Cube Trisection, Cake Sharing, Non-Congruent Pieces

cults3d

Human: Cube Division, Cake Distribution, Identical Pieces Very playful: Create lots of them, flip them around, connect them, and have fun! The current design is based on the well-known "cake distribution" problem. If you have a square (cube) cake with icing all around, how can you cut it in a way so that three people each get the same amount, including icing? The essential idea is to use the center of the square and think of the square edges as the bases of some triangles, which all have the same altitude. We can slice a cube in a similar way and obtain three pieces with the same volume. There are certainly many ways to do that. In this design, I added some jigsaw connectors so that one can slide them into each other for a cube or, if desired, other shapes. Please note that, in spite of the connectors, the three pieces still have the same volume! Two versions of hollowed-out pieces are included in case one wants boxes. A plain version, without connectors, is also included. The cube is 50mm^3. #### Identical Trisections Of course, a cube can be trisected into three identical pieces in many different ways (see my other designs). Have fun!