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19 April 2024
| m 04:35 | Pi is Irrational diffhist +50 Robkahn131 talk contribs | ||||
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N 04:30 | Pi Squared is Irrational/Proof 1/Lemma 2 changes history +5,207 [Robkahn131 (2×)] | |||
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04:30 (cur | prev) −9 Robkahn131 talk contribs | |||
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04:26 (cur | prev) +5,216 Robkahn131 talk contribs (Created page with "== Pi Squared is Irrational/Proof 1: Lemma == <onlyinclude> Let $n \in \Z_{> 0}$ be a positive integer. Let $A_n$ be defined as: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x$ Let $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Note that $\paren {q \pi}^2 = q^2 \paren {\dfrac p q} = p q$ is an integer. Then: :$A_n = \paren {4 n -...") | |||
| 04:27 | Pi Squared is Irrational/Proof 1 diffhist −4,346 Robkahn131 talk contribs | ||||
18 April 2024
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17:02 | Template:Eqn 3 changes history 0 [Prime.mover (3×)] | |||
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17:02 (cur | prev) −17 Prime.mover talk contribs (Didn't work. Ideas, anyone?) Tag: Manual revert | ||||
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17:01 (cur | prev) −17 Prime.mover talk contribs Tag: Reverted | ||||
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16:59 (cur | prev) +34 Prime.mover talk contribs Tag: Reverted | ||||
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06:32 | Pi Squared is Irrational/Proof 1 2 changes history +4,913 [Robkahn131; Prime.mover] | |||
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06:32 (cur | prev) +285 Prime.mover talk contribs | ||||
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00:34 (cur | prev) +4,628 Robkahn131 talk contribs (filled in a few clarifying details) | |||
16 April 2024
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N 06:53 | Pi Squared is Irrational/Proof 2 3 changes history +3,770 [Simcha Waldman; Prime.mover (2×)] | |||
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06:53 (cur | prev) −314 Simcha Waldman talk contribs (Re-editing and explaining) | ||||
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06:00 (cur | prev) +1,126 Prime.mover talk contribs | ||||
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05:06 (cur | prev) +2,958 Prime.mover talk contribs (Created page with "== Theorem == {{:Pi Squared is Irrational}} == Proof == {{tidy}} {{MissingLinks}} <onlyinclude> {{AimForCont}} $\pi^2$ is rational. Then $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Let us define a polynomial: :$\ds \map f x = \frac{(1-x^2)^n}{n!} = \sum_{m\,=\,n}^{2n}\frac{c_m}{n!}x^m,\quad:c_m\in\Z$ $\map f x = f(-x)$ and so we get {{begin-eqn}} {{eqn | l = f^{(k)}(x) = (-1)^kf^{(k)}(-x)...") | |||
| N 05:05 | Pi Squared is Irrational/Proof 1 diffhist +2,341 Prime.mover talk contribs (Created page with "== Theorem == {{:Pi Squared is Irrational}} == Proof == <onlyinclude> {{AimForCont}} $\pi^2$ is rational. Then $\pi^2 = \dfrac p q$ where $p$ and $q$ are integers and $q \ne 0$. Note that $\paren {q \pi}^2 = q^2 \paren {\dfrac p q} = p q$ is an integer. Now let: :$\ds A_n = \frac {q^n} {n!} \int_0^\pi \paren {x \paren {\pi - x} }^n \sin x \rd x $ Integration by Parts twice gives: {{b...") | ||||
15 April 2024
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N 20:13 | Talk:Pi Squared is Irrational 2 changes history +257 [Simcha Waldman; Prime.mover] | |||
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20:13 (cur | prev) +107 Prime.mover talk contribs | ||||
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19:43 (cur | prev) +150 Simcha Waldman talk contribs (Created page with "I would like to add a second proof to this page. ~~~~") | |||