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|Irrational number|irrational numbers}}. | |
− | {{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'' is ''exactly'' 20, and that if the system they were building didn't agree, there were 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. |
− | + | {{w|Floating point}} numbers are how computers store real numbers -- or rather, approximate them: a true real number requires infinite amounts of data to represent. The "floating-point handlers" would be the code performing the ''e''<sup>''π''</sup> - ''π'' calculation. | |
− | + | ACM is the {{w|Association for Computing Machinery}}, sponsoring the {{w|ACM International Collegiate Programming Contest|International Collegiate Programming Contest}}. | |
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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> ≈ -i, 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<sup>-35</sup>! | ||
+ | * The title text gives another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, close to ''π''. | ||
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. | ||
==Transcript== | ==Transcript== | ||
− | :Cueball: Hey, check it out: e | + | :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. | :Black Hat: Yeah. That's how I got kicked out of the ACM in college. | ||
:Cueball: ...what? | :Cueball: ...what? | ||
− | :Black Hat: During a competition, I told the programmers on our team that e | + | :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. | :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}} |