A cuboid is a kind of polyhedron consisting of 6 faces, each of which is a rectangle. In turn, a diagonal is a segment, one that connects opposite vertices of a parallelogram. Its length can be found in two ways.
You will need
- Knowing the length of all sides of a parallelogram.
Instruction
1. Method 1. Given a rectangular parallelepiped with sides a, b, c and a diagonal d. According to one of the properties of a parallelogram, the square of a diagonal is equal to the sum of the squares of its 3 sides. It follows that the length of the diagonal itself can be calculated with the support of extracting a square from a given sum (Fig. 1).
2. Method 2. It is possible that the cuboid is a cube. A cube is a rectangular parallelepiped in which every face is represented by a square. Therefore, all its sides are equal. Then the formula for calculating the length of its diagonal will be expressed as follows: d = a*?3
A parallelepiped is a special case of a prism in which all six faces are parallelograms or rectangles. A parallelepiped with rectangular faces is also called rectangular. A parallelepiped has four intersecting diagonals. Given three edges a, b, c, it is possible to find all the diagonals of the cuboid by performing additional constructions.
Instruction
1. Draw a rectangular box. Write down the driven data: three edges a, b, c. First build one diagonal m. To determine it, we use the quality of a rectangular parallelepiped, according to which all its corners are right.
2. Construct the diagonal n of one of the faces of the parallelepiped. Carry out the construction so that the famous edge, the desired diagonal of the parallelepiped and the diagonal of the face together form a right triangle a, n, m.
3. Detect the constructed face diagonal. It is the hypotenuse of another right triangle b, c, n. According to the Pythagorean theorem, n² = c² + b². Calculate this expression and take the square root of the resulting value - this will be the diagonal of face n.
4. Find the diagonal of the box m. To do this, in a right triangle a, n, m, find an unfamiliar hypotenuse: m² = n² + a². Substitute the known values, then calculate the square root. The resulting result will be the first diagonal of the parallelepiped m.
5. Similarly, draw in steps all the other three diagonals of the parallelepiped. Also, for all of them, perform additional constructions of the diagonals of adjacent faces. Considering the formed right triangles and applying the Pythagorean theorem, find the values of the remaining diagonals of the rectangular parallelepiped.
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Many real objects have the shape of a parallelepiped. Examples are the room and the pool. Parts that have this shape are not uncommon in industry. For this reason, the problem often arises of finding the volume of a given figure.
Instruction
1. A parallelepiped is a prism whose base is a parallelogram. A parallelepiped has faces - all the planes that form a given figure. Each has six faces, and all of them are parallelograms. Its opposite faces are equal and parallel to each other. In addition, it has diagonals that intersect at one point and are divided in half at it.
2. The parallelepiped is of 2 types. For the first, all faces are parallelograms, and for the second, all are rectangles. The final one is called a rectangular parallelepiped. It has all rectangular faces, and the side faces are perpendicular to the base. If a rectangular parallelepiped has faces whose bases are squares, then it is called a cube. In this case, its faces and edges are equal. An edge is a side of any polyhedron, which includes a parallelepiped.
3. In order to find the volume of a parallelepiped, you need to know the area of its base and height. The volume is found based on which particular parallelepiped appears in the conditions of the problem. An ordinary parallelepiped has a parallelogram at its base, while a rectangular one has a rectangle or a square, which invariably has right angles. If a parallelogram lies at the base of the parallelepiped, then its volume is found in the following way: V \u003d S * H, where S is the area of \u200b\u200bthe base, H is the height of the parallelepiped. The height of the parallelepiped is usually its lateral edge. The base of a parallelepiped can also contain a parallelogram that is not a rectangle. It is known from the planimetry course that the area of a parallelogram is equal to: S=a*h, where h is the height of the parallelogram, a is the length of the base, i.e. :V=a*hp*H
4. If the 2nd case occurs, when the base of the parallelepiped is a rectangle, then the volume is calculated using the same formula, but the area of the base is found in a slightly different way: V=S*H,S=a*b, where a and b are respectively the sides rectangle and parallelepiped edge.V=a*b*H
5. To find the volume of a cube, one should be guided by primitive logical methods. From the fact that all the faces and edges of the cube are equal, and at the base of the cube there is a square, guided by the formulas indicated above, it is possible to derive the following formula: V \u003d a ^ 3
A closed geometric figure formed by two pairs of parallel segments of identical length lying opposite each other is called a parallelogram. A parallelogram with all angles equal to 90° is also called a rectangle. In this figure, it is allowed to draw two segments of identical length connecting opposite vertices - diagonals. The length of these diagonals is calculated by several methods.
Instruction
1. If the lengths of 2 adjacent sides are known rectangle(A and B), then the length of the diagonal (C) is very primitive to determine. Assume that diagonal lies opposite the right angle in the triangle formed by it and these two sides. This allows you to apply the Pythagorean theorem in calculations and calculate the length of the diagonal by finding the square root of the sum of the squared lengths of the known sides: C \u003d v (A? + B?).
2. If the length of only one side is known rectangle(A), as well as the value of the angle (?), the one that forms with it diagonal, then to calculate the length of this diagonal (C) you will have to use one of the direct trigonometric functions - cosine. Divide the length of the driven side by the cosine of the famous angle - this will be the desired length of the diagonal: C \u003d A / cos (?).
3. If a rectangle is given by the coordinates of its vertices, then the task of calculating the length of its diagonal will be reduced to finding the distance between two points in this coordinate system. Apply the Pythagorean theorem to a triangle, the one that forms the projection of the diagonal on any of the coordinate axes. It is possible that the rectangle in two-dimensional coordinates is formed by the vertices A(X?;Y?), B(X?;Y?), C(X?;Y?) and D(X?;Y?). Then you need to calculate the distance between points A and C. The length of the projection of this segment on the X axis will be equal to the modulus of the coordinate difference |X?-X?|, and the projection on the Y axis - |Y?-Y?|. The angle between the axes is 90°, from which it follows that these two projections are legs, and the length of the diagonal (hypotenuse) is equal to the square root of the sum of the squares of their lengths: AC=v((X?-X?)?+(Y?- Y?)?).
4. To find the diagonal rectangle in a three-dimensional coordinate system, proceed in the same way as in the previous step, only adding the length of the projection onto the third coordinate axis to the formula: AC=v((X?-X?)?+(Y?-Y?)?+(Z?- Z?)?).
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In the memory of many, a mathematical joke remained: Pythagorean pants are equal in all directions. Use it to calculate diagonal rectangle .
You will need
- Sheet of paper, ruler, pencil, calculator with the function of calculating the roots.
Instruction
1. A rectangle is a quadrilateral with all right angles. Diagonal rectangle A line segment that connects two opposite vertices.
2. On a sheet of paper with a ruler and pencil, draw an arbitrary rectangle ABCD. It’s cooler to do this on a squared notebook sheet - it will be easier to draw right angles. Unite with a segment of the vertices rectangle A and C. The resulting segment AC is diagonal Yu rectangle ABCD.
3. Note, diagonal AC divided rectangle ABCD into triangles ABC and ACD. The resulting triangles ABC and ACD are right triangles, because angles ABC and ADC are 90 degrees rectangle). Remember the Pythagorean theorem - the square of the hypotenuse is equal to the sum of the squares of the legs.
4. The hypotenuse is the side of a triangle that is opposite the right angle. The legs are the sides of a triangle adjacent to a right angle. With regard to triangles ABC and ACD: AB and BC, AD and DC - legs, AC - universal hypotenuse for both triangles (desired diagonal). Therefore, AC squared = AB squared + BC squared, or AC squared = AD squared + DC squared. Plug in the lengths of the sides rectangle into the above formula and calculate the length of the hypotenuse (diagonal rectangle).
5. Let's say the sides rectangle ABCD are equal to further values: AB = 5 cm and BC = 7 cm. The square of the diagonal AC of a given rectangle calculated by the Pythagorean theorem: AC squared \u003d AB square + BC square \u003d 52 + 72 \u003d 25 + 49 \u003d 74 sq. cm. Using a calculator, calculate the square root of 74. You should get 8.6 cm (rounded up). Keep in mind that one of the properties rectangle, its diagonals are equal. So the length of the 2nd diagonal BD rectangle ABCD is equal to the length of diagonal AC. For the above example, this value is 8.6 cm.
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Tip 6: How to Find the Diagonal of a Parallelogram Given Sides
A parallelogram is a quadrilateral whose opposite sides are parallel. The straight lines connecting its opposite angles are called diagonals. Their length depends not only on the lengths of the sides of the figure, but also on the angles at the vertices of this polygon, therefore, without knowing the truth of one of the angles, it is only possible to calculate the lengths of the diagonals in exceptional cases. These are special cases of a parallelogram - a square and a rectangle.
Instruction
1. If the lengths of all sides of the parallelogram are identical (a), then this figure can also be called a square. The values of all its angles are equal to 90°, and the lengths of the diagonals (L) are identical and can be calculated using the Pythagorean theorem for a right triangle. Multiply the length of the side of the square by the root of two - the result will be the length of any of its diagonals: L=a*?2.
2. If it is known about a parallelogram that it is a rectangle with the length (a) and width (b) specified in the conditions, then in this case the lengths of the diagonals (L) will be equal. And here, too, use the Pythagorean theorem for a triangle in which the hypotenuse is the diagonal, and the legs are two adjacent sides of the quadrilateral. Calculate the desired value by extracting the root of the sum of the squared width and height of the rectangle: L=?(a?+b?).
3. For all other cases, the skill of the lengths of the sides alone is enough only to determine the value that includes the lengths of both diagonals at once - the sum of their squares, by definition, is equal to twice the sum of the squares of the lengths of the sides. If, in addition to the lengths of 2 adjacent sides of the parallelogram (a and b), the angle between them (?) is also known, then this will allow us to calculate the lengths of any segment connecting the opposite corners of the figure. Find the length of the diagonal (L?), lying opposite the driven angle, using the cosine theorem - add the squares of the lengths of adjacent sides, subtract the product of the same lengths by the cosine of the angle between them from the total, and extract the square root from the resulting value: L? = ?(a?+b?-2*a*b*cos(?)). To find the length of another diagonal (L?), you can use the parallelogram property given at the beginning of this step - double the sum of the squares of the lengths of 2 sides, subtract the square narrower than the calculated diagonal from the total, and extract the root from the resulting value. In a general form, this formula can be written as follows: L? = ?(a?+b?- L??) = ?(a?+b?-(a?+b?-2*a*b*cos(?))) = ?(a?+b?- a?-b?+2*a*b*cos(?)) = ?(2*a*b*cos(?)).
a, towards the base of the PP;
with his height.
- what do we need to know, what data do we have?
- What are the properties of a rectangular parallelepiped?
- Does the Pythagorean Theorem apply here? How?
- Is there enough data to apply the Pythagorean theorem, or do we need some more calculations?
Diagonal square, of a square cuboid (see the properties of a square cuboid) is equal to the sum of the squares of its three different sides (width, height, thickness), and, accordingly, the diagonal of a square cuboid is equal to the root of this sum.
I remember the school curriculum in geometry, you can say this: the diagonal of a parallelepiped is equal to the square root obtained from the sum of its three sides (they are denoted by small letters a, b, c).
The length of the diagonal of a rectangular prism is equal to the square root of the sum of the squares of its sides.
As far as I know from the school curriculum, class 9, if I'm not mistaken, and if memory serves, then the diagonal of a rectangular parallelepiped is equal to the square root of the sum of the squares of its all three sides.
the square of the diagonal is equal to the sum of the squares of the width, height and length, based on this formula we get the answer, the diagonal is equal to the square root of the sum of its three different dimensions, they denote by letters nсz abc
A rectangular parallelepiped (PP) is nothing more than a prism, the base of which is a rectangle. In PP, all diagonals are equal, which means that any of its diagonals is calculated by the formula:
Another definition can be given, considering the Cartesian rectangular coordinate system:
The PP diagonal is the radius vector of any point in space given by x, y and z coordinates in the Cartesian coordinate system. This radius vector to the point is drawn from the origin. And the coordinates of the point will be the projections of the radius vector (diagonal PP) on the coordinate axes. The projections coincide with the vertices of the given parallelepiped.
A cuboid is a kind of polyhedron consisting of 6 faces, at the base of which is a rectangle. A diagonal is a line segment that connects opposite vertices of a parallelogram.
The formula for finding the length of a diagonal is that the square of the diagonal is equal to the sum of the squares of the three dimensions of the parallelogram.
I found a good scheme-table on the Internet with a complete listing of everything that is in the parallelepiped. There is a formula to find the diagonal which is denoted by d.
There is an image of a face, a vertex, and other things important for the box.
If the length, height and width (a,b,c) of a cuboid are known, then the formula for calculating the diagonal will look like this:
Usually, teachers do not offer their students a bare formula, but make efforts so that they can derive it on their own by asking leading questions:
Usually, after answering the questions posed, students easily derive this formula on their own.
The diagonals of a rectangular parallelepiped are equal. As well as the diagonals of its opposite faces. The length of the diagonal can be calculated by knowing the length of the edges of the parallelogram emanating from one vertex. This length is equal to the square root of the sum of the squares of the lengths of its ribs.
A cuboid is one of the so-called polyhedra, which consists of 6 faces, each of which is a rectangle. A diagonal is a line segment that connects opposite vertices of a parallelogram. If the length, width and height of a rectangular box are taken as a, b, c respectively, then the formula for its diagonal (D) will look like this: D^2=a^2+b^2+c^2.
Diagonal of a cuboid is a line segment connecting its opposite vertices. So we have cuboid with diagonal d and sides a, b, c. One of the properties of a parallelepiped is that a square diagonal length d is equal to the sum of the squares of its three dimensions a, b, c. Hence the conclusion that diagonal length can be easily calculated using the following formula:
Also:
How to find the height of a parallelepiped?
It will be useful for high school students to learn how to solve USE problems for finding the volume and other unknown parameters of a rectangular parallelepiped. The experience of previous years confirms the fact that such tasks are quite difficult for many graduates.
At the same time, high school students with any level of training should understand how to find the volume or area of a rectangular parallelepiped. Only in this case they will be able to count on getting competitive scores based on the results of passing the unified state exam in mathematics.
Key points to remember
- The parallelograms that make up the parallelepiped are its faces, their sides are edges. The vertices of these figures are considered to be the vertices of the polyhedron itself.
- All diagonals of a cuboid are equal. Since this is a straight polyhedron, the side faces are rectangles.
- Since a parallelepiped is a prism with a parallelogram at its base, this figure has all the properties of a prism.
- The side edges of a rectangular parallelepiped are perpendicular to the base. Therefore, they are its heights.
Get ready for the exam together with Shkolkovo!
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You will find the necessary basic information in the "Theoretical reference" section. You can also immediately start solving problems on the topic "Rectangular parallelepiped" online. In the "Catalogue" section there is a large selection of exercises of varying degrees of difficulty. The base of tasks is regularly updated.
Check if you can easily find the volume of a cuboid right now. Disassemble any task. If the exercise is easy for you, move on to more difficult tasks. And if there are certain difficulties, we recommend that you plan your day in such a way that your schedule includes classes with the Shkolkovo remote portal.
Instruction
Method 2 Let's assume that the cuboid is a cube. A cube is a rectangular parallelepiped with each face represented by a square. Therefore, all its sides are equal. Then, to calculate the length of its diagonal, it will be expressed as follows:
Sources:
- rectangle diagonal formula
A parallelepiped is a special case of a prism in which all six faces are parallelograms or rectangles. A parallelepiped with rectangular faces is also called rectangular. A parallelepiped has four intersecting diagonals. If three edges a, b, c are given, you can find all the diagonals of a rectangular parallelepiped by performing additional constructions.
Instruction
Find the diagonal of the parallelepiped m. To do this, in a, n, m, find the unknown hypotenuse: m² = n² + a². Plug in the known values, then calculate the square root. The result obtained will be the first diagonal of the parallelepiped m.
Similarly, draw successively all the other three diagonals of the parallelepiped. Also, for each of them, perform additional construction of the diagonals of adjacent faces. Considering the formed right triangles and applying the Pythagorean theorem, find the values of the remaining diagonals.
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Sources:
- finding a parallelepiped
The hypotenuse is the side opposite the right angle. The legs are the sides of a triangle adjacent to a right angle. With regard to triangles ABC and ACD: AB and BC, AD and DC–, AC is the common hypotenuse for both triangles (the desired diagonal). Therefore, AC = AB square + BC square, or AC B = AD square + DC square. Plug in the lengths of the sides rectangle into the above formula and calculate the length of the hypotenuse (diagonal rectangle).
For example, sides rectangle ABCD are equal to the following values: AB = 5 cm and BC = 7 cm. The square of the diagonal AC of a given rectangle according to the Pythagorean theorem: AC squared \u003d AB square + BC square \u003d 52 + 72 \u003d 25 + 49 \u003d 74 sq. cm. Use a calculator to calculate the square root of 74. You should end up with 8.6 cm (rounded up). Keep in mind that one of the properties rectangle, its diagonals are equal. So the length of the second diagonal BD rectangle ABCD is equal to the length of diagonal AC. For the above example, this value
In the fifth century BC, the ancient Greek philosopher Zeno of Elea formulated his famous aporias, the most famous of which is the aporia "Achilles and the tortoise". Here's how it sounds: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 physical point To the eye, it looks like time slowing down until it stops completely 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.
