24 equal points on the circumference.

Question

I have a round flat wooden bottom with 9.5" diameter and I need to cut 24 "pickets" to fasten to the rim - it will look like a bowl when finished. How do I lay it out with a ruler making 24 flat spots for the 24 little boards? How wide would the boards be - inside measurement. The outside measurement will be greater because I'm going to angle each side cut 7.5 degrees. Thank you. For your kind assistance.

Answer 1

a 24 equal sided polygon has interior angles of I_a=(22/24)180=165 degrees

in radians I_a=(22/24)π radians

radius=4.75 in.

central angle for each board C_a=2π/24=π/12 radians

arc length for each board =4.75π/12 in.

around the circle, mark at each 4.75π/12=1.244 in.,,, in arc length

sand so there are lines between the points

each line should be 2(4.75)sin(π/24)=1.240 in.

check sort of 24(1.240)=29.76

2π(4.75)=29.85