217: e to the pi Minus pi - Revision history

DKMell: added link to 3023

2024-12-12T19:16:06Z

added link to 3023

172.68.205.123: /* Explanation */

2024-11-22T18:57:59Z

‎Explanation

172.70.243.32: /* Trivia */

2024-04-22T13:47:33Z

‎Trivia

162.158.87.206: /* Trivia */ better wiki-link

2024-04-22T13:46:23Z

‎Trivia: better wiki-link

162.158.87.206: /* Trivia */ No longer considered a coincidence, compare https://mathworld.wolfram.com/AlmostInteger.html and https://pastebin.com/VzqPG5Gk

2024-04-22T13:45:11Z

‎Trivia: No longer considered a coincidence, compare https://mathworld.wolfram.com/AlmostInteger.html and https://pastebin.com/VzqPG5Gk

Apollo11: moved radom math facts to trivia

2024-03-26T14:28:41Z

moved radom math facts to trivia

172.70.254.86: Add info on Ramanujan and title-text pi approximation

2023-10-10T11:30:08Z

Add info on Ramanujan and title-text pi approximation

172.69.22.49: /* Explanation */

2022-08-22T17:35:21Z

‎Explanation

Davidy22: Reverted edits by 108.162.246.124 (talk) to last revision by Lettherebedarklight

2022-05-27T06:53:54Z

Reverted edits by 108.162.246.124 (talk) to last revision by Lettherebedarklight

108.162.246.124 at 06:29, 27 May 2022

2022-05-27T06:29:01Z

@@ Line 18: / Line 18: @@
 The title text pokes fun at another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, equating close to π (deviating only from 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.
+A much later comic, [[1047: Approximations]], puts forth quite a few more mathematical coincidences, and [[3023: The Maritime Approximation]] does similarly for measurement units.
 ==Transcript==

@@ Line 16: / Line 16: @@
 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.
+The title text pokes fun at another coincidence: ∜(9² + 19²/22) ≈ 3.1415926525, equating close to π (deviating only from 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.

@@ Line 30: / Line 30: @@
 ==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}}.
+* 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}}.
 {{comic discussion}}

@@ Line 30: / Line 30: @@
 ==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 Jacobi identity.
+* 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}}

@@ Line 30: / Line 30: @@
 ==Trivia==
 * e<sup>π</sup> − π is an {{w|irrational number}}. 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>.
+* 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 Jacobi identity.
 {{comic discussion}}

@@ Line 15: / Line 15: @@
 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.
@@ Line 32: / Line 27: @@
 :Cueball: That's awful.
 :Black Hat: Yeah, they dug through half their algorithms looking for the bug before they figured it out.
 {{comic discussion}}

@@ Line 14: / Line 14: @@
 {{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 teams time, for which he got kicked out.
+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.
 Some random facts about the math here:

@@ Line 2: / Line 2: @@
 | number    = 217
 | date      = January 31, 2007
-| title     = e to the pi Minus thrembo
+| 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.