Equally Optimal Cuts

Geometry Level 3

If you cut a circle into the maximum number of parts using 3 straight cuts, is it possible for all of the parts to be equal area?

Yes No It depends on the radius of the circle

Michael Huang by Michael Huang , 29, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Marta Reece
Jun 20, 2017

Three cuts can cut the cake into 6 equal pieces.

But the maximum number of pieces one can produce with 3 cuts is 7.

7 pieces, however, cannot be made the same size with three straight cuts.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

It seems that it won't work, since you don't have enough degrees of freedom. You have to keep the cuts symmetric, thus you can adjust until the middle piece matches 3 of the edge pieces.

But it seems like the other 3 pieces will be bigger or smaller. Hard for me to offer proof of this, but your diagram helps to visualize it!

Steven Perkins - 3 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...