No number can claim more fame than pi. But why, exactly?
Defined as the ratio of the circumference of a circle to its diameter, pi, or in symbol form, π, seems a simple enough concept. But it turns out to be an "irrational number," meaning its exact value is inherently unknowable. Computer scientists have calculated billions of digits of pi, starting with 3.14159265358979323…, but because no recognizable pattern emerges in the succession of its digits, we could continue calculating the next digit, and the next, and the next, for millennia, and we'd still have no idea which digit might emerge next. The digits of pi continue their senseless procession all the way to infinity.
Ancient mathematicians apparently found the concept of irrationality completely maddening. It struck them as an affront to the omniscience of God, for how could the Almighty know everything if numbers exist that are inherently unknowable?
Whether or not humans and gods grasp the irrational number, pi seems to crop up everywhere, even in places that have no ostensible connection to circles. For example, among a collection of random whole numbers, the probability that any two numbers have no common factor — that they are "relatively prime" — is equal to 6/π2. Strange, no?
But pi's ubiquity goes beyond math. The number crops up in the natural world, too. It appears everywhere there's a circle, of course, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi also appears in the physics that describes waves, such as ripples of light and sound. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg's uncertainty principle.
Finally, pi emerges in the shapes of rivers. 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. Rivers that flow straight from source to mouth have small meandering ratios, while ones that lollygag along the way have high ones. Turns out, the average meandering ratio of rivers approaches — you guessed it — pi.
Albert Einstein was the first to explain this fascinating fact. He used fluid dynamics and chaos theory to show that rivers tend to bend into loops. 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. 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.
Because 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.
17 Facts to Crack the Mystery of Pi
1. Pi is officially defined as the ratio of the circumference of a circle to its diameter. But don’t try to pin it down—its decimals go on forever and ever. Because of its handiness in formulas in fields from trigonometry to cosmology and biology, pi is the most commonly recognized constant in the math world. Nice!
2. The exact origin of its discovery is unknown, but may have arisen from a hunt led by the Babylonians. Or the Egyptians. Maybe Dennis Rodman was involved (read: no one really knows).
3. Its first 144 digits add up to 666—which Satanists claim is “the mark of the beast.” Spooky.
4. Appropriately, the yearly celebration of pi begins on 3/14 at 1:59 p.m. Sing it: Today we’re gonna’ party like it’s 3.14159.
5. Humans have been searching for the end of pi’s infinite digits for 3,500 years. It cannot be solved by computers. Apple be damned!
6. Albert Einstein was born on pi day: March 14, 1879.
7. It’s irrational (who isn’t?) and transcendental (jealous).
8. It’s been represented by the 16th letter of the Greek alphabet, “π,” since the 1700s. You also refer it by the fraction 22/7 if you want to be imprecise about the whole thing.
9. It shows up everywhere on the earth. Literally. We have pi in our eyes.
10. During O.J. Simpson’s murder trial, the judge and FBI agent tried to show off their smarts by debating the value of pi.
11. Some have given their lives in the name of pi. Archimedes, a brilliant mathematician in ancient Greece, spent his life trying to solve the ratio, only to be murdered by a Roman soldier while yelling “do not touch my circles.”
12. Its Greek symbol was suggested by English mathematician William Jones in 1706. He would have loved emojis.
13. Comedian John Evans once famously quipped: "What do you get when you divide the circumference of a jack-o'-lantern by its diameter? Pumpkin pi.” Mmm.
14. In 2010, Japanese system engineer Shigeru Kondo and U.S. computer whiz Alexander Yee broke the record for most digits of pi calculated, making it to five trillion decimal places using nothing but desktop computers, 20 external hard drives, and their freaking genius brains.
15. If trying to solve the ratio isn’t torture enough, you can join the millions of people who attempt to memorize it each year. Chinese math guru Lu Chao currently holds the Guinness World Record for most memorized digits. He dished out 67,890 in 24 hours and four minutes. Ow, his brain.
16. Today is one of the few days of the year that walking in circles is encouraged and eating pie in the early afternoon isn’t awkward.
17. Spoiler alert! The secret code in Alfred Hitchcock’s 1966 thriller Torn Curtain is pi.
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