the truth about pi by aenea mickelsen

The Truth About Pi Math Concept Reader ca65as_lay_070106ap_ms.indd 3 1/7/07 8:44:03 AM DIGITAL FINAL PROOF Expedition: Antarctica by Aenea Mickelsen ca62xs_lay_061207ad_am.indd 4 1/9/07 9:09:15 AM DIGITAL FINAL PROOF Copyright © Gareth Stevens, Inc. All rights reserved. Developed for Harcourt, Inc., by Gareth Stevens, Inc. This edition published by Harcourt, Inc., by agreement with Gareth Stevens, Inc. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright holder. Requests for permission to make copies of any part of the work should be addressed to Permissions Department, Gareth Stevens, Inc., 330 West Olive Street, Suite 100, Milwaukee, Wisconsin 53212. Fax: 414-332-3567. HARCOURT and the Harcourt Logo are trademarks of Harcourt, Inc., registered in the United States of America and/or other jurisdictions. 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 ca65as_lay_070106ap_ms.indd 1 1/7/07 8:44:04 AM DIGITAL FINAL PROOF 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 ca65as_lay_070106ap_ms.indd 2 1/7/07 8:44:05 AM DIGITAL FINAL PROOF 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! ca65as_lay_070106ap_ms.indd 3 1/7/07 8:44:05 AM DIGITAL FINAL PROOF 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 ca65as_lay_070106ap_ms.indd 4 1/7/07 8:44:06 AM DIGITAL FINAL PROOF 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 ca65as_lay_070106ap_ms.indd 5 1/7/07 8:44:07 AM DIGITAL FINAL PROOF 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 ca65as_lay_070106ap_ms.indd 6 1/7/07 8:44:08 AM DIGITAL FINAL PROOF 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. ca65as_lay_070106ap_ms.indd 7 1/7/07 8:44:09 AM DIGITAL FINAL PROOF 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. ca65as_lay_070106ap_ms.indd 8 1/7/07 8:44:09 AM DIGITAL FINAL PROOF [...]... 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. .. 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... 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... England, is the home of the landmark London Eye Ferris wheel 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 — = 825 ≈ 3.14885 d 262 Next, Grant and his dad search for information about another Ferris wheel called the London Eye The London Eye... for both the diameter and the circumference of the big wheel Quickly, he enters the C measurements in the formula — = π The diameter of d the Prater is about 60.94 meters and the circumference is approximately 191.35 meters 191.35 ≈ 3.14 60.94 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... 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... 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 C formula — = π, he plugs in the numbers... researched the formula C — = π Courtney tells Grant that she measured the sound d 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... 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... ratio for pi, too 14 ca65as_lay_070106ap_ms.indd 14 1/7/07 8:44:14 AM DIGITAL FINAL PROOF Students measured circles found all around their homes to find the ratio pi 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 . 07 by Aenea Mickelsen The Truth About Pi Math Concept Reader ca65as_lay_070106ap_ms.indd 1 1/7/07 8:44:04 AM DIGITAL FINAL PROOF 2 Toward the end of the afternoon on Tuesday, Mr. Griffin asks the. 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, . 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