David Turner shows that a rectangle can only be dissected into finitely many squares if its sides are in a rational proportion. Rec.puzzles archive: dissection problems . 75-75-30 triangle dissection . This isosceles triangle has the same area as a square with side length equal to half the triangle’s long side.
What’s the dissection of 75-75-30 isosceles triangle?
75-75-30 triangle dissection. This isosceles triangle has the same area as a square with side length equal to half the triangle’s long side. Ed Pegg asks for a nice dissection from one to the other. Similar division.
Where does the extra unit come from in dissection?
J. Roth dissects an aperiodic three-dimensional tiling involving zonohedra into another tiling involving tetrahedra and vice versa. Fake dissection. An 8×8 (64 unit) square is cut into pieces which (seemingly) can be rearranged to form a 5×13 (65 unit) rectangle. Where did the extra unit come from?
How to divide a square into three similar rectangles?
Preparing some exercises for my High School pupils I came across this question: How can you tile a square into three similar (ie., same shape, different size) rectangles ? With a bit of algebra it can be easily shown that there is one non-trivial solution (I mean, apart from three equal stripes) involving the Plastic number (aka Padovan constant).
What can you do with a dissection puzzle?
Cut squares and equilateral triangles into pieces and rearrange them to form each other or smaller copies of themselves. A dissection puzzle. T. Sillke asks for dissections of two heptominoes into squares, and of a square into similar triangles .
How are lines of dissection allowed in Tangram?
The way this is accomplished in Tangram is shown in Fig. 7. A diagonal square grid is superimposed onto the square whole such that the diagonal of the square measures four units and the area is eight square units. The only lines of dissection allowed are those that follow the grid or diagonals of the grid.
