#numbertheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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GTP-6 Astra: pedagogical report for Graduate / researcher new to the decompwlj: from Gaps to Divisor Geometry
https://decompwlj.com/GPT_Astra_decompwlj_graduate_report_2026-09-11.html#decompwlj #math #NumberTheory #AI #report #PrimeNumbers #GPT6 #Astra
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I've always found it cool that if you double the smaller acute angle in a 3-4-5 triangle you get the larger acute angle in a 7-24-25 right triangle. You can see this as a consequence of the double angle formula for sine. If \( \alpha \) is the smaller acute angle in a 3-4-5 triangle, then
\[ \sin (2\alpha) = 2\sin\alpha\cos\alpha=2\frac{3}{5}\frac{4}{5}=\frac{24}{25}\]
In fact, if the sine and cosine of an angle are both rational, then so will be the sine and cosine of twice that angle. This gives a way to turn Pythagorean triples into new Pythagorean triples!
For example, suppose \( \alpha \) is an acute angle in a right triangle with \(a^2 + b^2 = c^2 \). Then
\[ \sin 2\alpha = \frac{2ab}{c^2} \]
\[ \cos 2 \alpha = \frac{a^2-b^2}{c^2} \]By the Pythagorean identity
\[ \left(\frac{2ab}{c^2} \right)^2 + \left(\frac{a^2-b^2}{c^2} \right)^2 = 1\]
And so
\[ \left(2ab \right)^2 + \left(a^2-b^2 \right)^2 = \left(c^2\right)^2\]
which of course also follows directly from algebra.For example, using this process
\[ (3,4,5) \mapsto (7,24,25) \mapsto(336,527,625)\]