217: e to the pi Minus pi
|e to the pi Minus pi|
Title text: Also, I hear the 4th root of (9^2 + 19^2/22) is pi.
e is a mathematical constant roughly equal to 2.71828182846. π is another, roughly equal to 3.14159265359. Both are transcendental numbers.
The first panel discusses eπ − π, which is around 19.999099979 — very close to 20. Black Hat explains how he tricked a programming team into believing that eπ − π really equals 20 - instead of just being weirdly close - thus that any noticeable deviation from 20 results from errors in the code. This made them waste a lot of time trying to find a nonexistent bug until they realized that Black Hat was lying (clearly they had not known him for very long).
Floating point numbers are how computers store non-integer real numbers as decimals — or rather, in most cases, approximate them: infinite amounts of data would be required to represent most numbers in decimal form (exceptions are whole numbers and terminating decimals). The "floating-point handlers" would be the code performing the eπ − π calculation.
Some random facts about the math here:
- eπ − π is an irrational number, but this is not a trivial fact. It was proven by Yuri Valentinovich Nesterenko in the late 20th century.
- The mysterious almost-equation is believed to be a mathematical coincidence, or a numerical relationship that "just happens" with no satisfactory explanation. It can be rearranged to (π + 20)i ≈ −1, so cos(ln(π + 20)) ≈ −1. Piling on a few more cosines gives cos(π cos(π cos(ln(π + 20)))) ≈ −1, which is off by less than 10−35!
The title text pokes fun at another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, close to π (deviating only in the 9th decimal place). The humor comes from the fact that π is transcendental. Transcendental numbers are numbers that cannot be expressed through basic arithmetic with integers; one cannot end up with the exact value for any transcendental number (including π) by adding, subtracting, multiplying, dividing, exponentiating, and/or taking the nth root of any rational number, meaning the title text cannot possibly be true.
A much later comic, 1047: Approximations, puts forth quite a few more mathematical coincidences.
- Cueball: Hey, check it out: eπ − π is 19.999099979. That's weird.
- Black Hat: Yeah. That's how I got kicked out of the ACM in college.
- Cueball: ...what?
- Black Hat: During a competition, I told the programmers on our team that eπ − π was a standard test of floating-point handlers -- it would come out to 20 unless they had rounding errors.
- Cueball: That's awful.
- Black Hat: Yeah, they dug through half their algorithms looking for the bug before they figured it out.
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