Prime Square

3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.
Diagram by HT Jens Kruse Andersen.

Prime Square

Intriguing Geometric Dissections

Any two polygons with equal area can be dissected into a finite number of pieces to form each other. One of the most interesting dissection or geometric equidecomposition puzzles is that discovered by Harry Lindgren in 1951 (see Fig. 2 further below). As you know, in this kind of puzzles, the geometric invariant is the area, since when a polygon is cut and its pieces are distributed differently, the overall area doesn’t change.

Lindgren was the first to discover how to cut a dodecagon into a minimal number of pieces that could pave a square, when rearranged differently. His solution is very elegant, he first built a regular Euclidean pavement by cutting a dodecagon as shown in fig. 1.a, then arranging the four pieces symmetrically on the plane (fig 1.b). The tessellation achieved with these pieces corresponds, by superposition, to a regular paving of squares. The example in fig. 2 shows how the puzzle appears once finished.

dodecagon fig. 1

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