Induction: Diagonals in a Convex Polygon

[@seal3081]

wow thanks for posting this up. I'm learning induction right now. Usually I would have expanded the term and go from there. It's nice to know I can look at it from another perspective. Much love from Canada.

[@glenprideaux]

Eddie, I love your work but I think the logic used here is circular. Using T_{k+1}=D_{k+1} - D_k to prove D_{k+1}=D_k+T_{k+1}, but that's a tautology and proves nothing. A better approach, I think, would be to use a geometric explanation of why T_{k+1}=k-1: add a point between P_k and P_1 and how many new diagonals are added? The new point can connect to k existing points, but 2 of these are edges, not diagonals, giving us k-2; in addition the line segment connecting P_k and P_1 was an edge but is now a diagonal so we have k-1 additional diagonals.

[@asthargf]

Thank you. I've just watched the video and I thought the same, that he is using circular logic. Thank you for adding an extra/alternative explanation ^^

[@azizmanva8432]

Exactly my thought. The logic is circular.

[@big_mike7950]

This logic is flawed. You essentially just "proved" that Dk+1 = Dk + Dk+1 - Dk. This isn't how to solve this problem.

[@pancada2010]

Hi, I'm from Brazil. I can not understand much Inglês but I'm learning a little math. Very nice!

[@yoavshati]

How is your English now?

[@summerxx9493]

How is your English now?

[@joebush640]

how about now?

[@pancada2010]

Hi, Could you help me with this n^2 | (n+1)^n- 1, with n ∈ N?

[@joebush640]

no