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.
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, and clearly they weren't very knowledgeable in mathematics).
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 integers and terminating decimals). The "floating-point handlers" would be the code performing the eπ − π calculation.
ACM is the Association for Computing Machinery, which at the time of writing sponsored the International Collegiate Programming Contest. It is likely that it was this competition, in which Black Hat wasted his team's time, for which he got kicked out.
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 3.932×10−35.
The title text pokes fun at another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, equating 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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