5.06.2015

The six faces of a parallelepiped

Here is such a question: "Parallelepiped. Explain where he has six faces?". If mathematics is not able to clearly explain to you the parallelepiped design, then I'll try to do it. Will speak only about the faces of the parallelepiped, without delving into other structural details of the mathematical model, we are not in the showroom, and I'm not a manager trying to sell you an outdated model of the parallelepiped.

So, imagine that you, as if nothing had happened, went to sleep in his rectangular (this clarification is important) room. And at night you wake up in the current model of the box in full size! No need to panic. Easy start counting the brink of mathematical miracle. The wall with the window - this is the first bound. The wall opposite the window - this is the second face. The walls of the left and right of the window - this is the third and fourth edges. The floor - this is the fifth face. Ceiling - this is the sixth and final face. Great mathematical revelation: the number of faces does not depend on the order of their conversion, the main thing - do not miss it.

If you are up to this point has not yet fallen asleep, the next question is what to do next? Mentally, we develop a mathematical papyrus entitled "Set Theory", looking for the head of "Infinite math scores sheep" and start counting. People say this is very good mathematical procedure helps insomnia.

Just I want to honestly admit that I have lied a little. Not a rectangular room is a working model of a rectangular parallelepiped, but quite the contrary - a cuboid is a mathematical model of the room. This is particularly evident during the repair. The area of ​​the walls will be the surface area of ​​the side faces of the cuboid. The area of ​​floor or ceiling is determined as well as in the area of ​​the base of the box. Of course, the builders made their nuances in the rules for determining the areas of math, but we will not specify now.

Incidentally, the rectangular room is entirely dependent on the quality of construction. It is only in ancient Greece mathematics was so developed that famous building of the Parthenon in Athens was built with almost no right angles and straight lines. There's a base architecture of the building was laid not a mathematical perfection, and optical illusions. I'm afraid of modern mathematics such a task is not on the shoulder - too high in the clouds, they soar. But we digress from faces of a parallelepiped.

If you count the face of the parallelepiped you wanted during the day and not at night, then pull out from the wardrobe of a rectangular box with shoes. The bottom of the box - it is one face, it is also the lower base of the box. The lid of the box - a second side, she's upper base. The four walls of a shoebox - it faces the third to sixth.

We have considered six faces of a rectangular parallelepiped. If angles are not straight and curves? In this case we are dealing with a conventional parallelepiped, not rectangular. On the number of faces is not affected. Well, think, a little crushed a parallelepiped. By the way, mathematics bend rectangular parallelepipeds or align usual? I'm on the algebra of interesting to see. However, the mathematician's simple: uttered the sacred mantra "Let there be given a parallelepiped" and that he had gleaming white chalk on a blackboard. Life is complicated. There are many ways to straighten the curvature and parallelepipeds - by a heavy sledgehammer, to flirty "Oh, please!". About algebra of these methods can not even ask.

Seriously speaking, the algebra and rectangular, and the usual parallelepipeds is exactly the same. Bends and leveled a parallelepiped using sines of the angles between the ribs. In all corners of the rectangular parallelepipeds straight sinuses and their unity. Lazy math just does not write these sinuses in formulas. In conventional Parallelepipeds sines of the angles is less than one, so willy-nilly have to mathematicians in their formulas to write.

In conclusion, as they say teachers, fix the passed material. As a fixative use a simple children's coloring book, which paint the six faces of a parallelepiped.

The six faces of a parallelepiped. What is a parallelepiped. Mathematics for blondes.
The six faces of a parallelepiped

I recall that the parallelepiped, unlike the quadrangular prism opposing faces are parallel, and the base is a quadrilateral with parallel sides: square, rectangle, diamond or parallelogram. However, mathematicians believe that a parallelepiped is a kind of prism. So they have written in the definition. With the same success it can be argued that the prism is a kind of parallelepiped. Simply rewrite the definition, as a textbook on mathematics - it is not the Bible.

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