It’s story time at the chalkboard!
A pi lover named Calvin Smith has shared with us something special that we’d like to share with you. Calvin has written a short story that will be a lot of fun to tell, and show, to your students! Read it through, and imagine how you might stand at the chalkboard, draw a number line, and sketch out the “characters” and the action as you read it aloud. Thanks, Calvin!
Pi felt lost. He knew that he was a number, but he didn’t know his exact location on the number line.
When he was very young, somebody had told him that he was 3.1. He had looked at the number line, and that didn’t feel like home.
Three was close by and called out, “Pi must not be a real number because he doesn’t have a place on the number line.”
This made Pi feel even worse. Sometimes, Three was mean to him.
Three pushed his advantage further. “I have a home! Look, it is 3. In fact, I am a very special number – I am prime!”
Four, who was on the other side of Pi, said to Three, “You are odd! All you prime numbers are odd.”
Two, overhearing all of this, spoke up and said, “I am prime too, but I’m not odd like Three.”
Nine heard Four and said, “It’s okay to be odd. I am odd and I’m a square.”
Four answered, “I am a square too, but I’m certainly not odd.”
This wasn’t helping Pi. He asked, “Does anybody know where my place on the number line is?”
Nine spoke up. “I hear it is 3.14159.” Nine could be a real know-it-all sometimes.
Pi went to that spot on the number line, and it felt good, but he could tell that it still wasn’t exactly his home.
Three taunted Pi again. “Ha ha, I told you so, you aren’t a real number. You don’t have a place on the number line!”
“At least I’m not odd!” Pi wasn’t certain of this, but he was ready to claim it.
Three and Nine shouted in unison: “It’s okay to be odd!”
All the odd numbers up and down the number line spoke up. An infinite number of voices chimed in at once. “Yeah, odd numbers rock!”
This still wasn’t helping Pi. He asked again, “Can somebody please tell me where my place on the number line is?”
This time Zero spoke up. “Maybe I can help. My job is to make numbers’ lives easier. The definition of Pi is the ratio of the circumference of a circle to its diameter. It looks like this:
Let’s draw a circle around me with a diameter of one. One Half, please make a circle around me.”
One Half was happy to be brought into the discussion. Some ignored him because he was just a fraction. He walked around Zero, careful to maintain his exact distance of ½ from Zero all the time. He proudly looked at the perfect circle that he made.
Zero said, “See, now we have a circle with a diameter of one because the distance from ½ on the positive side of the number line to ½ on the negative side equals one. Now, how many times can One lie down around the circle?”
One wanted to see where this was going, so he carefully lay down around the circle. He found that he fit three times with some space left over.
Zero said, “Okay, we have 3. Now let’s see how many times One Tenth can fit into the space left over.”
One Tenth checked the space and saw that he could fit only once with some space left over.
Zero said, “Now we have 3.1. Now let’s see how many times One Hundredth can fit into the space left by One Tenth.”
One Hundredth checked and saw that he fit four times with some space left over.
Zero said, “Now you see, we have 3.14.”
Pi said, “This is great! How long until we have my exact address on the number line?”
Zero answered, “Well, we can do this forever and never get your exact address. We will just keep getting closer.”
Pi was disappointed. He still didn’t know where his place on the number line was.
Zero continued, “But I can show you your exact place without putting a number address on it. Look at our circle. It has a diameter of One. And we were dividing the circumference by the diameter to get your exact number. Since the diameter of this number is One, we were dividing by One.”
Pi didn’t understand what Zero was getting at.
Zero explained further. “Don’t you see? If you divide a number by One, you get the number you started with. Since we divided by One to get Pi, then the number that we divided must also be Pi. The circumference of this circle is equal to Pi because the diameter is one. It looks like this:
Diameter=One and Circumference/Diameter=Pi.
Since the circumference of this particular circle equals pi, just straighten it out into a line, lay it on the number line and you have your exact location.”
Pi straightened out the circle and found his exact spot on the number line. It was the absolute perfect location. He didn’t care if he knew what the address was. Pi had found his home.
Copyright 2013 Calvin Smith. Commercial rights reserved. You may freely copy for non-commercial use.