That's pretty trivial. The difference of two consecutive perfect squares is always oddpic.twitter.com/isCkQAqYib
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That's pretty trivial. The difference of two consecutive perfect squares is always oddpic.twitter.com/isCkQAqYib
It might be trivial, but as a math teacher, I see it as a way to make (n+1)^2+n^2=2n+1 visual for learners. Any additional way to look at an idea is a treasure for me, especially a visual one!
Using the same idea, here's a
visual to show that the sum of the first odd numbers is a perfect square.
1+3+5+7+...+(2n-1)=n²































You’re so romantic...


(n+1)^2 - n^2 = 2n + 1 Which is a linear sequence of odd integers.
Likewise (n + 2)^2 - n^2 = 4n + 4 Which is a linear sequence of multiples of four. Easy to visualize since the perimeter of every square is a multiple of four. We can then induce that any number of the form 4n + 2 cannot be represented by the difference of integer squares.
Duh, cause odd is (Even+1) 1 making the corner, and therefore the even numbers equally spaced out in 2 perpendicular dimensions. This therefore would not work out with the integer of 1, but would with three and so on... 2x+1
It does work for 1 as the diff of the two squares 1*1 and 0*0
Right! I love when you can do number theory visually - it’s a nice property of the field and makes it a great starter for Real Big Kid Math
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