Take a square piece of paper oriented with its top horizontal. Fold it along any line that passes through the center and forms an angle of between 0 and 45 degrees with the horizontal.
The outline of the resulting shape is a nonagon.
What angle will maximize the perimeter of this nonagon?
What angle will maximize the area of this nonagon?
Is there any other single fold (not through the center) that can do better for either of these?
--> The angle that will maximise the area of the nonagon is 22.5 degrees.
--> The approximate value of the angle that will maximize the perimeter of the nonagon is 33.50803 degrees.
Edited on April 10, 2024, 8:42 am
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