9781607341611 - What’s your angle, Pythagoras - a math adventure

A Math Adventure  by Julie Ellis illustrated by Phyllis Hornung

 To Tim for patiently helping me with the math concepts,

 To Tim for patiently helping me with the math concepts, and to Olive for hours of babysitting. — J.E. For Chris — P.H. Text copyright © 2004 by Julie Ellis Illustrations copyright © 2004 by Phyllis Hornung All rights reserved, including the right of reproduction in whole or in part in any form. Published by Charlesbridge, 85 Main Street, Watertown, MA 02472 (617) 926-0329 • www.charlesbridge.com

Library of Congress Cataloging-in-Publication Data Ellis, Julie, 1961What’s your angle, Pythagoras? : a math adventure / by Julie Ellis ; illustrated by Phyllis Hornung. p. cm. Summary: In ancient Greece, young Pythagoras discovers a special number pattern (the Pythagorean theorem) and uses it to solve problems involving right triangles. ISBN 978-1-60734-161-1 1. Pythagorean theorem—Juvenile literature. [1. Pythagorean theorem. 2. Geometry.] Geometry.] I. Hornung, Phyllis, ill. II. Title. QA460.P8 E38 2002 516.22—dc21 2002002380

Long ago in ancient Greece, there lived a curious boy named Pythagoras. Pythagoras just couldn’t help poking his nose into places. Sometimes, his curiosity got  him in trouble, but sometimes it paid off. 3

One day, Pythagoras sat in the shade of an old olive tree. He could see the harbor and the sparkling

One day, Pythagoras sat in the shade of an old olive tree. He could see the harbor and the sparkling  blue sea around the t he island where he lived. Nearby, two workmen were building a temple. They began to argue. “This ladder is too short to reach the roof,” Pepros grumbled. “That’s not possible,” said Saltos. “The wall is 12 feet tall, so I made the ladder 12 feet long.” Pepros roared, “The ladder only reaches the roof when it is flat against the wall, and then no one can climb it! This is as bad as the columns on the porch!” Pythagoras poked his head out from  behind the tree. “What’s wrong with the columns?” he asked.

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Pepros frowned. “It’s that pesky  Pythagoras again. “Stop bothering us! At this rate, we’ll never finish the temple!” 5

As th wkm argued, P}go crp  aound  o  o id of h bdng. Fo col    b   So coltns d o  lef. Oh  d o  gh "Th colun1s 'v nvr hod up  oo a i hs 'I \Vi h h r Pag  omn 1 cod do o , hnkng o h 1 h  ho    Stl

At he dokt a mn gre . "I an1 the bu Ncfepke, bu  ople caU m Ne. m ee for h ls" ygo \v xd  m a  b. b . H yu b nyng un e•   k Ne  odded.   me  a I e  b  ue. '  di  g e be  g? Pygs skd king   ook oumn bck  me 'Y n1usl be    ude.• .•,,

Nf smied n uck out i he 'T r  i pil o hat's bee u y 1 fai o g." Yo u

c a

knoe  o u oe? Po a

Nf Le M ea O}, i o o o u s! J u te oe o 1ae  � riange. I l i   a u  e 1 mak   q o a exc c i   r u stne." ngl 

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Nf lt Pyhagora hold hc ope. Pthagoras n1ad

Nf lt Pyhagora hold hc ope. Pthagoras n1ad o ials, ials , but o had t t a. Ho\v Ho\v lo  do yo ma h side?" h ak.

"Oh I've how o too mh alad kl Nf a h too a h o. h o' yo nu alo o\v? n

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As hi athr and Nef talked, Phgo foud an od pc f op and tied n i. H pulld the o nto irt ianges. FinJy, he adc a tg h �e1d r gh  I hd 3 ln h  o o  4 lth o oh s, d 5 h� on h l ongest e u've ot  it"  i  he.

.

J hen yaor yaors' s' f cld hi1  Ct·y  a

J hen yaors' yaor s' f cld hi1  Ct·y  a of ils, o. Ncf d  ll cy h rest." " would cy hm Nf d, b v  m

hb o I  Yol ha o mak o p." Wh y go o  ho ho  f  buld) h d \hl yo   rst of h l Ill  h o  o o Gumb Pyhagor�s·s h hdd ck o  ship pated Pyho on h hd B  ood o

nd h s  fo m h ad  h dsad o  ho Ad do� o 

Pythagors ookd ound th  uny cod.  e 1idde tood  au b�c mad of son. H oo o J out o  ra ju t to � how they o d o d k ound th ba< "l c pu  bak qikly, h thot H d  o of th d  o oe d of th t ba . He ddd o o o o d t n  sqa

"Som of ese crtes have blue e, e,  Paors sid. oon d nd blu e we ceed }v Pythagor� 1nd  �qu f blu e nd a big su  of ed d e   .

H  d1g � ·ok  \h  od, « t sc i a ih  a! I sides ae 3. 4 n 5 s o."

He couned he e. "Sg,  ou T 9 l  te   pu 1c 16  s n t lu u qu 2 5 es Thee ae xcy 25 le n he big ed d bue :q Sddn y a voce dmadd " What d you  y a do?

Ncf rushed into he ouard. Pyagoa' ah right behind hm wha wha all h ?" Nf apped. oy/ ythagoa • wa� gog o pu h tiles bck B I ond o somth ng nrng "T'n

.

,. 1 don'  h yo ond!, ind N. Look Look a hs nss"

h� at "Pyaor p up h id n n And hu- \Ye have nan nan 1or top\ o mak oay

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Th nxt day, Pgor  s far t l o home. Pgo dw  cure of tl  t quares e o p l1e l1 

T qu wth 3 tl o ec sie ha 9 le te o \Vth 4 o    6 , d  oe wt 5 o ech i  2 5 il  •

So in  qua  g of  i d , in1 l,    o e   'o u. I'll cll  · ' \Vhcn I 1  ur by f ree   i thre a d Ill te t �." ,

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1 2 3 1 2

1 2  

Pyagoras drew a ne piu. ,Thre sqae plus fo qa qls v squad," h aid to hmlf

won  h squares o hc �i o oh rgh  tngc a  h a ay? h thoht. "I

Py y fle\v o he ship when he got om. H couldn' \Vai o ll Salos a  bu th c< ll koed ko ed rope r ope d  c·  of he rgh ria�e.

Whn h got o th uninishd tn1ple, Sat an Pcro w nt h. Th r  on th groun \Vh Ppo Ppo had tho t "ht r oul b sv t lm f th botto \' aut fve ft fro th  Pyho thouh Pos s tht th l  2 ft hh .

H r  n n th  r nd t 5+ ' 5 � l

        -          

?.

69 69

=

hats t! h a  to b  t on  x th lad and had ho

At ho Phor< t ut  p p lokd t t  "I ·o  h s to hsf 24

13

X

3

Ta nght Phagors nnouned, 4(1 fo o t isac o1 hre to C!"

Hi h ly hok on a g. His 1o hr d Hw  h b on? Pagoas w ' isovd  p h wo or an rit angl.   i o f�urc o h t ow F  i i om h o C" is fth r ood  So I no  my   o so n.'

25

Pnaors sted t xpi. At ha l t, So d Pc  1  ufg h rd s if ey  c p   F

_.,

P d t yhg Yo did �m o or lddr!" 'H o be h o ?" ?" h f ked, w

Sto

hok  head . "No! He m ae o ladder  pefc

Sto hok  head . "No! He m ae o ladder  pefc lngt. W l be bl o nish e roo now, Ppos d The l \ve' hav o o i f he cok ba es of l1e colu  ' '

"

ybe I cn hp Pyt oras od. u e my o ke ig angles. I ou u e  i  tt a ngle o ke  ba es

Pythagors' fater said, c'Son c'Son o SC(Od tough ayb o hould t e abot he tanc o e.�

 Samo� fo·  righ ng Ryo  xpled "Or  \'l  Roe nd Ce. I   e d of e ang a , nd l, 1 n  m  e ae a: +   - c� o g o   e o ee o e . .

·vu can ee bO\' 

b1 qs 34,25.

Q b· c·  " 1 . 1 � 8 �   ,90 o 3 2 = ' +

=





nd , th  nc b re  Cte  had to fld wh ne mutp by iel u 2 . 'f

 eady kn\v 48 eJ 904 Tf t m "

ti  bu  e 40 Tt' t g .

Everyone \vas amazd Pyg  Py g os' os' fath cped im on e bk. "Good ig, ot! Youl1ake  fn mc ody

Paor' mo  y (•Ph h  ue hi quik mnd o o n . "

H f oddd 4So \h o e inkn, ou could b a l  �no  ee o hing o n.  ou coc

Phagoa He opd gre gs n   

t

do

3

A w dys later, yhgoras �a s fthe's b

ing io te o.

A w dys later, yhgoras �a s fthe's b

ing io te o. H er ra o g im.

�os you w ! I mde   Cte i cod ,   th e id� ung 1 Pho look p  h fatr d d (Y vee r, oo I j d o ca ho"' o oo   n tbc i l."

Htorcal Not

Phor (pie-·HAGuhus) \va  on  ek  lnd of roud 569 RCF. Te c evn of his chidoo  uow.  oudd a schoo  . ou Ity a vng n Egt nd h Me s.  w   poo>hr msicn,  nd onom b  h i tno s  nb s a mn  mo famous co i •a \e no c  on Thoem:

b

1

+ 1

=

l

b ae two legs of  rign g, d c   ed oppot h rgt g. when a d