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@fermatslibrary | |||||
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Here's a visual proof that (2a+1)²=8Tₐ+1, where Tₐ is a triangle number Tₐ = 1+2+...+a
⚫️🔴🔴🔴🔴⚫️⚫️⚫️⚫️
⚫️⚫️🔴🔴🔴⚫️⚫️⚫️🔴
⚫️⚫️⚫️🔴🔴⚫️⚫️🔴🔴
⚫️⚫️⚫️⚫️🔴⚫️🔴🔴🔴
🔴🔴🔴🔴🔵🔴🔴🔴🔴
🔴🔴🔴⚫️🔴⚫️⚫️⚫️⚫️
🔴🔴⚫️⚫️🔴🔴⚫️⚫️⚫️
🔴⚫️⚫️⚫️🔴🔴🔴⚫️⚫️
⚫️⚫️⚫️⚫️🔴🔴🔴🔴⚫️
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jcmdubreuil
@jcmdubreuil
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2. velj |
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(2a + 1)²=8Tₐ + 1
⇔
4a² + 4a + 1 = 8Tₐ + 1
⇔
4a² + 4a = 8Tₐ
⇔
a² + a = 2Tₐ
⇔
a(a + 1) = 2Tₐ
⇔
a(a + 1)÷2 = Tₐ
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Lecoss
@julien_lecoz
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2. velj |
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We already know how to simplify Ta thx Gauss
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.
@Expert_Says
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2. velj |
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Is there any visual proof for this product rule of triangular numbers
T(mn) = T(m) T(n) + T(m − 1) T(n − 1) ( m,n ≥ 1)
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Jens Kristian Egsgaard
@EgsgaardJens
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2. velj |
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RE5CEPT
@Luis49Valera
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2. velj |
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UMBRELLA CORPORATION
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Roger Sauer
@rsauer3473
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2. velj |
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When Diarmuid Feeney (1834-1906) sought visual proof of his wife Siobhan’s unfaithfulness, he used flypaper, groats, and a piece of cheap muslin to catch them in flagrante delicto. His mailman was found in the closet. As was his delicto.
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Hayder
@haydermakkaoui
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2. velj |
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This is beautiful but feels like we are missing so much fun in multidimensional algebra as we can't visualize it in such a way.
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AncientSwordRage
@PureFerret
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2. velj |
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That makes more sense now...
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donavon "spread love" west
@donavon
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2. velj |
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Thanks. I was really confused by your first tweet. pic.twitter.com/rnMRNJn51C
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Nikolas
@knottyboy26
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2. velj |
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I am waiting to see how many will get offended by this math post. pic.twitter.com/LhTesYok1X
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