The sum of all edges of a parallelepiped is equal to 288 cm. Find the sum of the lengths of all edges of a rectangular parallelepiped - calculation procedure

1) Parallelepiped - this is called a prism, the base of which is a parallelogram. All faces of a parallelepiped are parallelograms. A parallelepiped whose four lateral faces are rectangles is called a straight parallelepiped. A right parallelepiped whose six faces are all rectangles is called rectangular.

2) A rectangular parallelepiped has 12 edges. Moreover, among them there are equal ones and there are 4 of them.

3) Thus, (13 + 16 + 21) * 4 = 50 * 4 = 200 cm is the sum of the lengths of all the edges of the parallelepiped.

Answer: 200 cm.

The concept of a rectangular parallelepiped

A cuboid is a polyhedron constructed from six faces, each of which is a rectangle. Opposite faces of a parallelepiped are equal. A rectangular parallelepiped has 12 edges and 8 vertices. The three edges emerging from one vertex are called the dimensions of a parallelepiped, or its length, height and width. Thus, a rectangular parallelepiped has four edges of equal length: 4 heights, 4 widths and 4 lengths.

For example, they have the shape of a rectangular parallelepiped:

• brick;
• domino;
• Matchbox;
• aquarium;
• a pack of cigarettes;
• diplomat;
• box.

A special case of a rectangular parallelepiped is a cube. Cube is geometric body in the shape of a rectangular parallelepiped, but all its faces are square, so all its edges are equal. A cube has 6 faces (equal in area), 12 edges (equal in length) and 8 vertices.

Calculating the sum of the lengths of all edges of a rectangular parallelepiped

Let us denote the dimensions of the parallelepiped: a - length, b - width, c - height.

Given: a = 13 cm, b = 16 cm, c = 21 cm.

Find: the sum of the lengths of all edges of a rectangular parallelepiped.

Since a rectangular parallelepiped has 4 heights, 4 widths and 4 lengths (equal to each other), then:

1) 4 * 13 = 52 (cm) - the sum of the lengths of the parallelepiped;

2) 4 * 16 = 64 (cm) - the total value of the width of the parallelepiped;

3) 4 * 21 = 84 (cm) - the sum of the heights of the parallelepiped;

4) 52 + 64 + 84 = 200 (cm) - the sum of the lengths of all the edges of a rectangular parallelepiped.

Thus, to find the sum of the lengths of all edges of a rectangular parallelepiped, we can derive the formula: Z = 4a + 4b + 4c (where Z is the sum of the lengths of the edges).

You have difficulty solving a geometric problem involving a parallelepiped. Theses for solving such problems based on the properties parallelepiped, expressed in a primitive and accessible form. To realize is to decide. Similar larger tasks will not cause you any difficulties.

Instructions

1. For convenience, we introduce the following notations: A and B sides of the base parallelepiped; C is its side face.

2. Thus, at the base parallelepiped lies a parallelogram with sides A and B. A parallelogram is a quadrilateral whose opposite sides are equal and parallel. From this definition it follows that opposite side A lies equal side A. Because the opposite faces parallelepiped are equal (follows from the definition), then its upper face also has 2 sides equal to A. Thus, the sum of all four of these sides is equal to 4A.

3. The same can be said about side B. The opposite side is at the base parallelepiped equal to B. Upper (opposite) face parallelepiped also has 2 sides equal to B. The sum of all four of these sides is 4B.

4. Side faces parallelepiped are also parallelograms (follows from the properties parallelepiped). Edge C is simultaneously a side of 2 adjacent faces parallelepiped. Because the opposite sides parallelepiped are equal in pairs, then all its side edges are equal to each other and equal to C. The sum of the side edges is 4C.

5. Thus, the sum of all edges parallelepiped: 4A+4B+4C or 4(A+B+C) A special case of direct parallelepiped– cube The sum of all its edges is equal to 12A. Thus, the solution of a problem regarding a spatial body can invariably be reduced to the solution of problems with plane figures, into which this body is divided.

Helpful advice
Calculating the sum of all the edges of a parallelepiped is not a difficult task. It is necessary to primitively and accurately understand what a given geometric body is and know its properties. The solution to the problem follows from the very definition of a parallelepiped. A parallelepiped is a prism whose base is a parallelogram. A parallelepiped has 6 faces, all of which are parallelograms. Opposite edges are equal and parallel. This is the main thing.

In geometric problems, quite often there is a need to find some characteristics of a rectangular parallelepiped. In fact, this task is not difficult.

In order to solve it, you need to know the properties of the parallelepiped. If you understand them, then solving problems later will not be so difficult. As an example, let's try to find the sum of the lengths of all the edges of a rectangular parallelepiped.

Quick navigation through the article

Preparation

To make it convenient, you need to decide on the notation: let’s call the sides of the rectangular parallelepiped A and B, and its side face C.

Now, if you look closely, you can conclude that at the base of the rectangular parallelepiped lies a parallelogram. All its edges will have the lengths of sides A and B.

It will be possible to find the sum of the lengths of all edges only if you understand what a parallelogram is. For those who don’t remember, it should be said that a parallelogram is a quadrilateral whose opposite sides are equal and parallel.

Reasoning

A parallelogram has opposite sides equal to each other. It turns out that opposite side A lies the same side A. Based on the definition of a parallelogram, it is clear that its upper edge is also equal to A. It turns out that the sum of the lengths of all sides of a given parallelogram is equal to 4A.

Similar reasoning can be given for side B - it turns out that the sum of the sides of a parallelogram created from side B will be equal to 4 B.

If you look closely, you can conclude that the side faces of a rectangular parallelepiped are also parallelograms. Moreover, edge C simultaneously refers to two adjacent faces of the rectangular parallelepiped. And similar to the reasoning presented above, the sum of the lengths of all edges will be equal to 4 C.

Solution

Now all that remains is to find the sum of the lengths of all the edges by simply summing up all the rectangular parallelograms. And it turns out that this amount is equal to: 4A+4B+4C or 4(A+B+C).

May be considered special case, when it is necessary to find the sum of the lengths of all the edges not of a rectangular parallelepiped, but of a cube - in this case this sum will be equal to 12 A.

In order to solve any geometric problems, you always need to know the definitions well, as you have just seen.

“Calculating the volume of a parallelepiped” - 2. Volume of a rectangular parallelepiped. Task 1: Calculate the volumes of the figures. 1. Mathematics 5th grade. 3. 4.

“Rectangular parallelepiped grade 5” - What is volume? Rectangular parallelepiped. Another formula for the volume of a rectangular parallelepiped. Volume of a rectangular parallelepiped. Formula for the volume of a cube. Example. Volume of a cube. Vershin - 8. Mathematics, 5th grade Logunova L.V. Ribs - 12. Cube. Cubic centimeter. The edge of the cube is 5 cm. There are 6 faces.

“Lesson Rectangular parallelepiped” - 12. C1. IN 1. Length. Parallelepiped. Peaks. Ribs. A1. Width. D. Edges. D1. 8. B. Rectangular parallelepiped.

“Volume of a parallelepiped” - So, according to the rule for calculating volume, we get: 3x3x3=27 (cm3). Even in ancient times, people needed to measure the quantities of certain substances. Volumes of liquids and solids are usually measured in liters. In Ancient Babylon, cubes served as units of volume. Now let's define what volume units are? Lesson topic: Volume of a parallelepiped.

“Rectangular parallelepiped” - Parallelepiped. Rectangular parallelepiped. Municipal educational institution "Gymnasium" No. 6. The word was found among the ancient Greek scientists Euclid and Heron. The work was completed by Alina Mendygalieva, a student of class 5 “B”. Length Width Height. A parallelepiped is a hexagon, all of whose faces (bases) are parallelograms. Peaks. The faces of a parallelepiped that do not have common vertices are called opposite.

“Volume of a rectangular parallelepiped” - Edges. 3. BLITZ – SURVEY (Part I). A, c, c, d. Volumetric. Which edges are equal to edge AE? AE, EF, EH. 1. Any cube is a rectangular parallelepiped. Squares. 5. A cube has all equal edges. 8. Rectangle. 12. 3. All faces of a cube are squares. Name the edges that have vertex E.

There are a total of 35 presentations in the topic

In the fifth century BC, the ancient Greek philosopher Zeno of Elea formulated his famous aporias, the most famous of which is the “Achilles and the Tortoise” aporia. Here's what it sounds like:

Let's say Achilles runs ten times faster than the tortoise and is a thousand steps behind it. During the time it takes Achilles to run this distance, the tortoise will crawl a hundred steps in the same direction. When Achilles runs a hundred steps, the tortoise crawls another ten steps, and so on. The process will continue ad infinitum, Achilles will never catch up with the tortoise.

This reasoning became a logical shock for all subsequent generations. Aristotle, Diogenes, Kant, Hegel, Hilbert... They all considered Zeno's aporia in one way or another. The shock was so strong that " ...discussions continue to this day; the scientific community has not yet been able to come to a common opinion on the essence of paradoxes...were involved in the study of the issue mathematical analysis, set theory, new physical and philosophical approaches; none of them became a generally accepted solution to the problem..."[Wikipedia, "Zeno's Aporia". Everyone understands that they are being fooled, but no one understands what the deception consists of.

From a mathematical point of view, Zeno in his aporia clearly demonstrated the transition from quantity to . This transition implies application instead of permanent ones. As far as I understand, the mathematical apparatus for using variable units of measurement has either not yet been developed, or it has not been applied to Zeno’s aporia. Applying our usual logic leads us into a trap. We, due to the inertia of thinking, apply constant units of time to the reciprocal value. WITH physical point From a perspective, it looks like time slowing down until it stops completely at the moment when Achilles catches up with the turtle. If time stops, Achilles can no longer outrun the tortoise.

If we turn our usual logic around, everything falls into place. Achilles runs at a constant speed. Each subsequent segment of his path is ten times shorter than the previous one. Accordingly, the time spent on overcoming it is ten times less than the previous one. If we apply the concept of “infinity” in this situation, then it would be correct to say “Achilles will catch up with the turtle infinitely quickly.”

How to avoid this logical trap? Remain in constant units of time and do not jump to reciprocals. In Zeno's language it looks like this:

In the time it takes Achilles to run a thousand steps, the tortoise will crawl a hundred steps in the same direction. During the next time interval equal to the first, Achilles will run another thousand steps, and the tortoise will crawl a hundred steps. Now Achilles is eight hundred steps ahead of the tortoise.

This approach adequately describes reality without any logical paradoxes. But this is not a complete solution to the problem. Einstein’s statement about the irresistibility of the speed of light is very similar to Zeno’s aporia “Achilles and the Tortoise”. We still have to study, rethink and solve this problem. And the solution must be sought not in infinitely large numbers, but in units of measurement.

Another interesting aporia of Zeno tells about a flying arrow:

A flying arrow is motionless, since at every moment of time it is at rest, and since it is at rest at every moment of time, it is always at rest.

In this aporia logical paradox it can be overcome very simply - it is enough to clarify that at each moment of time a flying arrow is at rest at different points in space, which, in fact, is motion. Another point needs to be noted here. From one photograph of a car on the road it is impossible to determine either the fact of its movement or the distance to it. To determine whether a car is moving, you need two photographs taken from the same point at different points in time, but you cannot determine the distance from them. To determine the distance to a car, you need two photographs taken from different points in space at one point in time, but from them you cannot determine the fact of movement (of course, you still need additional data for calculations, trigonometry will help you). What I want to point out Special attention, is that two points in time and two points in space are different things that should not be confused, because they provide different opportunities for research.

Wednesday, July 4, 2018

The differences between set and multiset are described very well on Wikipedia. Let's see.

As you can see, “there cannot be two identical elements in a set,” but if there are identical elements in a set, such a set is called a “multiset.” Reasonable beings will never understand such absurd logic. This is the level of talking parrots and trained monkeys, who have no intelligence from the word “completely”. Mathematicians act as ordinary trainers, preaching to us their absurd ideas.

Once upon a time, the engineers who built the bridge were in a boat under the bridge while testing the bridge. If the bridge collapsed, the mediocre engineer died under the rubble of his creation. If the bridge could withstand the load, the talented engineer built other bridges.

No matter how mathematicians hide behind the phrase “mind me, I’m in the house,” or rather, “mathematics studies abstract concepts,” there is one umbilical cord that inextricably connects them with reality. This umbilical cord is money. Applicable mathematical theory sets to the mathematicians themselves.

We studied mathematics very well and now we are sitting at the cash register, giving out salaries. So a mathematician comes to us for his money. We count out the entire amount to him and lay it out on our table in different piles, into which we put bills of the same denomination. Then we take one bill from each pile and give the mathematician his “mathematical set of salary.” Let us explain to the mathematician that he will receive the remaining bills only when he proves that a set without identical elements is not equal to a set with identical elements. This is where the fun begins.

First of all, the logic of the deputies will work: “This can be applied to others, but not to me!” Then they will begin to reassure us that bills of the same denomination have different bill numbers, which means they cannot be considered the same elements. Okay, let's count salaries in coins - there are no numbers on the coins. Here the mathematician will begin to frantically remember physics: on different coins there is different quantities dirt, crystal structure and atomic arrangement of each coin is unique...

And now I have the most interest Ask: where is the line beyond which the elements of a multiset turn into elements of a set and vice versa? Such a line does not exist - everything is decided by shamans, science is not even close to lying here.

Look here. We select football stadiums with the same field area. The areas of the fields are the same - which means we have a multiset. But if we look at the names of these same stadiums, we get many, because the names are different. As you can see, the same set of elements is both a set and a multiset. Which is correct? And here the mathematician-shaman-sharpist pulls out an ace of trumps from his sleeve and begins to tell us either about a set or a multiset. In any case, he will convince us that he is right.

To understand how modern shamans operate with set theory, tying it to reality, it is enough to answer one question: how do the elements of one set differ from the elements of another set? I'll show you, without any "conceivable as not a single whole" or "not conceivable as a single whole."

Sunday, March 18, 2018

The sum of the digits of a number is a dance of shamans with a tambourine, which has nothing to do with mathematics. Yes, in mathematics lessons we are taught to find the sum of the digits of a number and use it, but that’s why they are shamans, to teach their descendants their skills and wisdom, otherwise shamans will simply die out.

Do you need proof? Open Wikipedia and try to find the page "Sum of digits of a number." She doesn't exist. There is no formula in mathematics that can be used to find the sum of the digits of any number. After all, numbers are graphic symbols with which we write numbers, and in the language of mathematics the task sounds like this: “Find the sum of graphic symbols representing any number.” Mathematicians cannot solve this problem, but shamans can do it easily.

Let's figure out what and how we do in order to find the sum of the digits of a given number. And so, let us have the number 12345. What needs to be done in order to find the sum of the digits of this number? Let's consider all the steps in order.

1. Write down the number on a piece of paper. What have we done? We have converted the number into a graphical number symbol. This is not a mathematical operation.

2. Cut one resulting picture into several pictures containing individual numbers. Cutting a picture is not a mathematical operation.

3. Convert individual graphic symbols into numbers. This is not a mathematical operation.

4. Add the resulting numbers. Now that's mathematics.

The sum of the digits of the number 12345 is 15. These are the “cutting and sewing courses” taught by shamans that mathematicians use. But that is not all.

From a mathematical point of view, it does not matter in which number system we write a number. So, in different number systems the sum of the digits of the same number will be different. In mathematics, the number system is indicated as a subscript to the right of the number. WITH a large number 12345 I don’t want to fool my head, let’s look at the number 26 from the article about . Let's write this number in binary, octal, decimal and hexadecimal number systems. We won't look at every step under a microscope; we've already done that. Let's look at the result.

As you can see, in different number systems the sum of the digits of the same number is different. This result has nothing to do with mathematics. It’s the same as if you determined the area of ​​a rectangle in meters and centimeters, you would get completely different results.

Zero looks the same in all number systems and has no sum of digits. This is another argument in favor of the fact that. Question for mathematicians: how is something that is not a number designated in mathematics? What, for mathematicians nothing exists except numbers? I can allow this for shamans, but not for scientists. Reality is not just about numbers.

The result obtained should be considered as proof that number systems are units of measurement for numbers. After all, we cannot compare numbers with different units of measurement. If the same actions with different units of measurement of the same quantity lead to different results after comparing them, it means it has nothing to do with mathematics.

What is real mathematics? This is when the result of a mathematical operation does not depend on the size of the number, the unit of measurement used and on who performs this action.

Sign on the door He opens the door and says:

Oh! Isn't this the women's restroom?
- Young woman! This is a laboratory for the study of the indephilic holiness of souls during their ascension to heaven! Halo on top and arrow up. What other toilet?

Female... The halo on top and the arrow down are male.

If such a work of design art flashes before your eyes several times a day,

Then it’s not surprising that you suddenly find a strange icon in your car:

Personally, I make an effort to see minus four degrees in a pooping person (one picture) (a composition of several pictures: minus sign, number four, degree designation). And I don’t think this girl is a fool who doesn’t know physics. She just has a strong stereotype of perceiving graphic images. And mathematicians teach us this all the time. Here's an example.

1A is not “minus four degrees” or “one a”. This is "pooping man" or the number "twenty-six" in hexadecimal notation. Those people who constantly work in this number system automatically perceive a number and a letter as one graphic symbol.