So three-digit numbers require nine multiplications, while 100-digit numbers require 10,000 multiplications. The grade school or “carrying” method requires about n 2 steps, where n is the number of digits of each of the numbers you’re multiplying. If you’re multiplying two two-digit numbers, you end up performing four smaller multiplications to produce a final product. We stack two numbers, multiply every digit in the bottom number by every digit in the top number, and do addition at the end. Most everyone learns to multiply the same way. “If you want to know how fast computers can solve certain mathematical problems, then integer multiplication pops up as some kind of basic building brick with respect to which you can express those kinds of speeds.” “In physics you have important constants like the speed of light which allow you to describe all kinds of phenomena,” van der Hoeven said. Van der Hoeven describes their result as setting a kind of mathematical speed limit for how fast many other kinds of problems can be solved. The complexity of many computational problems, from calculating new digits of pi to finding large prime numbers, boils down to the speed of multiplication.
“Everybody thinks basically that the method you learn in school is the best one, but in fact it’s an active area of research,” said Joris van der Hoeven, a mathematician at the French National Center for Scientific Research and one of the co-authors. The paper marks the culmination of a long-running search to find the most efficient procedure for performing one of the most basic operations in math. On March 18, two researchers described the fastest method ever discovered for multiplying two very large numbers. We're also on Facebook & Google+.Four thousand years ago, the Babylonians invented multiplication. This process will gradually tighten the loop, until chaos causes the river to suddenly double back on itself, at which point it will begin forming a loop in the other direction.īecause the length of a near-circular loop is like the circumference of a circle, while the straight-line distance from one bend to the next is diameter-like, it makes sense that the ratio of these lengths would be pi-like.įollow Natalie Wolchover on Twitter nattyover or Life's Little Mysteries llmysteries. The slightest curve in a river will generate faster currents on the outer side of the curve, which will cause erosion and a sharper bend. He used fluid dynamics and chaos theory to show that rivers tend to bend into loops. Turns out, the average meandering ratio of rivers approaches - you guessed it - pi.Īlbert Einstein was the first to explain this fascinating fact. Rivers that flow straight from source to mouth have small meandering ratios, while ones that lollygag along the way have high ones. A river's windiness is determined by its "meandering ratio," or the ratio of the river's actual length to the distance from its source to its mouth as the crow flies.
Finally, pi emerges in the shapes of rivers.
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