the truth about pi by aenea mickelsen

The Truth
About Pi
Math Concept Reader
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Expedition:
Antarctica
by Aenea Mickelsen
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Copyright © Gareth Stevens, Inc. All rights reserved.
Developed for Harcourt, Inc., by Gareth Stevens, Inc. This edition published by
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HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the
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Printed in the United States of America
ISBN 13: 978-0-15-360207-8
ISBN 10: 0-15-360207-4
1 2 3 4 5 6 7 8 9 10 175 16 15 14 13 12 11 10 09 08 07
by Aenea Mickelsen
The Truth About Pi
Math Concept Reader
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2

Toward the end of the afternoon on Tuesday, Mr.
Griffin asks the students in his class to think about
circles again. That morning they reviewed circumference
and diameter of circles. Now Mr. Griffin wants to talk
about the ratio pi. “The ratio pi has fascinated people for
thousands of years,” he tells the class. “For more than
4,000 years, people have known that the ratio of the
circumference of a circle to its diameter is pi. While no
one knows for certain who first calculated pi, we do know
that Ancient Greek and Chinese mathematicians used
this value. Some mathematicians think that the Egyptians
used pi when they built the pyramids.”
Mr. Griffin explains that pi is an irrational number.
That means that it cannot be written as the ratio of two
integers. The digits after the decimal do not terminate,
meaning there is not a countable number of digits in pi. Mr.
Griffin also points out that the digits in pi do not repeat,
nor do they occur in a repeating pattern. Mathematicians
who have used supercomputers to calculate pi have not
found even a simple repeating pattern.
Chapter 1:
The Amazing
World of Pi
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3
While the class discusses pi, Mr. Griffin writes just a
part of its value on the board.
Mr. Griffin shares some other interesting pi facts with
his class. People in the 1800s were able to calculate pi to

about 1,000 digits. That was before they had calculators
and computers to help them. They did their computations
by hand. In 1999, Dr. Yasumasa Kanada at the University
of Tokyo calculated 206,158,430,000 decimal digits of pi.
Then, in 2002, he and his team broke its own world record
by calculating more than six times that, or 1.2411 trillion
decimal digits. Mr. Griffin tells his students that a trillion
is a million million or 1,000,000,000,000.
Calculating the decimal digits of pi isn’t the only way
people have set records. Mr. Griffin tells the class about
a Japanese man who memorized 83,431 digits of pi. Akira
Haraguchi set that record on July 2, 2005. Reciting all of
those digits took him many hours.
Mr. Griffin grins and announces that any student who
memorizes 25 digits or more will get bonus math class
points. They don’t have to go as high as 83,000, though!
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4
A fun thing some people do with the number pi is to
find their birthday within the decimal digits. “A computer
program will do it for you,” Mr. Griffin says as he shares
with the class where to find his birthday. He was born on
October 6, 1964, which can also be written as 10/6/64.
The number 10664 occurs in pi after 177,303 decimal
digits. He promises the class that the next morning they
can each enter their birthdays in the online calculator to
find out where they occur in pi.
Mr. Griffin turns on his computer and the projector so
the class can see an image on his screen. The image shows

two circles, one that is small and hard to see, and another
that is much larger. First he looks at the circumference and
diameter of the small circle and writes
C
—
d


= π. Together
the class does the math, and the students discover that
the equation is true. Circumference divided by diameter
equals pi, or approximately 3.14. The students then do
the math for the larger circle. They get exactly the same
result!
The circumference of a circle divided by its diameter is equal to
pi, or approximately 3.14.
1.2 cm 5.0 m
C ≈ 3.8 C ≈ 15.7
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5
As his class is getting ready to leave for the day, Mr.
Griffin tells everyone that the equation
C
—
d


= π is true
for any circle. Sometimes rounding causes the digits in

the quotient to be a bit different than pi, because of the
rounding that might happen in the measurements of the
circumference and diameter. Even if the measurements
aren’t exact, the quotients should still be a little bit more
than three.
The equation is even true for man-made circles like
Ferris wheels, Mr. Griffin tells his students.
The students gather their backpacks and file out of
the classroom. Two of the students, Grant and Courtney,
live next door to each other. They walk home from
school together most days. While they walk the three
blocks to their houses, they discover that they are both
determined to memorize at least 25 digits of pi in order
to get extra points Mr. Griffin promised. They agree to
help each other recite the digits. Grant tells Courtney
that he is curious about Ferris wheels and wants to see if
what Mr. Griffin said about the relationship between the
circumference and the diameter of a circle is true.
The equation
C
—
d


= π is true of any circle—even a giant Ferris
wheel.
Diameter
Circumference
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6
After he says goodbye to Courtney, Grant walks
in his front door. His dad greets him as he strolls into
the kitchen. Grant tells his dad what he learned about
circles and about pi. He asks his dad if he will help him
investigate Ferris wheels and find out whether what Mr.
Griffin said about pi holds true for all circles.
Together, they go to the computer and begin to search
the Internet for information about Ferris wheels. As they
search, Grant and his dad discover all kinds of information
about the history of Ferris wheels. They learn that the
World’s Colombian Exposition, held in Chicago in 1893,
commemorated the 400th anniversary of Columbus’s
landing in America. The World’s Colombian Exposition
was also called the Chicago World’s Fair. The people in
charge of planning the fair wanted to create a structure
to rival the famous Eiffel Tower. The Eiffel Tower was
built in 1889 for the Paris World’s Fair, which honored the
100th anniversary of the French Revolution.
Chapter 2:
Ferris Wheels
Around the
World
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7
Daniel H. Burnham was a famous architect from
Chicago who had helped to design some of the earliest
skyscrapers. He was in charge of finding a suitable design
for the new structure for the Chicago World’s Fair. One

evening at a banquet for engineers, he expressed his
frustration at not having found anything. Someone in
the crowd had an idea and doodled a design on a napkin
during the dinner.
That someone was George Washington Gale Ferris.
He was an engineer and a bridge builder who owned
his own company, G.W.G. Ferris & Co., and he had
experience inspecting, testing, and erecting large steel
structures.
Merry-go-rounds were popular carnival rides in
the 1800s. Ferris decided to design a kind of vertical
merry-go-round that he hoped would be equally popular.
He knew the ride had to be gigantic since he was
competing with the famous Eiffel Tower.
George Washington Gale Ferris created the Ferris wheel for the
1893 Chicago World’s Fair at the urging of Daniel H. Burnham.
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8
People did not know what to think of Ferris’s design,
so the project did not get started until December 16, 1892.
The final product needed to be ready by May 1, 1893.
That meant Ferris had a little over four months to raise
the $355,000 needed to pay for the wheel. He also had to
locate, construct, and assemble more than two thousand
tons of steel for the Ferris wheel.
By the end of March 1893, the Ferris wheel had been
built in Detroit, Michigan, and transported to Chicago. It
took 150 railroad cars to hold all of the pieces. At the time,
the Ferris wheel’s 45-foot axle (the bar on which the wheel

rotates) weighed 45 tons and was the largest piece of steel
ever forged.
William F. Gronau was Ferris’s partner. He had the
responsibility of putting the wheel together. The diameter
of the Ferris wheel was about 262 feet–about the height of
a 25-story building! Two 140-foot steel towers supported
it. The circumference of the wheel was approximately
825 feet. Each of the 36 cars on the Ferris wheel could
hold 60 people. That meant about 2,160 people could ride
at the same time.
Ferris had only a little more than four months to raise funds
and build his show-stopping amusement ride. The wheel used
more than two thousand tons of steel.
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Grant enters these measurements into the formula
for pi. He calculates that for the original Ferris wheel, the
relationship between the circumference and the diameter
was a number a bit greater than three.

C
—
d


= ≈ 3.14885

Next, Grant and his dad search for information about
another Ferris wheel called the London Eye. The London

Eye is a landmark in London, England, that was originally
planned as part of the millennium celebration. People were
supposed to be able to ride the London Eye on New Year’s
Eve, 1999. There were some technical difficulties, however,
so it wasn’t until three months later that people were finally
able to climb on board for a ride.
The diameter of this enormous wheel is about 135 meters,
while its circumference is 424 meters. The London Eye has
32 capsules that can each carry as many as 25 people.
A complete revolution on the London Eye takes about
30 minutes.
Grant and his dad use the formula
C
—
d


= π
and plug in the
London Eye dimensions.
≈ 3.14
The equation is true again! It seems that Mr. Griffin was
right about pi.
262
825
135
424
London, England, is the home of the landmark London Eye
Ferris wheel.
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10
Grant searches some more and finds two huge Ferris
wheels in Japan. One is called the Cosmo Clock and is
found in Yokohama, Japan. He reads that it rises 369 feet
above the ground and has a diameter of 328 feet. Grant
cannot find a circumference measurement for the Cosmo
Clock.
His dad explains that they can figure out this Ferris
wheel’s circumference by using a different form of the
equation. Since circumference divided by diameter equals
pi, then another form of the equation that would work is pi
times diameter equals the circumference.
Grant and his dad do the math. They agree they will
use 3.14 for π.
C
= πd
C ≈ 3.14 x 328
C ≈ 1,029.92
T
he circumference of the Cosmo Clock must be about
1,029 feet.
The Sky Dream Fukuoka is another Ferris wheel in
Japan. Grant and his dad are able to find the diameter
measurement of this ride, but not the circumference.
The diameter is about 112 meters so they multiply this
value by 3.14 and find that the circumference is about
351.68. The Sky Dream Fukuoka has a circumference
of about 352 meters.
The Cosmo Clock in Yokohama, Japan, rises 369 feet above

the ground.
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11
Grant finds a Ferris wheel called the Prater in
Vienna, Austria, that was built more than 100 years ago.
Despite its age, the Prater is still in use. Grant is excited
to find measurements for both the diameter and the
circumference of the big wheel. Quickly, he enters the
measurements in the formula
C
—
d


= π. The diameter of
the Prater is about 60.94 meters and the circumference is
approximately 191.35 meters.
≈ 3.14
Grant discovers that using more precise measurements
for the circumference and diameter helps the quotient
come closer to pi.
Grant decides to look for the largest Ferris wheel in
the United States. He finds information about the Texas
Star at Fair Park in Dallas, Texas. The Texas Star is the
largest Ferris wheel in all of North America. It has a
diameter of about 212 feet and it holds as many as 260
people. The wheel’s circumference is about 665.5 feet.
Grant divides 665.5 by 212 and calculates that, once again,
the ratio is a number very close to 3.14.

60.94
191.35
The Prater Ferris wheel in Vienna, Austria, is more than 100
years old.
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12
Grant is pleased that his research has been so
successful. Now he wonders what other circles he can
measure and test. He knows that the equation for pi works
for big circles like Ferris wheels, but he’s not sure if it
holds true for smaller circles. Grant slowly walks around
his house, keeping his eyes open for circles to measure.
When he steps into the garage, he notices his bike
hanging from its mount. A bike tire would be a perfect
way to test pi on smaller circles!
Together, Grant and his dad pull the bike off of its
mount and measure the diameter of the bike’s front tire.
They find that it is about 26 inches across. Next, they
carefully measure the circumference, with one person
holding the measuring tape in place while the other
person slowly winds it around the tire. That measurement
is about 81.7 inches. They compute that 81.7 divided by 26
is a number very close to 3.14. It doesn’t seem to matter if
they measure big circles or small ones. The ratio between
a circle’s circumference and its diameter is always the
same.
Chapter 3:
Circles at
Home

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13
By this time, Grant is sure that Mr. Griffin is correct
about pi, but he still wants to measure one more household
circle. He walks around his house again. In his room he
sees the drum his grandmother sent him from one of
her trips. He decides to measure the circumference and
diameter of one end of his drum.
He uses the standard side of his measuring tape and
finds that the circumference of the end of his drum is
about 50.25 inches. He stretches the measuring tape across
the drum to find that its diameter is 16 inches. With his
formula
C
—
d


= π, he plugs in the numbers.
≈ 3.14
Grant also knows that circumference is related to
radius. Out of curiosity, he uses the formula C = 2πr.
When he does the calculation his answer is:
C ≈ 2 x 3.14 x 8
C ≈ 50.25
He enjoys proving once again that the ratio really
works.
16
50.25

Grant used pi to figure out the circumference and diameter of a
drum he got as a gift from his grandmother.
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14
As Grant and Courtney walk to school the next day,
they discover that they both researched the formula

C
—
d


= π. Courtney tells Grant that she measured the sound
hole in her guitar, and when she did the calculations she
got a number very close to pi.
Grant asks her how she managed to measure the
circumference of the hole. Courtney explains her mom
helped her solve that problem. Courtney’s mom took a
piece of string and measured the hole with that. Courtney
then marked and measured the string to find the circle’s
circumference.
As they walk, Grant and Courtney also work on
memorizing the digits of pi. By the time they get to
school, they have each memorized more than 15 digits.
They hope that by tomorrow they will be ready to recite
the 25 digits to Mr. Griffin for the bonus points.
After the bell rings and they join their class, Grant and
Courtney discover that others went home and investigated
the ratio for pi, too.

Courtney used a string to measure the circumference and
diameter of the sound hole in her guitar.
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Mr. Griffin is thrilled that so many students
investigated circles. He asks the class to describe what
circles they found at home and how they measured them.
Scott tells the class that he measured his mom’s favorite
mixing bowl in the kitchen and that the circumference
was 48 inches. Sure enough, Scott said he found that when
he divided 48 by 3.14, he calculated 15.3 inches for the
diameter. That was almost exactly what the tape measure
showed.
Other students had similar experiences when they
tried measuring household circles. Shari says she measured
several wheels on her little brother’s toys, and every
one of them proved that the relationship between the
circumference and the diameter is a number a bit larger
than three.
Mr. Griffin asks his class to talk about what they have
learned. The students agree that pi remains constant, no
matter what circumference or diameter a circle has, no
matter how big or small the object—no matter what.
Students measured circles found all around their homes to find
the ratio pi.
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Glossary

axle a shaft or bar on which a wheel rotates
circumference the distance around a circle
diameter a line segment through the center of a circle, with endpoints
on the circle
Ferris wheel an amusement park ride consisting of a huge revolving
wheel carrying seats
irrational number a number that cannot be written as a ratio of two
integers. One example of an irrational number is the ratio pi.
millennium a period of 1,000 years. A millennium is also the
celebration of a 1,000th anniversary.
pi the ratio of a circumference of a circle to its diameter
radius a line segment with one endpoint at the center of a circle and the
other endpoint on the circle
ratio a comparison of two numbers or quantities
Photo credits: cover, title page © Oswald Eckstein/zefa/Corbis; p. 5 © Paul Almasy/Corbis;
p. 7 (left) Ferristree.com; pp. 7 (center, right), 8 Library of Congress; p. 9 © Peter Adams/
Corbis; pp. 10, 13 © Corbis; p. 11 © Barry Lewis/Corbis; pp. 14, 15 Russell Pickering.
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Think and Respond
1. The tire of a race car has a circumference of about 87.4 inches and a
diameter of 27.83 inches. What is the ratio of the circumference to
the diameter rounded to the nearest hundredth?
2
. One of the paint cans in Grant’s garage has a diameter of
3.12 inches and a circumference of 9.81 inches. What is the ratio
of the circumference to the diameter? Round your answer to the
nearest hundredth.
3
. A large truck used in the copper mines uses tires with a diameter

of about 153 inches. What is the circumference of a tire that size?
Use 3.14 for π.
4
. Explain how you could find the circumference of a circle if you knew
its diameter.