Editing 217: e to the pi Minus pi

{{comic
| number    = 217
| date      = January 31, 2007
| title     = e to the pi Minus pi
| image     = e_to_the_pi_minus_pi.png
| titletext = Also, I hear the 4th root of (9^2 + 19^2/22) is pi.
}}

==Explanation==
{{w|e (number)|e}} is a {{w|mathematical constant}} roughly equal to 2.71828182846. {{w|pi|π}} is another, roughly equal to 3.14159265359.

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.

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 team's time, for which he got kicked out.

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 {{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. This coincidence was discovered by Ramanujan while {{w|squaring the circle}} in 1914.

A much later comic, [[1047: Approximations]], puts forth quite a few more mathematical coincidences.

==Transcript==
:Cueball: Hey, check it out: e<sup>π</sup> − 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 e<sup>π</sup> − 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.

==Trivia==
* e<sup>π</sup> − π is an {{w|irrational number}}. It was proven by {{w|Yuri Valentinovich Nesterenko}} in the late 20th century.
* Until recently, the mysterious almost-equation e<sup>π</sup> − π ≈ 20 was believed to be a {{w|mathematical coincidence}}, or a numerical relationship that "just happens" with no satisfactory explanation. In September 2023, an explanation was found based on the {{w|Theta_function#Jacobi_identities|Jacobi identities}}.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Black Hat]]
[[Category:Math]]
[[Category:Programming]]