Biting off a Record-Breaking Piece of Pi
Peterson, I., Science News
Biting off a record-breaking piece of pi
"Compute but verify" is the strategy at the core of a remarkable new method for calculating pi ([pi])--the ratio of a circle's circumference to its diameter. In a recent demonstration of the method's power, two mathematicians at Columbia University in New York City used it to compute pi to 480 million decimal places, shattering the previous record of 201 million digits (SN: 4/2/88, p. 215).
"Our goal is to develop a better understanding of the arithmetic properties of [constants such as pi]," says David V. Chudnovsky, who with his brother Gregory discovered the key formulas for the computation. With so many digits of pi now available for analysis, the Chudnovskys are seeing the first hints of subtle patterns in the distribution of pi's digits, suggesting the digits may not be truly random.
Computing pi also gives the largest and fastest computers a thorough workout, pinpointing subtle flaws in their hardware and software. "It is really the ultimate stress test--a cardiogram for a computer," Chudnovsky says. In the course of their calculations, the Chudnovskys identified unexpected quirks peculiar to the computers they used.
The new formula, or identity, discovered and used by the Chudnovskys expresses pi as a complicated sum. By evaluating more and more terms in such a sum, mathematicians get closer and closer to the true value of pi. This particular identity gets closer to pi faster than any other known formula. …