Editing 217: e to the pi Minus pi
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==Explanation== | ==Explanation== | ||
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| − | + | ''e'' is a mathematical constant roughly equal to 2.71828182846. ''π'' is another, roughly equal to 3.14159265359. Both are {{w|transcendental number}}s. | |
| − | {{w| | + | The first panel discusses {{w|Gelfond's constant|''e''<sup>''π''</sup>}} − ''π'', which is around 19.999099979 — very close to 20. [[Black Hat]] explains how he tricked a programming team into believing that ''e''<sup>''π''</sup> − ''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). |
| − | + | {{w|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 {{w|integers}} and {{w|terminating decimal}}s). The "floating-point handlers" would be the code performing the ''e''<sup>''π''</sup> − ''π'' calculation. | |
| − | The title text pokes fun at another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, | + | ACM is the {{w|Association for Computing Machinery}}, which at the time of writing sponsored the {{w|ACM International Collegiate Programming Contest|International Collegiate Programming Contest}}. It is likely that it was this competition, in which Black Hat wasted his teams time, for which he got kicked out. |
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| + | Some random facts about the math here: | ||
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| + | * ''e''<sup>''π''</sup> − ''π'' is an irrational number, but this is not a trivial fact. It was proven by {{w|Yuri Valentinovich Nesterenko}} in the late 20th century. | ||
| + | * The mysterious almost-equation is believed to be a {{w|mathematical coincidence}}, or a numerical relationship that "just happens" with no satisfactory explanation. It can be rearranged to (π + 20)<sup>i</sup> ≈ −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<sup>−35</sup>. | ||
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| + | 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 {{w|transcendental number|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. | A much later comic, [[1047: Approximations]], puts forth quite a few more mathematical coincidences. | ||
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:Cueball: That's awful. | :Cueball: That's awful. | ||
:Black Hat: Yeah, they dug through half their algorithms looking for the bug before they figured it out. | :Black Hat: Yeah, they dug through half their algorithms looking for the bug before they figured it out. | ||
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{{comic discussion}} | {{comic discussion}} | ||
