### How many times can you fold a paper?

One really thinks that jet-lag (that time difference of executives who travel flying and suffering in his own body) is a modern phenomenon, and the truth is that it is true. But however was discovered no less than a few hundred years ago peak, there was a case of jet lag in the Renaissance and wait tell you because the history is worth: he was returned when Magellan's expedition, and took the surprise of his life when he saw that it was missing a day.
And is thus: a common paper thickness is more or less a tenth of a millimeter. If one bends it in two, the thickness doubles, and will duplicate whenever we bend it. It is difficult to imagine with astonishing speed would increase the thickness of paper silo followed by bending and folding: cor only 20 folds would have fifty meters. But that's nothing: with 28 folds would outstrip the 8800 meters of height of Mount Everest and with 38 folds the twelve thousand kilometers that measures the diameter of the Earth. [And that does nothing: If we continue doubling e] paper, after 43 folds the thickness would outstrip the 380 thousand kilometers that separate us from the Moon, and after 52 folds, the hundred and fifty million km that separate us from the Sun.
But even so, we are not more than at the beginning: after having bent 58 times, the thickness of the paper will be greater than the width of the solar system (which is approximately 12 billion kilometers) and with 70 folds would go beyond Alfa Centauro, who is the star closest to Earth and that is 4 years light (one light yearthe distance that light travels in a year, equivalent to ten million km millo­nes). 86 folds the paper would be wider than our Galaxy and with 90 folds would reach Andromeda, more nearshoring to Earth Galaxy and is light to two million years. With 100 folds, he would be halfway of the observed more distant objects in the universe, ten billion light years away, and with a fold over, would be wider than the entire known universe.
These surprising results are due to the rapid growth of the geometric progressions (1, 2, 4, 8, 16, 32, etc.), which increase at a pas­mosa speed and intuitive anti: there is a legend that linked this phenomenon to the origin of chess. According to this legend, Sissa, the Indian inventor of the big game, presented it to the King and it asked what I wanted as a reward, Sissa asked "something very simple: a grain of wheat in the first box, two in the second, four in the third, eight in the fourth and thus to complete the game board". The King was amazed by the modesty of Sissa, immediately agreed, ordered to bring a bit of wheat and started to fill the boxes.
We can (or perhaps cannot) imagine the surprise of the King when he found that grains are consumed with astonishing speed and that all wheat realm was insufficient to satisfy the request of Sissa. At the same time as chess, the King had learned the fantastic growth of a geometric progression: ordered by Sissa grains grow rapidly than the thickness of the paper do­blado of which we talked about at the beginning.
It might seem to you unlikely, but with a little patience you can convince yourself: If you don't want to risk fold ninety times a role and get out of the Galaxy, try "Sissa variant". Get (or draw) a chessboard (64 squares) and replace the grains of wheat (hard to find in our urban culture) by grains of rice, which is the same for the case. You will see that starting with a grain in the first and doubling the amount of grains in each box is insufficient everything existing in the world rice to fill the Board. And you will see, incidentally, that rice, for geometric progressions, is better than wheat; When you find it impossible to follow (or simply when you get tired or get bored), can use the rice to cook a paella.