Circumference of the Earth Using Pizza

Unit 1 The Pizza Theory
Thanks to Mycroft
Name ______________________
Date ____________ Per. _____
Determining the circumference of the whole Earth might be difficult,
even though Eratosthenes did it over 2000 years ago. How about calculating the circumference of a pizza instead?
But, there’s a catch. You only get to work with one slice per group.
Materials: Slice of Pizza (Toppings are optional), Other materials as requested
List (1) What you need, (2) What you did, (including your calculation) and (3) The answer you obtained
For example...
Materials: Lots of money and a telephone. Procedure: A. Call 1-800-GET PIZZA, B. Wait for the
delivery guy to arrive. C. When he comes, offer him half of the pie if he’ll drive to the library, look up
Earth’s circumference & phone you. D. When he calls, give him your credit car number as a reward.
(Not!!!) Data: 1.5 x 10^12m (distance to sun) /3.75 x 10 ^7 x 39.37 inches/m = 8.86 x 10^21 inches.
Your own Materials, Procedure and Data:
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
____________________________________________________________________________________
Pizza Theory Page Mon, Sep 18, 2006 © TMcG Mon, Sep 18, 2006

Unit 1 Key to: The Pizza Theory
The most logical way to do this exercise is to use a single slice of pizza, set up a
proportion similar to the proportion Eratosthenes used and then calculate Earth’s
circumference.
Materials: Pizza Slice, Meter stick, Protractor
Procedure:
1. Obtain one slice of pizza.
2. Measure the length of the outer edge of the slice. (Distance d)
3. Measure the angle of the cut.. (Angle a)
4. Set up a proportion and solve for C. (Circumference)
(See below)
a
360° = Distance d
Circumference
5. Circumference = 38 inches (= 0.965 m)
a =the angle os the cut of pizza
Distance d = The length of the slice along the outside
Pizza Theory Page Mon, Sep 18, 2006 © TMcG Mon, Sep 18, 2006

Unit 1 The Pizza Theory Tips
Difficulty: Easy
Content: Important.
Preparations: Buy enough pizzas for the whole class. (or classes)
(You may want to ask the pizza guy to cut narrow slices.)
Materials: Pizza, Protractors & Rulers or Meter sticks
Time: ~ 20 Minutes
Suggestions for the Teacher: Bring out the protractors and measuring tools
only when students request them.
Student Intro: Explain the problem Eratosthenes faced.
If you can, obtain a copy of. “The Librarian Who Measured the Earth”
by Kathryn Lasky, Kevin Hawkes (Illustrator)
Little Brown & Co; ISBN: 0316515264
Post-Lab: Compare the various values calculated by differnt groups.
Extensions: The traditional ESCP Size of the Earth lab or
“The Greek Geometer” by Thomas McGuire (TMcG)
Pizza Theory Page Mon, Sep 18, 2006 © TMcG Mon, Sep 18, 2006