fold the circle to make 8 equal parts what fraction of the circle is each part?
Answers
Answer:
How do you cut a circular cake into eight equal pieces?
Be unstoppable with financing offers by HP.
If you want 8 congruent parts, 4 straight cuts through the center will get you 8 pizza slices (ie sectors). If you space the cuts at angles of 45 degrees, you’ll get 8 congruent slices.
If you only want 8 regions with the same area but don’t care about the cuts being straight, you can do better. Letting the radius of the circle be R, cut a circle of radius R/sqrt(2) centered around the center of the large circle. This smaller circle will have area 1/2 of the larger circle. Then, with two straight cuts through the center at right angles, you’ll get 8 regions of equal area: 4 small 90 degree pizza slices, and 4 crusts around the outside. So 3 cuts is certainly possible.
But if you are willing to allow self-intersecting cuts, I expect you could do it with just one cut. I’m thinking of creating 7 circles or 1/8 the area of the large circle inside the circle arranged so that one circle is tangent to the large circle, each other circle is tangent to 2 others. Hold on, I’ll switch devices and draw a picture.
Edit:
Oh, no, you can’t do it with 7 circles, but you could do it with 8 irregular regions. Here’s all my solutions. The far right one is one cut, starting at S and ending at E, following the arrows:
If the question is about minimum length of cuts, I’m not sure how to find a minimum. The first option above has the shortest length of the three presented, but I don’t think I could prove that it’s the absolute minimum solution.