卵のかたちの認識1 : トーラス(円環面)の断面に関する研究

抄録

I regarded an oval as a cross section of a torus (defined as closed curve E) cut by a plane II, parallel to the axis of rotation. Closed curve E is expressed as follows: [numerical formula] where a is the distance from the axis of rotation to plane II, and r is the distance from the axis of rotation to the center of the generating circle. I showed four shapes for closed curve E, which are similar to those of "real" eggs, by varying a values under constant r values. Then I demonstrated that shapes constructed by a computer are fairly similar to the "real" egg's shapes. I assumed that the most important function performed by the oval shapes of eggs is that eggs can stay near the original place when they are forced to roll. I showed that the greater the a value is, the shorter the radius of rotation of rolling eggs is.