# Difference between revisions of "217: e to the pi Minus pi"

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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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| 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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"e" is a mathematical constant that is about equal to 2.71828182846. π is about equal to 3.14159265359. | "e" is a mathematical constant that is about equal to 2.71828182846. π is about equal to 3.14159265359. | ||

− | Computers use "floating point" numbers to store decimals. As noted in the comic, e^π - π is 19.999099979. However, Hat | + | Computers use "floating point" numbers to store decimals. As noted in the comic, e^π - π is 19.999099979. However, [[Black Hat]]'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). ACM is the Association for Computing Machinery; it sponsors the International Collegiate Programming Contest. |

− | ACM is the Association for Computing Machinery; it sponsors the International Collegiate Programming Contest. | ||

− | + | 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). | |

==Transcript== | ==Transcript== | ||

:Cueball: Hey, check it out: e^pi-pi is 19.999099979. That's weird. | :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^pi-pi was a standard test of floating-point handlers--it would come out to 20 unless they had rounding errors. | :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. | ||

− | {{comic discussion}} | + | {{comic discussion}} |

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[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||

[[Category:Comics featuring Black Hat]] | [[Category:Comics featuring Black Hat]] | ||

[[Category:Math]] | [[Category:Math]] | ||

+ | [[Category:Programming]] |

## Revision as of 08:56, 20 February 2013

e to the pi Minus pi |

Title text: Also, I hear the 4th root of (9^2 + 19^2/22) is pi. |

## Explanation

"e" is a mathematical constant that is about equal to 2.71828182846. π is about equal to 3.14159265359.

Computers use "floating point" numbers to store decimals. As noted in the comic, e^π - π is 19.999099979. However, Black Hat'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). ACM is the Association for Computing Machinery; it sponsors the International Collegiate Programming Contest.

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).

## Transcript

- 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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# Discussion

Asserting that the programmers' algorithms truncated to three decimal digits is an unsupported and unnecessary extrapolation. Most floating-point implementations use binary, not decimal, and 19.999099979 *looks* very much like a rounding error in binary floating-point that has accumulated over several operations. Daddy (talk) 12:39, 29 April 2013 (UTC)

The third bullet-point above needs changing... (9^2+(19^2/22))=97.4090909091 which is close to pi to the fourth power, so it should be (as noted in the text) (9^2+(19^2/22))^1/4 Squirreltape (talk) 19:27, 25 February 2014 (UTC)

- Actually, in-case you didn't notice, it says "∜(9² + 19²/22)", not just the sum on its own. I checked the sum on my calculator, and it is equal to what the page is saying. "∜(9² + 19²/22)" means "4th root of (9^2+19^2/22)" (What the title text is saying), or on Windows Calculator, "(9^2+19^2/22) yroot(4)" (Basically what the sum is saying). So, the 3rd bullet point is correct. --Katavschi (talk) 22:48, 23 April 2014 (UTC)

It says above that (π + 20)^i ≈ -i, but this should be (π + 20)^i ≈ -1. Proof: π + 20 ≈ e^π => (π + 20)^i ≈ (e^π)^i = e^(πi) = -1.

The ACM competitions are famous for being under tight time pressure. Making your own team waste time would absolutely get you kicked out (and make enemies) Mountain Hikes (talk) 04:40, 23 September 2015 (UTC)

- "If they thought about the mathematics"

hm, are you saying it is obvious that e^ pi - pi is not 20? How would you know without approximating it? The sum of two irrationals is not necessarily irrational. 162.158.34.194 01:58, 26 October 2015 (UTC)

- approximate e^pi using slightly bigger numbers than e and pi (say e: 2.7183 and pi: 3.1416) and subtract a value that is slightly smaller than pi (say 3.1415). The result is less than 20 and a upper limit for e^pi - pi 141.101.93.49 19:59, 22 August 2016 (UTC)