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#numbertheory — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #numbertheory, aggregated by home.social.

  1. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  2. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  3. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  4. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  5. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  6. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  7. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  8. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  9. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  10. 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 ➡️ decompwlj.com/weight-level-jum

    #decompwlj #math #NumberTheory #numbers #sieve #Claude #Anthropic #Opus5

  11. 🎩 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.
    eli.thegreenplace.net/2026/how #numbertheory #calculation #HackerNews #ngated

  12. 🎩 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.
    eli.thegreenplace.net/2026/how #numbertheory #calculation #HackerNews #ngated

  13. 🎩 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.
    eli.thegreenplace.net/2026/how #numbertheory #calculation #HackerNews #ngated

  14. 🎩 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.
    eli.thegreenplace.net/2026/how #numbertheory #calculation #HackerNews #ngated

  15. 🎩 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.
    eli.thegreenplace.net/2026/how #numbertheory #calculation #HackerNews #ngated

  16. "wlj atlas" has a new home ➡️ 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

  17. "wlj atlas" has a new home ➡️ 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

  18. "wlj atlas" has a new home ➡️ 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

  19. "wlj atlas" has a new home ➡️ 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

  20. "wlj atlas" has a new home ➡️ 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

  21. 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

    \[\begin{align}
    &\Delta(x + y + z) - \Delta(x + y) \\
    &{} - \Delta(y + z) - \Delta(x + z) \\
    &{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
    \end{align}\]

    #Mathematics #Arithmetic #NumberTheory #TriangularNumbers

  22. 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

    \[\begin{align}
    &\Delta(x + y + z) - \Delta(x + y) \\
    &{} - \Delta(y + z) - \Delta(x + z) \\
    &{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
    \end{align}\]

    #Mathematics #Arithmetic #NumberTheory #TriangularNumbers

  23. 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

    \[\begin{align}
    &\Delta(x + y + z) - \Delta(x + y) \\
    &{} - \Delta(y + z) - \Delta(x + z) \\
    &{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
    \end{align}\]

    #Mathematics #Arithmetic #NumberTheory #TriangularNumbers

  24. 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

    \[\begin{align}
    &\Delta(x + y + z) - \Delta(x + y) \\
    &{} - \Delta(y + z) - \Delta(x + z) \\
    &{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
    \end{align}\]

    #Mathematics #Arithmetic #NumberTheory #TriangularNumbers

  25. 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

    \[\begin{align}
    &\Delta(x + y + z) - \Delta(x + y) \\
    &{} - \Delta(y + z) - \Delta(x + z) \\
    &{} + \Delta(x) + \Delta(y) + \Delta(z) = 0.
    \end{align}\]

    #Mathematics #Arithmetic #NumberTheory #TriangularNumbers