Digit Hunters
Calculating the value of pi has been a fascinating challenge since ancient times. In the beginning, knowing pi's value was important for calculating areas, volumes, and other quantities involving land and property. But calculating the value of pi quickly became a pursuit for its own sake. Few practical applications required a value of pi to more than a handful of decimal places.
In about 1650 B.C., the Egyptian scribe Ahmes wrote out a set of math problems. In one problem, he assumed that the area of a circular field with a diameter of 9 units is the same as the area of a square with a side of 8 units. So, for Egyptians, this meant that pi was equal to 4 times 8/9 times 8/9, which is 3.16049…—a little less than its true value.
More than a thousand years later, the Greek mathematician and physicist Archimedes (287-212 B.C.) found the value 3.1419 for pi. His estimate was off by less than three ten-thousandths, and the numbering system he used to calculate it didn't even have a symbol for 0!
Archimedes
In the fifth century A.D., the Chinese astronomer Tsu Ch'ungchih and his son figured out that pi is about 355/113, or 3.1415929. This is only about eight millionths of a percent more than the true value of pi, which is 3.14159265….
Meanwhile, throughout the first millennium, the Romans and others were working with less accurate values of pi. In 1220, Fibonacci (see "Fibonacci and His Rabbits") wrote that pi is approximately 864/275, which is about 3.141818. That's close to the value used much earlier by the ancient Greeks.
Soon after that, Europeans began making great strides in zeroing in on the true value of pi, expressed in decimal digits. In 1585, a Dutch mathematician rediscovered 3.1415929 without knowing that the Chinese had already found this value more than a thousand years earlier.
Eight years later, another Dutch mathematician, Adriaan van Roomen, accurately calculated the first 15 decimal digits of pi, and then Willebrord Snellius found the first 35 digits.
By 1722 Japanese mathematician Takebe Kenko had calculated 41 digits. In the 1800s, various mathematicians pushed the calculation of pi to hundreds of digits, but nearly always some of the digits proved to be incorrect.
With the advent of electronic digital computers in the twentieth century, the pi world's record climbed to thousands of digits, then millions, then billions, then trillions!
Decimal Digits of Pi: World Record (2020)
Number of decimal digits: 50 trillion
Computed by:Timothy Mullican
Year: 2020
Amount of computer time required: 303 days
Most common digit among the first 200 billion: 8 (appears 20,000,291,044 times)
Least common digit: 6 (appears 19,999,869,180 times)
Last known digit: 8
TRY IT!
Calculate pi using the classic method of Archimedes.
The method involves measuring the perimeters of two regular polygons (in this case, hexagons)—one inscribed inside a circle and the other circumscribed around the outside of the circle.
A circle (black) shown with an inscribed hexagon (blue) and a circumscribed hexagon (mauve).
The circle is larger than one polygon and smaller than the other, so you can measure the perimeter of each polygon and calculate the average of the two perimeters to estimate the circumference of the circle.
Because any circle's circumference divided by its diameter equals pi, your estimated circumference divided by the diameter is an approximation of pi.
The larger the number of sides on the two polygons, the more accurate the approximations of pi. In the diagram (above), the polygons are hexagons. Archimedes used ninety-six-sided polygons. By the 1600s, mathematicians were using polygons with thousands of sides to find more and more digits of pi.
See also "Pick a Digit, Any Digit."
NEXT: Targeting Pi
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