Memorizing Pi

Nerds seem to be mesmerized by the idea of memorizing π to the maximum number of digits possible. Since π is irrational, and therefore infinite, this is inherently an exercise in futility. Nevertheless, thousands of nerds have applied themselves to the task. The current world record holder is Chao Lu of China, who in 2005 recited π to 67,890 decimal places. Presumably he then collapsed and wept.

But how many digits of π do you actually need to compute the numbers you need in your daily life? Did a hear a resounding “NONE!” there? Well, you might be surprised. For example, let’s say you’re an amoral real estate developer who has just greased enough palms to bulldoze a property full of low-income housing and put up fashionable high-priced condominiums. The area is one mile in radius, so you know you can build a boatload of condos. But how many, exactly, might that be? To know that number, you’d have to compute the area, and for that you need π. The formula for the area of a circle is A= π * r^2, the famous “pie are square” of the ancient hillbilly joke. If you take π as 0 digits of decimal accuracy, it becomes simply ‘3’, so the area is 3 square miles. But that answer is actually .14 sq. miles (almost 4 million square feet) less than the actual area. You can build a lot of condos on that amount of land. So clearly, our hypothetical contractor will want to know π to more digits than that. It turns out that π to 4 digits (3.1415) is just about close enough. It comes up only 2583 sq. ft. short of the actual area. Of course, you might be able to squeeze one more condo into that much space, so 5 digits is probably best; using 3.14159 leaves only 74 sq. ft., much too small a spot on which to place even the smallest condominium. But if he wanted to make sure he had it down to an accuracy of 1 sq. ft., he’d have to know π to 7 digits: 3.1415926.

But what if you’re an astronaut trying to hit Mars? Mars is, at its closest, 34.65 million miles from earth. Let’s say that you’ve got a hotshot cowboy astronaut (aren’t they all) piloting your spacecraft who can get you into Mars orbit if you come within one Martian diameter of where you’re supposed to be. Turns out that π to 4 digits is enough. But if you want to be within 3 ft. of your target, you’d need π to 11 digits: 3.14159265358.

So when do you need π to 10,000 digits in real life? Never, obviously. I know it to 15 digits and have never needed even close to that much accuracy. So go ahead and be satisfied with knowing that π=3.1416 (rounded, of course). I doubt you’ll ever need much more than that. But if you do, you always can look it up online. Here it is to 1 million digits.

BONUS: There is a theoretical maximum linear distance which is the circumference of the universe. There is also a shortest possible length, which is incredibly small, called the planck length. What are the maximum number of digits of π you would need to calculate the circumference of the universe(hint: its diameter is approximately 93 billion light years) to within plus or minus one planck length? Okay, begin…

ANSWER: Not that anyone asked, but the answer is 39 (sorry, not 42). But we’ve gone ahead and calculated it to one trillion places, just in case.

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