Who doesn’t like π?

Pi, or π, is a letter from the Greek alphabet used by mathematicians. π signifies this weird number: 3.14159265359… or 3.14 for short. It is the ratio of a circle’s circumference to its diameter. Circumference is how big around a circle is. The diameter is how wide a circle is from side to side if you draw a line through its center. Diameter x 3.14 = circumference. This is true of any circle, no matter how big or small.

MrNystrom has a great video about how to think about π.

Pi has been around for 4000 years, but Archimedes of Syracuse (287–212 bc) was the first mathematician to calculate π accurately.


Archimedes came up with his best ideas in the bath tub.

So back to the Romans. If you want to measure miles across the Roman Empire, how would you do it? Counting steps and paces as you march along isn’t very accurate—it’s too easy to lose count. What if you used a circle—like a wheel? I mentioned that chariot wheels were made a standard size, like many things in the Roman Empire.


A chariot wheel is 4 feet across at its widest point—that’s the diameter. Let’s calculate a chariot wheel’s circumference—how big around the wheel is. You can calculate the circumference by multiplying its diameter by π. π = 3.14. Four feet x 3.14 = 12.56 feet.

Now, there are 5280 feet in one mile. 5280 divided by 12.56 = 42 revolutions of the chariot wheel. All we have to do now is count every time the wheel goes around. At 42 times, we’ll know we’ve reached a mile.

Counting how many times a chariot wheel goes around still seems like a big pain in the neck, doesn’t it? Archimedes thought so, too.

Side note: March 14, 3/14, is known as π Day. On π Day a grocery store in my town sells pies for $3.14.

pie day559

Back to the beginning of The Western Civ User’s Guide to Time & Space

One response to “Who doesn’t like π?

  1. Pingback: Archimedes and his odometer | John Manders' Blog

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