How to find the length of all edges of a parallelepiped. We find the sum of the lengths of all edges of a rectangular parallelepiped - the order of calculation
In geometric problems, it is quite often necessary to find some characteristics of a rectangular parallelepiped. In fact, this is an easy task.
In order to solve it, you need to know the properties of the parallelepiped. If you understand them, then it will not be so difficult to solve problems later. As an example, let's try to find the sum of the lengths of all edges of a cuboid.
Quick article navigation
Training
In order to make it convenient, it is necessary to decide on the notation: let's call the sides of a rectangular parallelepiped A and B, and its side face - C.
Now, if you look closely, we can conclude that a parallelogram lies at the base of a rectangular parallelepiped. All its edges, in this case, will have side lengths 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 do not remember, it should be said that a parallelogram is a quadrilateral, the opposite sides of which are equal and parallel to each other.
reasoning
A parallelogram has opposite sides equal to each other. It turns out that the same side A lies opposite side A. Based on the definition of a parallelogram, it is clear that its upper face is also equal to A. It turns out that the sum of the lengths of all sides of this parallelogram is 4A.
Similar reasoning can be given for side B - it turns out that the sum of the sides of the parallelogram created from side B will be 4 V.
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 a rectangular parallelepiped. And similarly to the reasoning presented above, the sum of the lengths of all edges will be equal to 4 C.
Solution
Now it remains to find the sum of the lengths of all the edges by simply summing all the rectangular parallelograms. And it turns out that this sum is: 4A + 4B + 4C or 4 (A + B + C).
You can consider a special case when it will be necessary to find the sum of the lengths of all 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 just saw.
You have a difficulty in solving a geometric problem related to a box. Theses for solving such problems based on properties parallelepiped, expressed in a primitive and accessible form. To understand is to decide. Similar tasks larger will not cause you difficulties.
Instruction
1. For convenience, we introduce the designations: A and B sides of the base parallelepiped; C is its lateral 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 the side A equal to it. From the fact that 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 4A.
3. The same can be said about side B. The opposite side to it 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. From the fact that the opposite faces parallelepiped are pairwise equal, then all its lateral edges are equal to each other and equal to C. The sum of the lateral edges is 4C.
5. So 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 the problem regarding a spatial body can invariably be reduced to the solution of problems with flat figures, into which this body is divided.
Useful advice
Calculating the sum of all the edges of a parallelepiped is a simple task. It is necessary to master primitively what a given geometric body is, and to 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. The parallelepiped has 6 faces, and all of them are parallelograms. Opposite faces are equal and parallel. This is the main thing.
Let's say Achilles runs ten times faster than the tortoise and is a thousand paces behind it. During the time during which Achilles runs this distance, the tortoise crawls a hundred steps in the same direction. When Achilles has run a hundred steps, the tortoise will crawl another ten steps, and so on. The process will continue indefinitely, Achilles will never catch up with the tortoise.
This reasoning became a logical shock for all subsequent generations. Aristotle, Diogenes, Kant, Hegel, Gilbert... All of them, in one way or another, considered Zeno's aporias. The shock was so strong that " ... discussions continue at the present time, the scientific community has not yet managed to come to a common opinion about the essence of paradoxes ... mathematical analysis, set theory, new physical and philosophical approaches were involved in the study of the issue; none of them became a universally accepted solution to the problem ..."[Wikipedia," Zeno's Aporias "]. Everyone understands that they are being fooled, but no one understands what the deception is.
From the point of view of mathematics, Zeno in his aporia clearly demonstrated the transition from the value to. This transition implies applying instead of constants. As far as I understand, the mathematical apparatus for applying variable units of measurement has either not yet been developed, or it has not been applied to Zeno's aporia. The application of our usual logic leads us into a trap. We, by the inertia of thinking, apply constant units of time to the reciprocal. From a physical point of view, it looks like time slowing down to a complete stop at the moment when Achilles catches up with the tortoise. If time stops, Achilles can no longer overtake the tortoise.
If we turn the logic we are used to, everything falls into place. Achilles runs at a constant speed. Each subsequent segment of its 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 infinitely quickly overtake the tortoise."
How to avoid this logical trap? Remain in constant units of time and do not switch to reciprocal values. In Zeno's language, it looks like this:
In the time it takes Achilles to run a thousand steps, the tortoise crawls 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 one hundred steps. Now Achilles is eight hundred paces 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 insurmountability of the speed of light is very similar to Zeno's aporia "Achilles and the tortoise". We have yet 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 of a flying arrow:
A flying arrow is motionless, since at each 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, the logical paradox is overcome very simply - it is enough to clarify that at each moment of time the flying arrow rests at different points in space, which, in fact, is movement. There is another point 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 the fact of the movement of the car, two photographs taken from the same point at different points in time are needed, but they cannot be used to determine the distance. To determine the distance to the car, you need two photographs taken from different points in space at the same time, but you cannot determine the fact of movement from them (naturally, you still need additional data for calculations, trigonometry will help you). What I want to point out in particular is that two points in time and two points in space are two different things that should not be confused as they provide different opportunities for exploration.
Wednesday, July 4, 2018
Very well the differences between set and multiset are described in Wikipedia. We look.
As you can see, "the set cannot have two identical elements", but if there are identical elements in the set, such a set is called a "multiset". Reasonable beings will never understand such logic of absurdity. This is the level of talking parrots and trained monkeys, in which the mind is absent from the word "completely." Mathematicians act as ordinary trainers, preaching their absurd ideas to us.
Once upon a time, the engineers who built the bridge were in a boat under the bridge during the tests of 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. Let us apply mathematical set theory to mathematicians themselves.
We studied mathematics very well and now we are sitting at the cash desk, paying salaries. Here a mathematician comes to us for his money. We count the entire amount to him and lay it out on our table into different piles, in which we put bills of the same denomination. Then we take one bill from each pile and give the mathematician his "mathematical salary set". We explain the mathematics that he will receive the rest of the bills only when he proves that the set without identical elements is not equal to the set with identical elements. This is where the fun begins.
First of all, the deputies' logic will work: "you can apply it to others, but not to me!" Further, assurances will begin that there are different banknote numbers on banknotes of the same denomination, which means that they cannot be considered identical elements. Well, we count the salary in coins - there are no numbers on the coins. Here the mathematician will frantically recall physics: different coins have different amounts of dirt, the crystal structure and arrangement of atoms for each coin is unique ...
And now I have the most interesting question: where is the boundary beyond which 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 here is not even close.
Look here. We select football stadiums with the same field area. The area of the fields is the same, which means we have a multiset. But if we consider the names of the same stadiums, we get a lot, because the names are different. As you can see, the same set of elements is both a set and a multiset at the same time. How right? And here the mathematician-shaman-shuller takes out a trump ace 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 will 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 they are shamans for that, 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 "Sum of Digits of a Number" page. She doesn't exist. There is no formula in mathematics by which you can 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 elementarily.
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's say we 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 to a number graphic symbol. This is not a mathematical operation.
2. We cut one received picture into several pictures containing separate numbers. Cutting a picture is not a mathematical operation.
3. Convert individual graphic characters to numbers. This is not a mathematical operation.
4. Add up 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" from shamans used by mathematicians. But that's not all.
From the point of view of mathematics, it does not matter in which number system we write the 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 of 12345, I don’t want to fool my head, consider the number 26 from the article about. Let's write this number in binary, octal, decimal and hexadecimal number systems. We will not consider each step under a microscope, we have 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 like finding the area of a rectangle in meters and centimeters would give you completely different results.
Zero in all number systems looks the same and has no sum of digits. This is another argument in favor of the fact that . A question for mathematicians: how is it denoted in mathematics that which is not a number? What, for mathematicians, nothing but numbers exists? For shamans, I can allow this, but for scientists, no. Reality is not just about numbers.
The result obtained should be considered as proof that number systems are units of measurement of 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, then this has nothing to do with mathematics.
What is real mathematics? This is when the result of a mathematical action does not depend on the value of the number, the unit of measure used, and on who performs this action.
Ouch! Isn't this the women's restroom?
- Young woman! This is a laboratory for studying the indefinite holiness of souls upon ascension to heaven! Nimbus on top and arrow up. What other toilet?
Female... A halo on top and an arrow down is male.
If you have such a work of design art flashing before your eyes several times a day,
Then it is not surprising that you suddenly find a strange icon in your car:
Personally, I make an effort on myself to see minus four degrees in a pooping person (one picture) (composition of several pictures: minus sign, number four, degrees designation). And I do not consider this girl a fool who does not know physics. She just has an arc stereotype of perception of graphic images. And mathematicians teach us this all the time. Here is an example.
1A is not "minus four degrees" or "one a". This is "pooping man" or the number "twenty-six" in the hexadecimal number system. Those people who constantly work in this number system automatically perceive the number and letter as one graphic symbol.
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 right parallelepiped. A right box in which all six faces are rectangles is called a rectangular box.
2) A cuboid has 12 edges. Moreover, among them there are equal and there are 4 of them.
3) Thus, (13 + 16 + 21) * 4 = 50 * 4 = 200 cm - 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 built from six faces, each of which is a rectangle. Opposite faces of the parallelepiped are equal. A cuboid has 12 edges and 8 vertices. Three edges coming out of the same vertex are called the dimensions of the box or its length, height and width. Thus, a cuboid has four edges of equal length: 4 heights, 4 widths and 4 lengths.
The shape of a rectangular parallelepiped is, for example:
- brick;
- dominoes;
- Matchbox;
- aquarium;
- a pack of cigarettes;
- diplomat;
- box.
A special case of a rectangular parallelepiped is a cube. A cube is a geometric body in the form of a rectangular parallelepiped, but at the same time all its faces are square, so all its edges are equal. A cube has 6 faces (equal to each other in area), 12 edges (equal to each other in length) and 8 vertices.
Calculating the sum of the lengths of all edges of a cuboid
Let's designate dimensions of a 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 cuboid.
Since a rectangular box has 4 heights, 4 widths and 4 lengths (equal to each other), then:
1) 4 * 13 \u003d 52 (cm) - the sum of the lengths of the parallelepiped;
2) 4 * 16 \u003d 64 (cm) - the total value of the width of the parallelepiped;
3) 4 * 21 \u003d 84 (cm) - the sum of the heights of the parallelepiped;
4) 52 + 64 + 84 = 200 (cm) - the sum of the lengths of all edges of a rectangular parallelepiped.
Thus, to find the sum of the lengths of all edges of a cuboid, we can derive the formula: Z = 4a + 4b + 4c (where Z is the sum of the lengths of the edges).
"Calculation of the volume of a parallelepiped" - 2. The volume of a rectangular parallelepiped. Task 1: Calculate the volumes of the figures. 1. Mathematics grade 5. 3.4.
"Rectangular parallelepiped grade 5" - What is volume? Rectangular parallelepiped. Another formula for the volume of a cuboid. The volume of a rectangular parallelepiped. The formula for the volume of a cube. Example. The volume of the cube. Vershin - 8. Mathematics, Grade 5 Logunova L.V. Ribs - 12. Cube. Cubic centimeter. The edge of the cube is 5 cm. Faces - 6.
"Lesson Rectangular parallelepiped" - 12. C1. IN 1. Length. Parallelepiped. Vertices. Ribs. A1. Width. D. Edges. D1. 8. B. Rectangular parallelepiped.
“The volume of the parallelepiped” - So, according to the rule for calculating the volume, we get: 3x3x3 \u003d 27 (cm3). Even in ancient times, people needed to measure the amount of any substances. In liters, volumes of liquids and bulk solids are usually measured. In ancient Babylon, cubes served as units of volume. Now let's define what are units of volume? Lesson topic: The volume of a parallelepiped.
"Rectangular parallelepiped" - Parallelepiped. Rectangular parallelepiped. MOU "Gymnasium" No. 6. The word was found among the ancient Greek scientists Euclid and Heron. The work was done by Student 5 "B" class Mendygalieva Alina. Length Width Height. A parallelepiped is a hexahedron, all of whose faces (bases) are parallelograms. Vertices. The faces of a parallelepiped that do not have common vertices are called opposite faces.
"The volume of a rectangular parallelepiped" - Ribs. 3. BLITZ - SURVEY (I part). A, c, d. Volumetric. Which edges are equal to edge AE? AE, EF, EH. 1. Any cube is a rectangular parallelepiped. Squares. 5. All edges of a cube are equal. 8. Rectangle. 12. 3. All faces of a cube are squares. Name the edges that have vertex E.
There are 35 presentations in total in the topic
Oratory as a prototype of journalism
Quotes about Napoleon - dslinkov — LiveJournal
Me vengeance The man on the bulldozer destroyed the city