Hello. :spin:
This is my first post, so sorry for the potential mistakes below.
A grid of dots has the dimensions m by n, where m is greater than or equal to n. Pick k dots from this grid in such a way that they form a polygon with k sides. In other words, no three dots can be collinear
I want to find a function N(k,m,n) that will determine the total number of possible ksided polygons using m, n, and k. So far, I have only managed to find the formula for k=3 and k=4, both of which are very long and messy, and doesn't really resemble each other. The formulae's accuracy are also somewhat questionable, but their outputs do correspond to the OEIS sequences A194193, A175383,
A262402, and A296367 so there's that. From k=5 onwards, I am more or less clueless.
Here are the links to a desmos graph containing the N3(k=3) and N4(k=4) formulas:
N3
N4
I'll also attach a PDF containing those formulas for easier readability, and a picture showing the grid and some examples.
Any ideas?
This is my first post, so sorry for the potential mistakes below.
A grid of dots has the dimensions m by n, where m is greater than or equal to n. Pick k dots from this grid in such a way that they form a polygon with k sides. In other words, no three dots can be collinear
I want to find a function N(k,m,n) that will determine the total number of possible ksided polygons using m, n, and k. So far, I have only managed to find the formula for k=3 and k=4, both of which are very long and messy, and doesn't really resemble each other. The formulae's accuracy are also somewhat questionable, but their outputs do correspond to the OEIS sequences A194193, A175383,
A262402, and A296367 so there's that. From k=5 onwards, I am more or less clueless.
Here are the links to a desmos graph containing the N3(k=3) and N4(k=4) formulas:
N3
N4
I'll also attach a PDF containing those formulas for easier readability, and a picture showing the grid and some examples.
Any ideas?
Attachments

69.8 KB Views: 1

18.4 KB Views: 6