(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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We already know how to simplify Ta thx Gauss
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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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UMBRELLA CORPORATION
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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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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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That makes more sense now...
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Thanks. I was really confused by your first tweet.pic.twitter.com/rnMRNJn51C
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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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