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 is close enough to 20 that the computer should be unable to tell the difference, and 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 whole 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: e^pi-pi 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 e^pi-pi 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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