I have a fixed size square on which I need to draw a regular pentagon to use as a classroom aid. This pentagon should take up as much of the square as possible, and does not need to have any of its sides aligned with those of the square (though that would be considered a bonus).
I’ve found instructions online for inscribing a regular pentagon inside a circle (mathopenref.com/printpentagon.html), but I need to draw inside a square. Is there a construction method for doing so?
Alternatively, if a regular pentagon is inscribed in a circle and the smallest possible square is drawn around the pentagon, is there a way to find the location of the center of the circle relative to that of the square and the ratio of the length of a side of the square to the circle’s radius?
Best Answer
Since no one is posting an answer, here’s the method I settled on for drawing one which is symmetrical on the diagonal of the square (which comments indicated would result in the largest possible pentagon).
This method requires only one measurement using a ruler (step 1), the rest is classical construction techniques using compass and straightedge.