Задача: змея

[cema]

Змея глотает свой хвост и начинает есть. Когда она остановится?

Update. В книжке по программированию только что прочитал: "Lisp can be likened to a self-licking lollypop". Хорошее, нужное чтение.

Comments

[cema.livejournal.com]

Will it ever be finished?

[chaource.livejournal.com]

It will be finished in this model, assuming that the relative velocity of the tail with respect to the mouth is constant.

In a more realistic model, the snake is a straight line segment with a constant finite width (initially). We assume that the snake can stretch sideways without limit, and that the snake has zero thickness (height), i.e. it is a two-dimensional figure. It will become wider as it swallows itself. During the final stages of the swallowing, the snake has to become infinitely wide.

In a yet more realistic model, the snake has to curl itself a circular shape as it prepares to swallow itself. We assume that the snake can stretch sideways indefinitely, but that the skin of the snake still has to maintain some finite constant width. Then the process cannot proceed until the end; the final stage is when the snake occupies entirely the area of some circle. The radius of this circle is such that the area of the circle is equal to the initial area of the snake.

[cema.livejournal.com]

Interestingly, these are all geometric models. Would physical or biological models be substantially more complicated (to build and to analyze)? What answers would they give?