#numbertheory — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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I prefer ChatGPT for site/app/visual/media. But i prefer Claude for reports: Pedagogical report for Graduate / researcher new to the decomposition into weight × level + jump in 8 pages ➡️ https://decompwlj.com/weight-level-jump-in-eight-pages.html
#decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5
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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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🎩 Ah yes, the ancient art of number #wizardry where one ponders the sheer magnitude of 52! #factorial, as if anyone without a PhD in #math and a love affair with calculators would care. 🧙♂️ Apparently, Eli has cracked the code to estimating factorial sizes, ensuring that no one will ever have to endure the terror of large numbers without guidance. 📜 Too bad nobody asked.
https://eli.thegreenplace.net/2026/how-big-are-factorials/ #numbertheory #calculation #HackerNews #ngated -
🎩 Ah yes, the ancient art of number #wizardry where one ponders the sheer magnitude of 52! #factorial, as if anyone without a PhD in #math and a love affair with calculators would care. 🧙♂️ Apparently, Eli has cracked the code to estimating factorial sizes, ensuring that no one will ever have to endure the terror of large numbers without guidance. 📜 Too bad nobody asked.
https://eli.thegreenplace.net/2026/how-big-are-factorials/ #numbertheory #calculation #HackerNews #ngated -
🎩 Ah yes, the ancient art of number #wizardry where one ponders the sheer magnitude of 52! #factorial, as if anyone without a PhD in #math and a love affair with calculators would care. 🧙♂️ Apparently, Eli has cracked the code to estimating factorial sizes, ensuring that no one will ever have to endure the terror of large numbers without guidance. 📜 Too bad nobody asked.
https://eli.thegreenplace.net/2026/how-big-are-factorials/ #numbertheory #calculation #HackerNews #ngated -
🎩 Ah yes, the ancient art of number #wizardry where one ponders the sheer magnitude of 52! #factorial, as if anyone without a PhD in #math and a love affair with calculators would care. 🧙♂️ Apparently, Eli has cracked the code to estimating factorial sizes, ensuring that no one will ever have to endure the terror of large numbers without guidance. 📜 Too bad nobody asked.
https://eli.thegreenplace.net/2026/how-big-are-factorials/ #numbertheory #calculation #HackerNews #ngated -
🎩 Ah yes, the ancient art of number #wizardry where one ponders the sheer magnitude of 52! #factorial, as if anyone without a PhD in #math and a love affair with calculators would care. 🧙♂️ Apparently, Eli has cracked the code to estimating factorial sizes, ensuring that no one will ever have to endure the terror of large numbers without guidance. 📜 Too bad nobody asked.
https://eli.thegreenplace.net/2026/how-big-are-factorials/ #numbertheory #calculation #HackerNews #ngated -
"wlj atlas" has a new home ➡️ https://decompwlj.org
- 100 sequences decomposed with 3D/2D three.js graphs.
- Cinema: fullscreen, slow rotation.
- Compare: two sequences with linked cameras.#decompwlj #math #NumberTheory #sequence #graph #threejs #3D #AI #ChatGPT #GPT6 #Astra
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"wlj atlas" has a new home ➡️ https://decompwlj.org
- 100 sequences decomposed with 3D/2D three.js graphs.
- Cinema: fullscreen, slow rotation.
- Compare: two sequences with linked cameras.#decompwlj #math #NumberTheory #sequence #graph #threejs #3D #AI #ChatGPT #GPT6 #Astra
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"wlj atlas" has a new home ➡️ https://decompwlj.org
- 100 sequences decomposed with 3D/2D three.js graphs.
- Cinema: fullscreen, slow rotation.
- Compare: two sequences with linked cameras.#decompwlj #math #NumberTheory #sequence #graph #threejs #3D #AI #ChatGPT #GPT6 #Astra
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"wlj atlas" has a new home ➡️ https://decompwlj.org
- 100 sequences decomposed with 3D/2D three.js graphs.
- Cinema: fullscreen, slow rotation.
- Compare: two sequences with linked cameras.#decompwlj #math #NumberTheory #sequence #graph #threejs #3D #AI #ChatGPT #GPT6 #Astra
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"wlj atlas" has a new home ➡️ https://decompwlj.org
- 100 sequences decomposed with 3D/2D three.js graphs.
- Cinema: fullscreen, slow rotation.
- Compare: two sequences with linked cameras.#decompwlj #math #NumberTheory #sequence #graph #threejs #3D #AI #ChatGPT #GPT6 #Astra
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Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition
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Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition
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Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition
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Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition
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Opus 5 - High-res PNG (slight offset from the origin):
The triangular numbers are all level-classified#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #triangular #numbers #TriangularNumbers #NumberTheory #sieve #arithmetic #classification #decomposition
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What if we had discovered triangular numbers before multiplication was invented? I came to this question after I found an identity that connects triangular numbers
\[ \Delta(x) = \frac{x(x-1)}{2} \]
with multiplication, namely
\[ x y = \Delta(x + y) - \Delta(x) - \Delta(y). \]
To see why this is true, just draw the large triangle with edge length of \( x + y \) and remove the two smaller triangle from it — then a lozenge with \( x y \) points remains.
So if we had a pocket calculator with a \( \Delta \) key instead of a multiplication key, then we could still do all integer calculations that involve only addition and multiplication. But what about algebra? Here my results are mixed so far. When trying to translate the commutative law
\[ (x y) z = x (y z) \]
into triangular arithmetic, I got a long formula which provided no insight. But associativity,
\[ x (y + z) = x y + x z \]
is equivalent to the nice formula
\[\begin{align}
&\Delta(x + y + z) - \Delta(x + y) \\
&{} - \Delta(y + z) - \Delta(x + z) \\
&{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
\end{align}\] -
What if we had discovered triangular numbers before multiplication was invented? I came to this question after I found an identity that connects triangular numbers
\[ \Delta(x) = \frac{x(x-1)}{2} \]
with multiplication, namely
\[ x y = \Delta(x + y) - \Delta(x) - \Delta(y). \]
To see why this is true, just draw the large triangle with edge length of \( x + y \) and remove the two smaller triangle from it — then a lozenge with \( x y \) points remains.
So if we had a pocket calculator with a \( \Delta \) key instead of a multiplication key, then we could still do all integer calculations that involve only addition and multiplication. But what about algebra? Here my results are mixed so far. When trying to translate the commutative law
\[ (x y) z = x (y z) \]
into triangular arithmetic, I got a long formula which provided no insight. But associativity,
\[ x (y + z) = x y + x z \]
is equivalent to the nice formula
\[\begin{align}
&\Delta(x + y + z) - \Delta(x + y) \\
&{} - \Delta(y + z) - \Delta(x + z) \\
&{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
\end{align}\] -
What if we had discovered triangular numbers before multiplication was invented? I came to this question after I found an identity that connects triangular numbers
\[ \Delta(x) = \frac{x(x-1)}{2} \]
with multiplication, namely
\[ x y = \Delta(x + y) - \Delta(x) - \Delta(y). \]
To see why this is true, just draw the large triangle with edge length of \( x + y \) and remove the two smaller triangle from it — then a lozenge with \( x y \) points remains.
So if we had a pocket calculator with a \( \Delta \) key instead of a multiplication key, then we could still do all integer calculations that involve only addition and multiplication. But what about algebra? Here my results are mixed so far. When trying to translate the commutative law
\[ (x y) z = x (y z) \]
into triangular arithmetic, I got a long formula which provided no insight. But associativity,
\[ x (y + z) = x y + x z \]
is equivalent to the nice formula
\[\begin{align}
&\Delta(x + y + z) - \Delta(x + y) \\
&{} - \Delta(y + z) - \Delta(x + z) \\
&{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
\end{align}\] -
What if we had discovered triangular numbers before multiplication was invented? I came to this question after I found an identity that connects triangular numbers
\[ \Delta(x) = \frac{x(x-1)}{2} \]
with multiplication, namely
\[ x y = \Delta(x + y) - \Delta(x) - \Delta(y). \]
To see why this is true, just draw the large triangle with edge length of \( x + y \) and remove the two smaller triangle from it — then a lozenge with \( x y \) points remains.
So if we had a pocket calculator with a \( \Delta \) key instead of a multiplication key, then we could still do all integer calculations that involve only addition and multiplication. But what about algebra? Here my results are mixed so far. When trying to translate the commutative law
\[ (x y) z = x (y z) \]
into triangular arithmetic, I got a long formula which provided no insight. But associativity,
\[ x (y + z) = x y + x z \]
is equivalent to the nice formula
\[\begin{align}
&\Delta(x + y + z) - \Delta(x + y) \\
&{} - \Delta(y + z) - \Delta(x + z) \\
&{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
\end{align}\] -
What if we had discovered triangular numbers before multiplication was invented? I came to this question after I found an identity that connects triangular numbers
\[ \Delta(x) = \frac{x(x-1)}{2} \]
with multiplication, namely
\[ x y = \Delta(x + y) - \Delta(x) - \Delta(y). \]
To see why this is true, just draw the large triangle with edge length of \( x + y \) and remove the two smaller triangle from it — then a lozenge with \( x y \) points remains.
So if we had a pocket calculator with a \( \Delta \) key instead of a multiplication key, then we could still do all integer calculations that involve only addition and multiplication. But what about algebra? Here my results are mixed so far. When trying to translate the commutative law
\[ (x y) z = x (y z) \]
into triangular arithmetic, I got a long formula which provided no insight. But associativity,
\[ x (y + z) = x y + x z \]
is equivalent to the nice formula
\[\begin{align}
&\Delta(x + y + z) - \Delta(x + y) \\
&{} - \Delta(y + z) - \Delta(x + z) \\
&{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
\end{align}\]
