A white regular polygon with area $1$ has a red circle inscribed(the circle touches the edges of the square), with a white regular polygon with the same amount of sides as the first one(the polygon's corners touch the circle) and this pattern continues forever, creating a pattern like this: (https://i.stack.imgur.com/IARUV.jpg) 1. What is the area that is coloured red if the polygon is a square?
- If you knew the amount of sides, what would be a formula to find the area coloured red, in terms of $s$ (for sides)