Malintent
Veteran Member
For a woodworking project... I want to cut a smooth circle from the outer perimeter of a constructed hexagon. I need to calculate how wide a board I need to construct the hexagon with, such that there is sufficient material to cut away to form a circle, while maintaining integrity of the construction..
It is a geometry question, stated simply as, "what is the maximum distance of a circle's circumference from an inscribed hexagon"? No luck finding an answer to that, so here is a more detailed means of expressing what I need to find out:
inscribe a hexagon within a circle, such that each of the 6 vertices of the hexagon are touching the circle. The radius of circle is equal to the length of each segment of the hexagon, as well as its radius.
At every center point of each segment of the hexagon, the circle's circumference is at its maximum distance from the hexagon's segment.
What is that distance?
That distance would be the exact width of the board, if used to construct the hex, where cutting the circle would just exactly separate the attached segments (not good). So I would take that distance and add the amount of material I need for structural integrity. I suppose the length of each board (segment of the hex) would need to be my desired final radius, plus 1/2 the distance I am looking for.
right?
It is a geometry question, stated simply as, "what is the maximum distance of a circle's circumference from an inscribed hexagon"? No luck finding an answer to that, so here is a more detailed means of expressing what I need to find out:
inscribe a hexagon within a circle, such that each of the 6 vertices of the hexagon are touching the circle. The radius of circle is equal to the length of each segment of the hexagon, as well as its radius.
At every center point of each segment of the hexagon, the circle's circumference is at its maximum distance from the hexagon's segment.
What is that distance?
That distance would be the exact width of the board, if used to construct the hex, where cutting the circle would just exactly separate the attached segments (not good). So I would take that distance and add the amount of material I need for structural integrity. I suppose the length of each board (segment of the hex) would need to be my desired final radius, plus 1/2 the distance I am looking for.
right?