Can you have an infinite number of chocolates by eating a continuous piece of 5×5 chocolate with the correct proportions? We explain this paradox that has been circulating on the internet and has been shown to be possible.
One of the most admired foods in the world. chocolate most of us love 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. What about a chocolate you bought? using math Is it possible to reproduce 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.) When you make a cut like this, swap the pieces and put them back in. We see that 1 piece is left out.
From this point of view, 1 piece is left out, moreover, it is still We see that the 5 x 5 piece retains its 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 “to make something out of nothing” possible. 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.
in 1924 Stefan Banach and Alfred Tarski This mathematical paradox, put forward by A.D., is theoretically possible by breaking a solid sphere into finite parts and reassembling these parts by translation and rotation without bending and stretching. two spheres identical to the original sphere shows that it is possible to create a mathematical formula.
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For example, in this paradox have 1 volume you are dividing the sphere 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.
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So where did the loss in the image go?
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As you can see in the image above 1 piece of extra chocolateWhen the chocolate is removed from the rest of the chocolate, 25 pieces can be handled again, but the area of that 1 piece of chocolate is narrowed from the whole of the chocolate. Although this illusion in the image is “Is such a thing possible?” unfortunately, we cannot continue to eat a chocolate forever.