Most of us love chocolate, one of the most admired foods in the world. There are thousands of different flavors of chocolate, depending on how it is made and the ratio of the things put in it. There is a big difference even between the chocolate of one brand and the chocolate of another brand, but we think that there is no one who does not like the intense flavor that a quality chocolate leaves in the mouth.
Because we love chocolate so much, we don’t want it to end. So, is it possible to multiply a chocolate you buy using mathematics forever? Of course, it is not possible to eat a tangible food that has a size and weight forever, but mathematics has a paradox that makes this possible in theory.
Can we produce an infinite number of chocolate chips by dividing the chocolate from the correct areas?
As you can see in the image above, let’s consider a chocolate consisting of 5 x 5 pieces. Let’s divide this chocolate in half at a certain angle and divide the above piece into some special pieces. (You can see how the chocolate crumbles in the GIF above.) In this way, when you make a cut and reposition the pieces, we see that 1 piece is left out.
From this point of view, we see that 1 piece is left out, and moreover, the 5 x 5 pieces still maintain their integrity. Which tells us, “Can we have endless chocolate?” begs the question. So is it really happening?
How exactly does the “Banach – Tarski paradox”, which pretends it’s possible to smash and eat chocolate forever, works?
The endless chocolate paradox is actually an example of the Banach – Tarski paradox, which has a place in mathematics. According to this paradox, it is possible to “make something out of nothing”. However, although it looks real in the image above, it has no reality in the world’s physics. If you apply this method in the real world, you can see that the size of the chocolate is reduced. In short, the GIF above has a trick.
Let’s get to the root of the Banach – Tarski paradox to get a better grasp of the matter.
This mathematical paradox, put forward by Stefan Banach and Alfred Tarski in 1924, shows that in theory it is possible to divide a solid sphere into finite parts and reassemble these parts by translation and rotation without bending and stretching, to form two spheres that are the same as the original sphere. is showing.
In this paradox, for example, you divide a sphere of volume 1 into unmeasurable parts. Since these pieces are immeasurable, they allow you to get the volume you want when they come together again. This paradox, of course, does not work correctly in the real world. In an abstract world, it is mathematically applicable.
So where did the loss in the image go?
As you can see in the image above, when the excess 1 piece of chocolate is removed from the rest of the chocolate, 25 pieces can be handled again, but the area of that 1 piece of chocolate from the whole of the chocolate is narrowed. Although this illusion in the image is “Is such a thing possible?” unfortunately, we cannot continue to eat a chocolate forever.
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