Squaring the Circle Is No Piece of Pi

Mathematicians have sliced, and now supercomputers have crunched, but the mystery of pi goes on and on and...

  • By Bruce Watson
  • Smithsonian magazine, May 2000, Subscribe
 

 

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    Many of us recall our first encounter with pi. It began with dry formulas: C = D. A = r2. (Remember? C = circumference; D = diameter; A = area; r = radius.) Inevitably, somebody told the old, old joke: "Pi are squared? [r2?] No way! Pie are round!" Stated simply, pi is the number you get when you divide the distance around a circle (circumference) by the distance through the middle (diameter). About 3. Easy, eh?

    But in that "about" lies the puzzle of pi. Mathematicians call pi an irrational number. That is, when you divide a circle's circumference by it's diameter, the answer comes out in decimals that go on forever without any pattern. Pi begins 3.14159265 ....and it never ends. Ever. This curiosity makes pi the most intriguing and celebrated of numbers, and the subject of several books, such as The Joy of  and A History of Pi, and numerous Websites. There are many irrational numbers whose decimals go on forever. But has anyone ever written poems about the square root of 2? How many other irrational numbers appear in college football cheers, in Star Trek, as the name of a fragrance or as the title of a recent film?

    For millennia, pi has plagued exacting minds. It first showed up in Egypt. Then Archimedes estimated pi at between 3 10/71 and 3 1/7. For 700 years, his was the most accurate pi. Only in the fifth century a.d. did a Chinese astronomer and his son find a better pi. Leonardo da Vinci pondered pi, as did Thomas Hobbes and Isaac Newton. In this century, supercomputers have calculated pi out to some 206 billion digits, but by all indications, pi's sequence remains amazingly random. The record for a pi recital from memory, which took nine hours, is 42,195 digits. Do not try this math at home.


    Many of us recall our first encounter with pi. It began with dry formulas: C = D. A = r2. (Remember? C = circumference; D = diameter; A = area; r = radius.) Inevitably, somebody told the old, old joke: "Pi are squared? [r2?] No way! Pie are round!" Stated simply, pi is the number you get when you divide the distance around a circle (circumference) by the distance through the middle (diameter). About 3. Easy, eh?

    But in that "about" lies the puzzle of pi. Mathematicians call pi an irrational number. That is, when you divide a circle's circumference by it's diameter, the answer comes out in decimals that go on forever without any pattern. Pi begins 3.14159265 ....and it never ends. Ever. This curiosity makes pi the most intriguing and celebrated of numbers, and the subject of several books, such as The Joy of  and A History of Pi, and numerous Websites. There are many irrational numbers whose decimals go on forever. But has anyone ever written poems about the square root of 2? How many other irrational numbers appear in college football cheers, in Star Trek, as the name of a fragrance or as the title of a recent film?

    For millennia, pi has plagued exacting minds. It first showed up in Egypt. Then Archimedes estimated pi at between 3 10/71 and 3 1/7. For 700 years, his was the most accurate pi. Only in the fifth century a.d. did a Chinese astronomer and his son find a better pi. Leonardo da Vinci pondered pi, as did Thomas Hobbes and Isaac Newton. In this century, supercomputers have calculated pi out to some 206 billion digits, but by all indications, pi's sequence remains amazingly random. The record for a pi recital from memory, which took nine hours, is 42,195 digits. Do not try this math at home.

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