Pi Day: How the 'irrational' number pushed the limits of computing

March 14 is, by act of Congress, officially designated Pi Day.

Think about it for a minute and, if remember your high school math, you will understand why: 3.14 are the first three digits of Pi, which represent the ratio of the circumference of a circle to its diameter. If you are a purist you celebrated this occasion at 1:59 a.m. today (159 being the next three digits). If you use a 12-hour clock you could also celebrate at 1:59 p.m.

The value of Pi, an irrational number that goes on forever, has been figured to more than a trillion digits. We have neither the need nor the space for that here, but the challenge has helped to push the boundaries of computing.

According to Wikipedia, the day was first commemorated by physicist Larry Shaw of the San Francisco Exploratorium in 1988. It was confirmed by Congress in 2009, when House Resolution 224 was passed by a vote of 391 to 10, making Pi Day possibly one of the last issues on which congressional Republicans and Democrats found agreement.

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The significance of Pi goes well beyond high school mathematics. “It’s one of a few numbers that seem to be fundamental and basic in math,” said Daniel W. Lozier, retired lead of the mathematical software group in the Applied and Computational Mathematics Division of the National Institute of Standards and Technology.

Calculating the value of Pi has become something of a competition to mathematicians, and also has become an important tool in computing, Lozier said.

“It has played a role in computer programming and memory allocation and has led to ingenious algorithms that allow you to calculate this with high precision,” he said. “It’s a way of pushing computing machinery to its limits.”

Because of the large strings of numbers involved, memory is a critical issue in doing calculations along with methods for efficient calculations.

“Pi serves as a test case for mathematical studies in the area of number theory,” Lozier said.

One of the landmarks in calculating Pi was a 1962 paper by Daniel Shanks and John W. Wrench Jr. in the Mathematics of Computation. In 1949, it took the early ENIAC computer 70 hours to figure 2,037 digits of Pi. In 1959, it took an IBM 704 4 hours and 20 minutes to calculate it to 16,157 places. The authors of the paper estimated that it would take 167 hours and more than 38,000 words of memory to calculate to 100,000 places, but that could not be done because the IBM 704 did not have that capacity.

Using a new program and a new computer, the IBM 7090, in 1961 they were able to take the value to 100,000 places in 8 hours and 43 minutes, which was 20 times faster. The authors predicted that it would be another five to seven years before computers had the capacity to figure the value to 1 million places. In 1989, an IBM 3090 was able to take it to 1 billion places, which was pushed to 200 billion by 1999 and to 1.24 trillion places in 2005.

The record today is held by Japan’s T2K Supercomputer, which figured the value to 2.6 trillion digits in about 73 hours, 36 minutes.

The House resolution on Pi Day notes that “mathematics and science are a critical part of our children’s education, and children who perform better in math and science have higher graduation and college attendance rates.”

Unfortunately, it also notes that American children score well behind students in many other countries in science and math, and that the United States has shown only minimal improvement in test scores since 1995.

So the House recognized the designation of Pi Day and supports its celebration around the world, encouraging schools and educators to observe the day with “appropriate activities that teach students about Pi and engage them about the study of mathematics.”

H.R. 224 is non-binding, however, which is why you probably spend March 14 at work rather than celebrating at home with your family. But whether at work or at home, there are many uses of Pi. The most common, and the one you probably remember from high school, is figuring the area of a circle: A=Pi R-squared, where A is the area and R is the radius.

It also can be used to determine the volume of three-dimensional objects, such as a cylinder, which is useful in figuring the displacement of an internal combustion engine. Astronomers use it in figuring orbits and distances.

Unfortunately, it is not much use in cryptography, although modern crypto algorithms depend on random numbers. As an irrational number that goes on endlessly without repeating itself, Pi might seem like a good source of a random sequence, but since the value of Pi has been figured to so many decimal places, any sequence chosen from it is likely to be far too predictable to be secure. 

About the Author

William Jackson is a Maryland-based freelance writer.


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