philosophical thought Show more
I can only feel one thing about life itself: the existence of things
Warning: Knowledges Show more
I think the solution to every solvable problem is
\( x \)
In the same logic, I just found that for two consecutive numbers \( x \) and \( y \), where \( y = x - 1 \), the sum of their squares is equal to \(x^2 + y^2 = x \times 2y + 1\)
E.g.: \( 31^2 + 30^2 = 31 \times \left( 2\times 30 \right) + 1 = 1861\)
(Yes I know you can just substitute for \( y = x - 1 \), but again I was just randomly thinking of this)
I can't seem to find the original photographer, but kudos for the timing
So, I just found some interesting property of squared numbers by myself (which probably has been found already, but i just thought of it) which is that you can know the difference between two squares of consecutive numbers without knowing their values
E.g. I want to know \( 41^2 - 40^2 \). I don't know what their values are, but I can use this formula I just thought of: \( 2x - 1 \) (\( x \) is the higher number) so \( 2 * 41 - 1 = 81\) so \( 41^2 - 40^2 = 81 \)
really cool stuff
I am myself.
I like programming, maths, pi and existing.
A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
\) for inline LaTeX, and
\] for display mode.