There's A Formula That Gives The First 18 Trillion Trillion Digits Of The Constant e

Brilliance | Dec. 17, 2017

Math can be dry, sure. But it can also blow your mind in unexpected ways. Take this formula for example: (1+9^-4^6x7)^3^2^85, which equals 2.71828... Besides looking like someone accidentally spilled about five extra exponents on it, this formula gives the you the first 18 trillion trillion digits of the mathematical constant e. No typo here—that's 18 trillion trillion. The formula is also pandigital, which is just plain strange.

Do You Know What Pandigital Means?

This exponents-gone-wild formula is a scarily accurate representation of the mathematical constant e. But, there's another weird-but-cool fact about this incredible formula: it's pandigital. As WolframMathWorld describes it, "A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities contain the digits 1 through 9. Sometimes exclusivity is also required so that each digit is restricted to appear exactly once." Is the fact that this formula pandigital relevant in any way? Not really. But hopefully you at least learned a new vocabulary word.

Why Do We Care About e So Much?

The mathematical constant e is one of the most important constants in math. It is sometimes called the Euler constant, after the Swiss mathematician Leonhard Euler, who was the first to use the letter e for the irrational number (the idea that he chose that letter because of his last initial is probably apocryphal).

What's so special about e? Take it from Popular Mechanics: "It's one of the most useful mathematical constants. If you graph the equation y=e<sup>x</sup>, what you'll find is that the slope of that curve at any given point is also e<sup>x</sup>, and the area under the curve from negative infinity up to x is also e<sup>x</sup>. e is the only number in all of mathematics that can be plugged into the equation y=n<sup>x</sup> for which this pattern is true. In calculus, which is all about finding slopes and areas, you can imagine that e is a pretty important number. It's also an important number in physics, where it shows up in the equations for waves, such as light waves, sound waves, and quantum waves."

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