Draw the line AX. Draw another line (using an index card) BY, perpendicular to AX. Cut out the rectangle ABDC, cut the line AX, and cut the line YB. In order to get a square in slanted position, move the left triangle to the right, and move the top triangle to the bottom right. Remark. Notice that the length BY is also s. (Why?) Task.
What happens when a square is divided into three rectangles?
If a square is divided into three similar (same shape, different size) rectangles, as in the figure, then the ratio of the two pieces along the vertical edge is the plastic number. Unbeknownst to me at the time, the question of this tripartite division evidently had at least two, earlier ‘in the print record’ occurrences.
How to divide a square into three equal stripes?
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). It has to be a very old problem but I hadn’t been able to find on the web any references or any real example (eg, in architecture) of this “Plastic proportion”… Any hint?
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.
Are there any lines of dissection in a puzzle?
The only lines of dissection allowed are those that follow the grid or diagonals of the grid. To put it another way, the basic structural unit is an isosceles right-angled triangle made by bisecting a grid square, and all larger puzzle pieces are composed of these unit triangles joined together different ways.
What do you mean by two dimensional dissection?
By way of introduction, we will first consider some simple two-dimensional geometrical dissections, which in their physical embodiment become assembly puzzles. To dissect means literally to cut into pieces. Just about any chunk of material cut into pieces becomes a sort of dissection puzzle.
