A Math Adventure

by Julie Ellis

illustrated by Phyllis Hornung

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, 1961-

What’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.]

I. Hornung, Phyllis, ill. II. Title.

QA460.P8 E38 2002

516.22—dc21

2002002380

3

Long ago in ancient Greece, there lived acurious boy named Pythagoras.

Pythagoras just couldn’t help poking hisnose into places. Sometimes, his curiosity gothim in trouble, but sometimes it paid off.

4

One day, Pythagoras sat in the shade of an oldolive tree. He could see the harbor and the sparklingblue sea around the island where he lived.

Nearby, two workmen were building a temple.They began to argue. “This ladder is too short toreach the roof,” Pepros grumbled.

“That’s not possible,” said Saltos. “The wall is12 feet tall, so I made the ladder 12 feet long.”

Pepros roared, “The ladder only reaches theroof when it is flat against the wall, and thenno one can climb it! This is as bad as thecolumns on the porch!”

Pythagoras poked his head out frombehind the tree. “What’s wrong withthe columns?” he asked.

5

Pepros frowned.“It’s that pesky Pythagoras again.

“Stop bothering us! At this rate, we’ll never finish the temple!”

•

As the workmen argued, P}'t.hagoras crept

around to the other ide of the building. Four

cohnl'nls stood on crooked ba e .

Sotnc coltuuns lcaucd lo the left. Olhcrs

tilted to the right.

"These colun1ns 'viii never hold up a roof,"

Pythagora aialo hitnsclf. ''I \Vi h there 'vere

something 1 could do to help.,.

Still thinking tlbout the prohlen1. he ran

hon1e for diluter .

7

At the dockt a man greeted them. "I an1 the builder

Ncferhcperhcrsekepcr, but people caU me Nef.

rm here for the tiles."

Pythagoras \vas excited to meet a real builder.

"Have you built anything around here?'• he a ked.

Nef nodded. "As a matter of fact, I helped to build

the lighthouc;e. ''

uHo,,., did you get the base so straight?" Pythagoras

asked. thinking of the crooked columns back at home.

'tYou n1usl be a ma ter builder .• ,

Ncf smiled and stuck out his chest. ''The secret is this special rope

that's been used by n1y family for ages."

"You u c a knotted rope to cut stone?,. P}'thagoras asked.

Nef L1ughed. "My dear bO}', this rope docs not cut stone!

J usc the rope to n1ake a �pedal triangle. I call il the

'right triangle' because it helps n1c make a nice,

square corner that's exactly lhc right

angle fur cutting stone."

13

14

Nef let Pythagoras hold lhc rope. Pythagoras n1adc

orne b·ianglcs, but none had the right angle ... Ho\v long

do you make each side?" he asked.

"Oh, I've shown you too much already, n chuckled

Ncf, ali he took back hi rope. "\Nhy don't you nu1

along no\v?"

As his father and Nef talked, Pythagora

found an old piece of rope and tied knot. in it.

He pulled the rope into different triangles.

FinaJJy, he rnadc a triangle that �een1ed right.

It had 3 lengths on one side, 4 lengths on

another side, and 5 length� on the longest side.

ul've got itf" he said to hit'nself.

15

16

Just then Pythagoras's father called hin1 ... Cat·ry this crate

of tiles, son. Ncf and I will carry the rest."

"I would carry them.'' Nef sighed, ''but rve hurt my

thumb so I can't. You'll have to make two trips."

When tney got to the house ef was building) he said,

''\"'hile you get the rest of the tiles, I'll get the nloney I owe

you." Grumbling, Pythagor�s·s father headed back

to the ship.

tef patted Pythagoras on the head. uBe a good hoy

and watch lhese tiles for me," he said as he disappeared

into the house. "And don�t touch anylhingJ"

Pythagoras looked around the sunny courtyard.

ln the 1niddle stood a statue ba�c made of stone.

He took some tiJes out of the crate ju t to �ee

how they would look around the ba<;e. "l can put

lhc1n back quickly,n he thought.

He made a row of three red tiles along one side

of the �tatlte base. He added two tnore row� of red

tiles� making a square.

17

"Some of these crates have blue tiles, ..

Pythagoras said. Soon red and blue tiles were

scattered ever}"vhere.

Pythagora� 1nade a �quare of blue tiles and

a big square of red and blue tiles.

He was adn1iring hi� ·work \vhen he noticed,

"«Jihis statue btlsc is a right triangle! Its sides are

3. 4. and 5 tiles long."

He counted the tiles. "Strange," he thought.

,.The 9 tiles in the red square plus tl1c 16 tiles in

the blue �quare equal 2 5 tiles. There are exactly

25 tiles in the big red and blue :,quare!"

Suddenly a voice demanded, "What do you

think you arc doing?,

19

20

Ncf rushed into the cour.tyard. Pyt:hagoras'.s father.

wa right behind him. ccwhat' all thi ?" Nef . napped.

"T'tn c;orr.y/' Pythagoras "aid. ••t wa� going to put the tiles

back. But I found out something interesting - ..

,. 1 don't care what you found!, interntpted Nef .

.. Look at this tness!"

"Pythagora�. pick up the tiles," hi� father

said ternly . .,And hurry- \Ye have tnany

n1orc stop\ to make today.u

The next day, Pythagora and his fatl1er set sail for home.

o pa the til1e, Pythagoras drew a picture of tl e tile quares l1e l1ad tnadc.

"The quare with 3 tiles on each side had 9 tile • the one

\Vith 4 on eact id had 16 tiles, and the one with 5 on each

ide had 2 5 tile .

"So, in a quar , the length of a ide, tin1es itself, is the

ntnnher of tile in the \\'hole quat·e. I'll call it · quaring' \Vhcn

I n1ulliply a nurnbcr by i�clf. Three · n1c · thre i three

qua red. I'll \Vrite it 3�."

1 2 3 1 2 3 'I 1 2 3 lf ? II'

1 =

2 2 2

3 ;:j :3 --

3; lf 'I I.{? 16 5 �

Pythagoras drew a new picture . .,Three squared plus

four squared equals five squared," he said to himself.

"I wonder if the squares on lhc �ide� of other right

tl'ianglc add up the same way?" he thought.

Pythagoras practically fle\v off

the ship when he got home. He couldn't

\Vait to tell Saltos and Pepros about the spc<;ial

knotted rope and the sect·et of the right trian�e.

23

24

When he got to the unfinished ten1ple, Saltos and Pcpro

were not there. The ladder wa on the ground \Vhere Pepros

had thro\vn it.

"That ladder would be easv to climb if the bottom \\'ere .,

about five feet from the wa11," Pythagoras thought "Pepros

said that the wall is 12 feet high."

d 1 h d d 52+ 12'" -- ?. He re\\' a triang e in t e irt an wrote

25 � ll.f'f - 169

''That's it! The ladder need to be 13 feet long."

He fixed the ladder and headed hon1c.

169 = 13 X 13

At home, Pythagora<; got out a rnap. He looked at it closely.

"I ·wonder ... " he said to himself.

That night Pythagoras announced,

4(1 found out the distance fro1n here to Crete!"

His father. nearly choked on a fig. His n1other

asked, "How can that be, son?"

Pythagoras answered, ''I discovered a pattern that works

for any right triangle. I used it to f�.gurc out the distance.

ow Father can sail straight from here to Crete."

lrlis father stood up. "Son, I cannot rislt my ship

because of some triangle.'' 25

26

"Father _., Pytnagoras started to explain. At that

t'llotnent, Saltos and Pcpros catne n1sh.ing in, puffing

hard as if they had t·aced up the hill.

Pepros turned to Pythagoras, .. You did �omething to our ladder!"

''Has Pythagoras been bothering you again?." his father asked, frowning.

Sa1to hook h. head. "No! He made our ladder the perfect

length. W will be able to finish the roof now.,

Pepros added, "The11 all \ve'll have to do is flX the crooked

ba es of tl1e col urn . ''

" aybe I can help,,. Pytlta oras offered. u e my ·ope to

make right angles. If you u e a ri 'ht angle to n1ake the ba es

, h·aight, the column l\•ill stand straight."

alto lauoh d. "Great ! Now we can fi11ish the tcn1ple on

tinte. You're \\relcomc to stop by and help u 1y time you like."

Pythagoras's father said, c'Son, on SC(;Olld thought, tnaybe you

should tell tne about the cmtancc to Crete.�'

Rythagora� explained, "Our island, Samo� .. fot·tn a right triangle

\\'l th Rhodes and Crete. If. I call the sides of the triangle

a, b, and li, 1 can use my right triangle pattet·n a: + b .. - c:�

to figure out the di tance frotn here to Crete . ..

28

·vou can ee bO\\' a.: b1 equals 34,225.

Q + b· = c·

111· ,.. 1 � 8 � = c"�

2.321 + 21,90� co':

3 .225 = c'2

"'fo find c, the di tance between here and Crete, 1 had

to fitld what nun1ber multiplied by itself equals 34,225 .

.,, already kne\v 148 equaJ 21,904. Thafs too mall.

"I tried 200, but 2001 equals 40,000. That's too big .

.,I tried 180, a11d 1so• equals 32,400. That's clo. e!

"Then, I tried 185 thncs 85. That's exactly 34,225.

So, the di tancc frotn our island to Crete i� 185 tnile . '

Everyone \vas amazed.

Pythagoras's father clapped

him on the back. "Good

thinking, sot'l! You,ll1nake

a fine merchant son1eday.,.

Pythagoras's mother said gcntlyi (•Perhaps

he can use his quick mind for other thing . "

His father nodded. 14Son, \\'ith your

clear thinking, you could be a general.

a �cnator, a teacher, or anything you lvant.

lfs your choice.''

Pythagoras s1niled. He hoped to do

great things in the future.

30

A few days later, Pythagoras �aw his father's boat

sailing into the harbot.

Hi� father ran to greet him.

��Pythagoras, you were right! I made il to Crete

in record tbnc," hi� father said� h·ugging hin1.

Pythagoras looked up at his father and said,

((You lvere right, too. I just had to lcam

ho'"' to look at things frotn

tbc right angl�."

Historical Note

Pythagora (pie-·rHAG-uh-rus) \va born on the

Greek i land of Sarno. around 569 RC.F. The actual

events of his childhood are unl<nown. He founded a

school in . outhenl Italy after traveling in Egypt and

the Middle fast. He was a phllosot>hcr. musician,

and astronomer. but he is tnost retnembered as a

mathematician. His mo "l famous discovery is \\•hat

\ve no\-v call the Pythagorean Theorem:

� b

a1 + b1 = cl

when a and b are two legs of a rignt triangle,

and c is the sede opposite the right angle.