How does a circle to go through one square crack More “narrow” than him? We see it in this article, where using the geometric properties of the square, we manage to make a little one Trucco di (Mate) Magic.
Pass a circle inside a more “narrow” square crack
The situation is this: we have a sheet which brings back to the center hole form square with the sides arranged a 45 ° compared to the sides of the sheetand a smaller sheet of circular shape, as in the figure. The diameter of the circle it is little bigger Compared to the diagonals of the square hole, so Not It is possible Give Way The circle through the hole.
However, it is possible to be able to pass the circle inside the hole by applying Three simple folds on the sheetas shown in the figure below.
Once the sheet is folded to form a “diamond”, We separate together the two internal implications of the sheet so that they can open them as in the figure. We will see a crack appear through which “Mate-Magically” the circle will be able to pass!
But how did we manage to increase the width of the hole simply by folding it?
The explanation of geometric makeup
What we did by folding the sheet in several parts was Align two consecutive sides with each other of the square and this has increased the breadth of the hole because the sum of two sides of a square it is always greater of his diagonal. It is as if we had crushed and pulled the square until it becomes a segment as long as the sum of two of his sides.
This trick it doesn’t always workbut only if the measures of the circle and the square photo respect one precise condition: The diameter of the circle is so greater than the diagonal of the square, but it must be less than the sum of the two sides (obviously).
In our case, for example, the circle has the same diameter to 5.2 cmwhile the square hole has the side equal to 3.5 cm and therefore diagonal equal to 3.5 cm x √2Meaning what 4.9 cm. This means that initially the circle cannot pass by being 5.2 greater 4.9. Once the sheet is folded, however, we come to have a hole of about 3.5 cm x 2Meaning what 7 cm.
