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New Math: When the Indiana Legislature (Almost) Changed Pi

Published: March 14, 2018

Today is Pi Day, the day we recognize the wonder of 3.14. Since 200 B.C., we’ve known we can calculate the area of a circle by (1) squaring the distance from the circle’s center to its edge, then (2) multiplying this value by 3.14 — the value of pi.

This number is the ratio of every circle’s circumference to its diameter. An irrational number, pi contains an infinite number of numbers behind the decimal point. (You can find it calculated to the 100,000th digit here.)

Back in 1894, an amateur mathematician in Solitude, Indiana, thought there had to be a better way to measure a circle’s area. Edward Goodwin believed that, using a compass and a ruler, he could create a square with the same area as a circle. And a square’s area would be so much easier to measure.

There was one problem with his method. It didn’t work. In fact, 12 years earlier, a mathematician had proven, mathematically, that it was impossible to calculate the area of a circle this way.

One reason Goodwin’s method didn’t work is that it changed the value of pi from 3.141592 etc. to 3.2. (As he expressed it, “The ratio of the diameter and circumference is as five-fourths to four.”)

Enchanted by his own genius, Goodwin copyrighted his method. Now he could earn a royalty whenever businesses and schools used his new, improved system.

But he knew the state of Indiana couldn’t afford the royalties that introducing his system into Indiana’s schools would involve. So he offered the state a deal: If Indiana’s legislature would officially acknowledge the validity of his system, he’d waive the royalty fees.

Representative Taylor I. Record was Goodwin’s state representative, and he thought it a generous offer. So, in 1897, he introduced House Bill 246, which declared, “a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side.”

If that sounds confusing to you, you’re not alone. Many legislators didn’t understand it either. Nonetheless, they passed the bill in the state House on February 5, 1897. Unanimously. No one stood up and said, “Wait. I’m not supporting this until I understand it.”


Professor Clarence Waldo

The Indianapolis newspapers were wholly supportive of Goodwin’s theory, though it appears they didn’t understand it any better than the legislators did.

And so the bill moved on to the Senate. Fortunately, a math professor from Purdue University was coincidentally in the capitol building when the bill was being debated. Professor Clarence Abiathar Waldo was aghast to hear the state might make this erroneous theory part of school curriculum. He cornered some senators to ask about the bill. They offered to introduce him to the learned Goodwin. Waldo declined, saying that he’d already met as many crazy people as he cared to know.

He explained to the senators why Goodwin’s method was flawed. Armed with this knowledge, they took to the Senate floor to mock the bill and Goodwin’s theory. Finally, a senator moved to postpone the bill. It was never brought up again.

It was easy to make fun of the idea after Waldo had spoken up. Even the newspapers changed their tune. The Indianapolis Journal observed, “The Senate might as well try to legislate water to run up hill as to establish mathematical truth by law.

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