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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 2. velj
Odgovor korisniku/ci @fermatslibrary
(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 2. velj
Odgovor korisniku/ci @jcmdubreuil @fermatslibrary
We already know how to simplify Ta thx Gauss
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. 2. velj
Odgovor korisniku/ci @fermatslibrary
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 2. velj
Odgovor korisniku/ci @Expert_Says @fermatslibrary
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RE5CEPT 2. velj
Odgovor korisniku/ci @fermatslibrary
UMBRELLA CORPORATION
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Roger Sauer 2. velj
Odgovor korisniku/ci @fermatslibrary
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 2. velj
Odgovor korisniku/ci @fermatslibrary
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 2. velj
Odgovor korisniku/ci @fermatslibrary
That makes more sense now...
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donavon "spread love" west 2. velj
Odgovor korisniku/ci @fermatslibrary
Thanks. I was really confused by your first tweet.
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Nikolas 2. velj
Odgovor korisniku/ci @fermatslibrary
I am waiting to see how many will get offended by this math post.
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