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MathPrinceps's profile
Laurens Gunnarsen
Laurens Gunnarsen
Laurens Gunnarsen
@MathPrinceps

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Laurens Gunnarsen

@MathPrinceps

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.

Joined June 2012

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    1. LilMathGirl‏ @lilmathgirl 4 Apr 2019
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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

      1 reply 0 retweets 4 likes
    2. Dee Crescitelli‏ @dcrescitelli 4 Apr 2019
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      Replying to @lilmathgirl

      Sweet dreams!

      1 reply 0 retweets 1 like
    3. Simon Gregg‏ @Simon_Gregg 4 Apr 2019
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      Replying to @dcrescitelli @lilmathgirl

      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.

      1 reply 0 retweets 2 likes
    4. Laurens Gunnarsen‏ @MathPrinceps 5 Apr 2019
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      Replying to @Simon_Gregg @dcrescitelli @lilmathgirl

      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.

      1 reply 0 retweets 2 likes
    5. Simon Gregg‏ @Simon_Gregg 5 Apr 2019
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      Replying to @MathPrinceps @dcrescitelli @lilmathgirl

      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,

      Simon Gregg @Simon_Gregg
      PM had asked what you get if you combine square and triangle numbers. I told my class I woke up this morning, and my brain had been working on his question and - as if by magic - I had an answer... pic.twitter.com/dsUXcoApxe
      2 replies 0 retweets 2 likes
    6. Laurens Gunnarsen‏ @MathPrinceps 5 Apr 2019
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      Replying to @Simon_Gregg @dcrescitelli @lilmathgirl

      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.

      2 replies 0 retweets 1 like
      Laurens Gunnarsen‏ @MathPrinceps 5 Apr 2019
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      Replying to @MathPrinceps @Simon_Gregg and

      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.

      9:42 AM - 5 Apr 2019
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      • Simon Gregg
      1 reply 0 retweets 1 like
        1. Laurens Gunnarsen‏ @MathPrinceps 5 Apr 2019
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          Replying to @MathPrinceps @Simon_Gregg and

          Oh, and by the way, numbers of the form n(3n - 1)/2 are called pentagonal -- for reasons I think you can already see.

          0 replies 0 retweets 1 like
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