I Came Up With This Proof In The Car

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Published 2024-06-20

The formula n(n-3)/2 is an easy way to find the number of diagonals a shape has. However, a formula without an explanation is boring. Thankfully, there are multiple proofs, but what does one look like?

All Comments (4)

@flyingxo 7 days ago

editing was so cool!!
@aashmanmittal4309 7 days ago

So that's how that formula is derived from. That makes more sense of why it works.
@Kyle-nm1kh 4 days ago

The -3 comes from the points that are impossible to connect to. The origin point, the left adjacent point, the right adjacent point. 3 impossible points subtracted from all possible 2 point line connections. Then you divide by 2 because there are two ways to create the exact same line: AB and BA and you only want 1. 😊 Think if it like a slightly more complicated base x height / 2 formula for getting the area of a triangle.