Incredible paradox napkin rings
• The incredible paradox napkin rings
Here is a statement in which you would not believe it: if you cut a core of orange or of the planet Earth so that the remaining rings were the same height, the amount of these rings will also be equal. What do you think about this? We warned that will not believe. Then read to the end.
This problem is known c XVII century. Her first formulated the Japanese mathematician Seki Kowa. His geometric proof eventually became known as "the problem of napkin rings," because the scope from which to core, is really very similar to the napkin rings.
When you cut a core of the sphere, in essence, you are removing it from the middle of the body is cylindrical in shape. Regardless of the radius of the sphere, if you have done the procedure of creating a ring napkin a certain height, any ring with such a height will have the same volume. For example, if you cut a core of the orange to create napkin rings height of 2 inches, then cut a core of the planet Earth to get the ring for napkins of the same height, you will have two rings with totally different diameters, but their internal volume is exactly the same. Wait a minute, how can that be? There are two ways to explain this strange phenomenon: using math without it. Version without mathematics is as follows: to the extent that it increases the scope, from which you cut the core, the same happens with the cylinder, you need to take to get the ring desired height. Removal of the core from orange to produce rings 2 inches high, requires the removal of a much smaller volume than the coring of giant sphere sized planet ring for the same height. The smaller the sphere, the thicker the resulting ring so small ring to a predetermined height napkin may have the same scope as the large ring napkin at the same height.
To find the volume of each of the two rings for the napkins with the help of mathematics, you should write down some simple equations that use the area of a circle, a little geometry and the Pythagorean theorem. You'll find that by doing all the work and simplifying the resulting equation, you get the following equation:
As you can see, the only variables that you need to know in order to calculate the volume of napkin rings - a ring height h. It turns out, sphere radius in the formula is not included, i.e. the volume of the ring does not depend on the field size. To get a detailed explanation, you can watch a video on the YouTube channel.
In bringing this problem to the extreme, we say that if you cut out the core of the golf ball and the Sun, creating napkin rings height of 1 inch, the two rings, too, would have exactly the same amount. And what about the pea and Jupiter? While the rings are the same height, their volume will remain exactly the same.
Now you can blow up the brain to their relatives and friends during the next family celebration, of course, if you have a family decided to insert napkins rings to decorate the holiday table.