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| title    = e to the pi Minus pi
 
| title    = e to the pi Minus pi
 
| image    = e_to_the_pi_minus_pi.png
 
| image    = e_to_the_pi_minus_pi.png
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| imagesize =
 
| titletext = Also, I hear the 4th root of (9^2 + 19^2/22) is pi.
 
| titletext = Also, I hear the 4th root of (9^2 + 19^2/22) is pi.
 
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}}
  
 
==Explanation==
 
==Explanation==
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{{w|e (number)|e}} is a {{w|mathematical constant}} roughly equal to 2.71828182846. {{w|pi|π}} is another, roughly equal to 3.14159265359.
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"e" is a mathematical constant that is about equal to 2.71828182846. π is about equal to 3.14159665359.
  
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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).
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Computers use "floating point" numbers to store decimals. As noted in the comic, e^π - π is 19.999099979. However, Hat Guy's teammates' algorithms truncate to 3 decimal digits — giving a result of 19.999. Yet the programmers thought that 19.999 should come out to 20 unless they had errors in their algorithms (they did not; 19.999 would be the correct result).
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ACM is the Association for Computing Machinery; it sponsors the International Collegiate Programming Contest.
  
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{{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.
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:In the title text, another mathematical coincidence is presented. The 4th root of (9^2 + 19^2/22) is 3.1415926525, which is extremely close to pi (≈3.1415926535).
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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.
 
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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.
 
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A much later comic, [[1047: Approximations]], puts forth quite a few more mathematical coincidences.
 
  
 
==Transcript==
 
==Transcript==
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:Cueball: Hey, check it out: e<sup>π</sup> − π is 19.999099979. That's weird.
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: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.
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:Cueball: ...what?
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:Cueball: . . . what?
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: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.
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: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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==Trivia==
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{{comic discussion}}  
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* e<sup>π</sup> − π is an {{w|irrational number}}. It was proven by {{w|Yuri Valentinovich Nesterenko}} in the late 20th century.
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<!-- Include any categories below this line-->
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* At the time when this comic was published, 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}}.
 
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{{comic discussion}}
 
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Black Hat]]
 
[[Category:Comics featuring Black Hat]]
 
[[Category:Math]]
 
[[Category:Math]]
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[[Category:Programming]]
 

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