Find the number of diagonals that can be drawn in an n-side polygon

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Homework Help Overview

The discussion revolves around determining the number of diagonals in an n-sided polygon, a topic within combinatorial geometry.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore a recursive approach to calculate the number of diagonals, with one suggesting a formula and another questioning its setup. There is also a discussion about the implications of counting diagonals from a single vertex and the potential errors in that method.

Discussion Status

The conversation is ongoing, with participants offering different methods and questioning the validity of certain approaches. Some guidance has been provided regarding recursion, but clarity on the reasoning behind the formulas is still being sought.

Contextual Notes

Participants are grappling with the definitions and assumptions related to diagonal counting, including the implications of vertex connections and the potential for miscounting.

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Find the number of diagonals that can be drawn in an n-side polygon.

The answer is n(n-3)/2.

I don't know how to do that.
 
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Set up a recursion for the number of diagonals in an n-gon: [itex]D_{n+1} = D_n + n - 2[/itex].
 
I don't understand how can I set up
[itex]D_{n+1} = D_n + n - 2[/itex].
 
How many diagonals can be drawn from 1 vertex? If you multiply that by the number of vertices you will get the wrong answer! Do you see why? How can you fix it?
 

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