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Of course, to do the right fit when assembled is a equilateral triangle, the pieces do not overlap, nor any excess pieces. An obvious consequence is, the triangle must be received by the area of a square. In addition, we will only cut the pieces to form the polygons rather cut the curve. (An intuitive, easy to see that if they just cut the curve rather more difficult to put together, makes it easier to create any pair). The image is not necessarily convex, concave that can.
The problem sgs above can be divided into two parts: the first is the existence of a puzzle so lets cut, and the second is to find ways to cut jigsaw that little piece just use the most. General The first part up to all forms of the same area, we get the following two problems:
Two articles on actually relatively independent of each other in terms of inference, each article needs a different approach, because a post just proves the existence, is also a must indicate the names of the best methods . (Take the proven existence a collage often be a way to cut out a lot of pieces, not to know much about how to optimally). So what do all this before the two are, not necessarily in order of article 1 and article 2 Papa to discuss all with Mirella 2, then by all 1.
Lesson 2, as well as a lot of other problems in mathematics, or technology, too: once found a solution, then the test solution is very easy, almost obvious. sgs But when not know the answer, but find it quite difficult, because there are so many different possibilities for selection, do a lot of different tests. Readers do not know the problem, try to find a solution before comparing with the following explanation.
A mathematical sgs reasoning sgs when having a difficult problem is, when not know how to solve it right, then we "get acquainted" with it by attacking on the spot "whisker" around it.
To start, we first compute the triangle edges are compared with square edges. Call edge equilateral triangle sgs is b, is a square edge. By the Pythagorean theorem, the square of the length of the High Street equilateral triangle is equal, which means that the height of the triangle are equal and the area of the triangle are equal split floor's height, ie by As space equilateral triangle with a square, ie by a squared, so taking the square root we get the following equation:, in other words, the ratio between b and a is. Of course, this is not to say anything about building a collage out over, just give us an estimate of the ratio between edge equilateral triangle with a square edge. This figure "obvious" is between 1 to 2. it is a bit larger than 1.5 "somewhat random", if not the specific properties are not well known, although this is not important much here.
One other step, can be observed that, when cut into squares are assembled into equilateral triangles, it also means that the triangles are cut out to be grafted into squares (also with pieces of it!). Mathematically speaking style, this is an equivalence relation. (This will be especially important when the first article, but here it was not needed, but it is still interesting to observe one more problem). If someone does not like a square cut into triangles transplant, then try to do the opposite, ie the triangle puzzle cut into squares are.
One more step to boot, is to prove that the only two pieces are not. Intuitive, this is almost obvious, but we try to demonstrate how closely watch, knows intuitively, why fool us. Try to see why this argument?
When the square turns into a triangle, the square corners to turn away. Turn somehow? Or is it being chopped off bangduong vuongdo cut the corner, or the top of it is lined on one side of the triangle
