Martin Gardner wrote in Scientific American 4 / 1977:
"Michael R. W. Buckley, in Journal of Recreational Mathematics, Vol. 8 (1975),
proposed the name tetrad for four simply connected planar regions,
each pair of which shares a finite portion of a common boundary."
Fig. 1. Two Tetrads made of three congruent and one other tile
In the first tetrad all 4 regions have the same area. The second tetrad has a big hole, the regions are similar (same shape).
Buckley asked: "Can a simply connected tetrad with four congruent component regions be constructed?"
In this presentation we only consider tetrads with four congruent component regions.
The tetrads may have holes.
Suggestion
We hope you don't remember the complicated tetrads of the main page.
As soon as you see simple solutions you will think this problem is easy. You will miss a lot of intellectual fun.
Therefore you should shut down your computer now, take a sheet of paper and try to find a tetrad with holes.
Can you also find a tetrad with no hole?
Come back to this site in a hour, a day or a week.. We will wait for you.
The first tetrad of fig. 1 is very interesting. There is a surprisingly easy way to construct an inner vertex.
The ratio of certain lengths is equal to the golden ratio.
Can you construct a vertex of the inner region and find the golden ratio?
Solutions