It’s late....but playing with the patterns of squared numbers.
Will post some of what I see tomorrow. Get ready...you know I’m going to ask.
Until then....goodnight allpic.twitter.com/JjtdoQqKgB
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Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.
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It’s late....but playing with the patterns of squared numbers.
Will post some of what I see tomorrow. Get ready...you know I’m going to ask.
Until then....goodnight allpic.twitter.com/JjtdoQqKgB
And me, just waking up. Realised there's an answer to my student PM's question, what happens if you combine s triangle and a square number.
Depends, of course, where the triangle number and the square number you're combining appear in the sequences of all triangle numbers and of all square numbers. But if you add the nth triangle number to the (n+1)st square number, you do indeed get something wonderful.
Simon Gregg Retweeted Simon Gregg
Yes, when PM first asked it I was thinking n for both square and triangle and nothing came to mind. But my subconscious must have been working on it!https://twitter.com/Simon_Gregg/status/1114097761878720513 …
Simon Gregg added,
Actually, when you add the nth triangle number to the nth square number, the result is also extremely interesting -- and intimately related (albeit in a somewhat subtle, algebraic way) to the result of adding the nth triangle number to the (n+1)st square.
If you add the (n-1)st triangle to the nth square, you get n(3n - 1)/2. But if you add the nth triangle to the nth square, you get n(3n + 1)/2 -- which, remarkably enough, is just (-n)(3(-n) - 1)/2. So one arises from the other by replacing n by -n.
Oh, and by the way, numbers of the form n(3n - 1)/2 are called pentagonal -- for reasons I think you can already see.
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