How many degrees does a hexagon have in its interior angles?

@ElwoodBlues

The number of exterior sides in that diagram start at 3 then go to 8. You probably know what I'm going to ask next: how many sides does it take before the figure finally becomes a circle? Or will it ever become a circle?

@rinkydinkydoink that's exactly how many of our early mathematicians solved some of the complicated problems by just adding more sides till it was virtually a circle

@ElwoodBlues I used a graphics renderer that filled weird polygons that I mapped out with color in a game engine that I created, and that graphics renderer used this fact 😄

@rinkydinkydoink asks You would make the equation parametric such that there were n equal sides, and then take the limit as n approaches infinity.

@ElwoodBlues exactly

@ElwoodBlues

An equation needs to be devised to make fit the seeming impossibility of there being an infinite number of sides? You're saying there are a definite end number of sides? Let's say the circle was
ever-expanding...

@ElwoodBlues

You're aware I have a limited knowledge of math. I am, too! But... are there any math problems that haven't been fully understood or explained?

@rinkydinkydoink There are definitely math problems that haven't been fully understood or explained. But this process of parametrically separating into n pieces, summing them up, and taking the limit as n goes to infinity, that process is the basis of calculus.

And calculus has successfully solved any number of problems and made any number of correct predictions.

In the graphic below they're doubling the number of slices (halving Δx) each step.