is 30. So what is
CC
owner making? the likelihood of you winning a coconut?
DD
6 7
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MMaatthhss
bbrraaiinn
000088__000099__118822443388__MMaatthh__BBrraaiinn..iinndddd 88 2277//0088//2211 66::0099 PPMM
MMaatthhss
bbbbrrrraaaaiiiinnnn
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Meninges Cerebrum Where thinking occurs LLooookkiinngg iinnssiiddee
Protective layers and memories are stored
that cushion the This cross-section of the skull
brain against shock Corpus callosum Links the reveals the thinking part of the
two sides of the brain
brain, or cerebrum. Beneath its
Skull Forms a
tough casing Hypothalamus Controls outer layers is the “white matter”
around the brain sleep, hunger, and body
temperature which transfers signals between
different parts of the brain.
Cerebellum Helps Pituitary gland Controls
the release of hormones
to control balance
and movement
AA BBRRAAIINN OOFF TTWWOO HHAALLVVEESS
The cerebrum has two hemispheres. Each deals
mainly with the opposite side of the body – data
Thalamus Receives from the right eye, for example, is handled in
sensory nerve signals
and sends them on the brain’s left side. For some functions,
Medulla Controls to the cerebrum including maths, both halves work
breathing, heartbeat,
together. For others, one half is
blood pressure,
and vomiting more active than the other.
LLEEFFTT--BBRRAAIINN SSKKIILLLLSS
LLaanngguuaaggee
The left side of your cerebrum is
The left side handles the meanings
responsible for the logical, rational
of words, but it is the right half that
aspects of your thinking, as well as for
puts them together into sentences
grammar and vocabulary. It’s here that
and stories.
you work out the answers to calculations.
SScciieennttiiffiicc RRaattiioonnaall tthhoouugghhtt
tthhiinnkkiinngg Thinking and reacting in a
Logical thinking is the job rational way appears to be
of the brain’s left side, but mainly a left-brain activity.
most science also involves It allows you to analyze a
the creative right side. problem and find an answer.
MMaatthheemmaattiiccaall WWrriittiinngg
sskkiillllss sskkiillllss
The left brain oversees Like spoken language, writing
numbers and calculations, involves both hemispheres. The
while the right processes right organizes ideas, while the left
shapes and patterns. finds the words to express them.
Left visual cortex Processes
signals from the right eye
MMEEEETT YYOOUURR
Your brain is the most complex organ
in your body – a spongy, pink mass made
up of billions of microscopic nerve cells. Its
BBRRAAIINNlargest part is the cauliflower-like cerebrum,
made up of two hemispheres, or halves,
linked by a network of nerves. The cerebrum
is the part of the brain where mathematics
is understood and calculations are made.
10
001100__001111__118822443388__MMeeeett__yyoouurr__bbrraaiinn..iinndddd 1100 2277//0088//2211 66::0099 PPMM
