113: Riemann-Zeta - Revision history

DKMell: error?

2024-12-14T00:42:50Z

error?

DKMell: minor fixes

2024-12-14T00:05:40Z

minor fixes

Jacky720: rv

2022-05-04T23:38:44Z

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Ex Kay Cee Dee at 23:38, 4 May 2022

2022-05-04T23:38:38Z

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Jacky720: rv

2022-05-04T21:08:20Z

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Ex Kay Cee Dee at 20:25, 4 May 2022

2022-05-04T20:25:03Z

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108.162.241.9: Decrapify

2022-05-04T19:30:53Z

Decrapify

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Ex Kay Cee Dee at 17:26, 4 May 2022

2022-05-04T17:26:35Z

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Davidy22 at 04:31, 4 May 2022

2022-05-04T04:31:16Z

Davidy22: Reverted edits by X. K. C. D. (talk) to last revision by Whymsie

2022-05-04T01:40:43Z

Reverted edits by X. K. C. D. (talk) to last revision by Whymsie

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@@ Line 14: / Line 14: @@
 Here, [[Randall]] appears to be talking to his significant other, comparing her to prime numbers and himself to the Riemann zeta function. It is mathematically correct and quite poetic, until he mentions that his relationship differs from the comparison because "The Riemann-zeta function couldn't have given you {{w|herpes}}." This implies that he has infected his lover with an incurable venereal disease. The comic effect of an abrupt change in tone like this is known as {{w|bathos}}.
-As the title text indicates, the graph in the picture is of the magnitude of ζ(''s'') for some section of the complex plane. Randall has forgotten the exact imaginary bounds of the graph, but he knows that the real axis goes from 0 to 2 and the imaginary axis goes from about 35''i'' to about 40''i''. The Z-axis is probably logarithmic, as the zeta function spans a large range of values.
+As the title text indicates, the graph in the picture is of the magnitude of ζ(''s'') for some section of the complex plane. Randall has forgotten the exact imaginary bounds of the graph, but he knows that the real axis goes from 0 to 2 and the imaginary axis goes from about 35''i'' to about 40''i''.
 ==Transcript==

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 A {{w|prime number}} is any natural number with exactly two natural factors (1 and itself). The set of prime numbers is infinite, but they are somewhat elusive; there is no known way to find very large prime numbers except by trial and error. Some regularities in the primes have been found, but none that can fully predict their distribution.
-The {{w|Riemann zeta function}}, errantly referred to as the Riemann-Zeta function in the comic, is a function that takes in {{w|complex numbers}} and returns complex numbers. It is defined for Re('s')>1 as <math>\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^s}</math>. For the rest of its domain (all complex numbers except 1), it is defined with {{w|analytic continuation}}. Its magnitude can be graphed in 3D, producing the "rippled curtain" referenced and depicted in the comic. There is a particular relationship between the Riemann zeta function and prime numbers, which makes the function a viable target for those attempting to understand primes.
+The {{w|Riemann zeta function}}, errantly referred to as the Riemann-zeta function in the comic, is a function that takes in {{w|complex numbers}} and returns complex numbers. It is defined for Re('s')>1 as <math>\zeta(s)=\sum_{n=1}^{\infty} \frac{1}{n^s}</math>. For the rest of its domain (all complex numbers except 1), it is defined with {{w|analytic continuation}}. Its magnitude can be graphed in 3D, producing the "rippled curtain" referenced and depicted in the comic. There is a deep relationship between the Riemann zeta function and prime numbers, which makes the function a useful target of study for those attempting to understand primes.
-Here, [[Randall]] appears to be talking to his significant other, comparing her to prime numbers and himself to the Riemann zeta function. It is mathematically correct and quite poetic, until he mentions that his relationship differs from the comparison because "The Riemann-Zeta function couldn't have given you {{w|herpes}}." This implies that he has infected his lover with an incurable venereal disease. The comic effect of an abrupt change in tone like this is known as {{w|bathos}}.
+Here, [[Randall]] appears to be talking to his significant other, comparing her to prime numbers and himself to the Riemann zeta function. It is mathematically correct and quite poetic, until he mentions that his relationship differs from the comparison because "The Riemann-zeta function couldn't have given you {{w|herpes}}." This implies that he has infected his lover with an incurable venereal disease. The comic effect of an abrupt change in tone like this is known as {{w|bathos}}.
-As the title text indicates, the graph in the picture is of the magnitude of ζ(''s'') for some section of the complex plane. Randall has forgotten the exact imaginary bounds of the graph, but he knows that the real axis goes from 0 to 2 and the imaginary axis goes from about 35''i'' to about 40''i''.
+As the title text indicates, the graph in the picture is of the magnitude of ζ(''s'') for some section of the complex plane. Randall has forgotten the exact imaginary bounds of the graph, but he knows that the real axis goes from 0 to 2 and the imaginary axis goes from about 35''i'' to about 40''i''. The Z-axis is probably logarithmic, as the zeta function spans a large range of values.
 ==Transcript==
-:[A z = fn(x, y) plot, with pointy spikes on the back sloping to a relatively flat front.]
+:[A z = fn(x,y) plot, with pointy spikes on the back sloping to a relatively flat front.]
 :You are like the prime numbers
@@ Line 23: / Line 23: @@
 :Tantalizingly regular but never quite the same
-:I am like the Riemann-Zeta function
+:I am like the Riemann-zeta function
 :A rippled curtain of the imagined and real
 :Deeply tied with you in ways incomprehensible
-:Although, strictly speaking, The Riemann-Zeta function couldn't have given you herpes
+:Although, strictly speaking, The Riemann-zeta function couldn't have given you herpes
 {{comic discussion}}

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