Greetings ladies and gentlemen!I am a new member in this well-structured and appropriately regulated community, introducing you to a general diagonal formula. I have shown few of my geometry teachers of this discovery; however, they disapprove of its use. Why do they disapprove of it? In addition, how can I further its use?

Our original, modern use of the formula for diagonal number (in the case of convex polygons).

$\displaystyle \frac{n^2-3n}{2}$

Gen. Diagonal Formula

$\displaystyle \frac{1}{2}\sum_{i=1}^v v-t$

Where $\displaystyle v$ represents the total number of vertices in a given form or shape, and $\displaystyle t$ represents the number of adjacent vertices in a given form or shape.

Here a few identities for this formula

$\displaystyle \frac{1}{2}\sum_{i=1}^c c+t$

Where $\displaystyle c$ represents the number of non-adjacent vertices in a given form or shape

$\displaystyle \frac{vc}{2}$

These formulas were primarily derived from this vertex identity.

$\displaystyle v=t+c$