Sum of an infinite geometric progression

The sum of an infi­nite geometric progres­sion is equal to $b_1/(1-q)$, where $b_1$ — the first term of the progres­sion, and $q$ — its common ratio ($|q|<1$). When $q=1/2$, the sum can be “calculated” geometrically.

If we take the area of the larger part as 1, then the sum of the areas of all parts obvi­ously equals 2.

If the field is not arbi­trary, but has an aspect ratio of $\sqrt{2}$, then all the resulting parts, when divided in half, will be similar to each other.

The model can be made of wood or card­board. For secondary school pupils it can serve as an illus­tra­tion of both the sum of an infi­nite geometric progres­sion with a common ratio of $1/2$ and the sum of powers of two. And for younger students — a puzzle.