the truth about pi by aenea mickelsen

Circumference divided by diameter equals pi, or approximately 3.14.. The circumference of a circle divided by its diameter is equal to pi, or approximately 3.14... Grant tells Courtney

The Truth

Expedition: Antarctica

by Aenea Mickelsen

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ISBN 13: 978-0-15-360207-8

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by Aenea Mickelsen

The Truth About Pi

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

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!

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

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

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

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.

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

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.

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 = πand 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.

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

The 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

The Cosmo Clock in Yokohama, Japan, rises 369 feet above the ground.

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.

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

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.

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.