tag:blogger.com,1999:blog-37090524521612558162023-02-04T12:09:28.503+02:00Mathematics For BlondesMathematics should be done by blondes - they don't know how to lie.
Attention! Residents of the European Union to visit the site is strictly forbidden - the evil cookie you eat with your computer! You have been warned.Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.comBlogger176125tag:blogger.com,1999:blog-3709052452161255816.post-86709243346844415772022-11-26T19:40:00.002+02:002022-11-26T19:49:26.717+02:00Sums classificationAnnotation
If you take any sum, then all other sums can be divided into three groups: identical sums, decomposition sums, and other sums. The classification criteria are the terms and the result of the addition.
Identical sums
Identical sums are combined into a separate group by the commutativity property. Sums from this group have pairwise identical terms and an equal number of terms. The Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-2163769157463417442022-11-22T22:55:00.003+02:002022-11-22T22:57:41.275+02:00Shift in arithmeticAnnotation
The use of a shift in arithmetic leads to the addition of terms with different units of measurement.
Consider the results of a shift in arithmetic addition. A shift is possible when performing addition in a column. For example, let's take a three-digit number and add to it the same number without a shift, with a shift by one position and with a shift by two positions. At the same timeНиколай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-55315289881704093942022-11-12T13:20:00.001+02:002022-11-12T13:20:34.937+02:00Trigonometry value table
Trigonometry value table for children
In trigonometry value table lists the sines, cosines, and tangents of multiples of 15 degrees from 0 to 90 degrees.
Trigonometry value table
Why is this table of trigonometry values for kids (and mathematicians)? Firstly, the values of trigonometric functions are not given in numerical form, but in the form of mathematical expressions using square roots. Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-68905384492996489452022-08-13T18:44:00.002+03:002022-11-26T09:02:22.245+02:00Mathematical operations with infinite seriesAnnotation
When performing mathematical operations with infinite series, it is necessary to follow the rules of the positional number system.
Number of terms
The number of terms of an infinite series, presented in the visible part of the series, must be considered as an analogue of writing a number using numbers in the positional number system. The number of terms in the visible part of the Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-82276317371245498662022-08-12T21:54:00.001+03:002022-08-12T21:57:21.676+03:00Permutation of terms in infinite sumsFrom the school bench, everyone knows the rule that appeared in antiquity: the amount does not change from the rearrangement of the terms. By default, it is assumed that the number of terms and their value remain unchanged. If we change the number of terms or change the value of at least one of them, there can no longer be any talk of rearranging the terms. In this case, we have moved from one Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-33460500031920867212022-08-11T15:43:00.003+03:002022-08-11T15:44:02.719+03:00Multiplication by zero in physicsTo finish talking about multiplication by zero, consider an example from physics. There, all laws are written using multiplication. But, unlike mathematicians, physicists understand at least a little what they are talking about.
And so, for simplicity, consider Ohm's law. The simplest option: multiplying current by resistance gives voltage. I specifically use the language and style of Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-80575954922078127722022-08-11T13:56:00.006+03:002022-08-13T23:22:32.880+03:00Multiplication by zero in geometryConsider multiplication by zero in geometry. Multiplying the length by the width gives the area. Whatever mathematicians tell you, all the formulas for the areas of any geometric shapes come down to this simple formula. It’s just that for different figures there are different correction factors, but we’ll talk about this some other time.
We have a rectangle and a formula to calculate its area. Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-68850949607480453492022-08-08T13:55:00.004+03:002022-08-13T23:19:42.127+03:00Multiplication by zero and zero elementMathematicians claim that when multiplied by zero, multiplication occurs and "multiplying by zero (zero element) gives a number equal to zero." Let's look at a couple of examples.
Zero on the football field
We go to the stadium to watch European football. This is exactly what blondes need. Firstly, beautiful gerls are shown on TV. Secondly, in European football, twenty-two millionaires kick the Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-88952592903158614332022-07-28T23:42:00.008+03:002022-08-17T15:45:57.430+03:00Multiplication by zeroIn the comments to the article "Multiplication by zero" of the Russian version of this site, I was asked an interesting question:
Nikolai, I read the article halfway, but still ... There are two apples in front of me (fact). Further, I, like a "sorcerer", multiply them by zero and still see two apples in front of me! Although, according to the laws of arithmetic, they should have disappeared Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-19794654607665230262022-01-29T09:59:00.001+02:002022-01-29T10:00:02.244+02:00Squaring the circleSquaring the circle. The solution of the problem. Almost accurate. Math draw.
Squaring the circle. The solution of the problem. Almost accurate.
This construction is not a solution to the problem of squaring the circle, but it forced me to get my hands on the math and do all the verification calculations. If the correct solution should give a segment with a length of 1.77245 radii, then the Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-9266210000484013672022-01-01T13:54:00.003+02:002022-01-01T14:00:15.169+02:00Signs greater than and less thanHow to remember signs greater than and less than? A very long time ago, when I was little and went to school, the teacher taught us this. Even as an adult, I have always used this method.
We always do more with our right hand than with our left. If we bend our right arm at the elbow and raise it above our head, we get the "GREATER THAN" sign. We do less with our left hand. A bent and raised leftНиколай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-81254316264060291072021-10-30T11:17:00.002+03:002021-10-30T11:21:05.498+03:002 to the power zero fiveHow much is 2 to the power zero five? A trick question, like everything mathematicians come up with for us. In short, transformations look like this.
2 to the power zero five
Now let's take a closer look at the logic of mathematicians. Raising a number to an integer power is the multiplication of these numbers. Raising a number to a fractional power is extracting the root of a number, with Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-62252429144254144802021-10-16T13:36:00.003+03:002021-10-16T13:38:56.794+03:00101 cubed. Bad example. How to find 101 cubed using abbreviated multiplication formulas? I have already shown how, using the cubes of the sum formula, one can calculate one hundred and one in a cube. There I presented one number 101 as the sum of two numbers 100 and 1. The use of simpler (more convenient in calculations) numbers makes the calculation easier.
On the Internet, I saw an example of using other formulas, Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-1033670902470691322021-07-25T23:09:00.002+03:002021-07-25T23:10:37.016+03:00Cube of 101Today we will look at an example of how you can find one hundred and one cubed using the abbreviated multiplication formulas. In other words, how to raise cube of 101 using the abbreviated multiplication formula.
The following cry for help was heard in the comments:
Help please, problem (example) from the physics and mathematics school (Russia), grade 8:
101^3
I don't understand how to solve Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-4455710431902987432020-12-20T09:43:00.005+02:002021-06-12T09:30:05.635+03:00Plus on minus what gives?Positive and negative numbers were invented by mathematicians. The rules for multiplying and dividing positive and negative numbers were also invented by mathematicians. We need to learn these rules in order to tell mathematicians what they want to hear from us.
It's easy to remember the rules for multiplying or dividing positive and negative numbers. If two numbers have different signs, the Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-71941561144321239912019-11-02T21:42:00.000+02:002019-11-02T21:42:52.367+02:00Borsch trigonometry. Addition.I will not tell you recipes for cooking borsch, I will talk about mathematics. What is borsch? These are vegetables cooked in water according to a specific recipe. I will consider two source components (vegetable salad and water) and the final result is borsch. Geometrically, this can be thought of as a rectangle in which one side is a salad, the other side is water. The sum of these two sides isНиколай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-18738790356828253162019-10-19T15:59:00.001+03:002021-10-16T12:23:27.827+03:00Mathematicians lieI watched the video One minus one plus one minus one - Numberphile. Mathematicians lie. They did not perform an equality test in the course of their reasoning.
Mathematicians lie
Confirmation of my reasoning about infinite sets.
If you take a closer look at all the manipulations, the error will immediately become visible. The example is written on one line and "equality" is based on the Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-77066566158309216242019-09-29T15:17:00.001+03:002019-09-29T15:29:30.555+03:00Infinite setConcluding the discussion of sets, you need to consider an infinite set. The fact is that the concept of "infinity" acts on mathematicians, like a boa constrictor on a rabbit. A trembling horror of infinity deprives mathematicians of common sense. Here is an example:
Infinite set
Alpha denotes a real number. The equal sign in the above expressions indicates that if you add a number or Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-85878464083527731172019-08-29T23:13:00.000+03:002019-09-29T15:27:40.374+03:00Set and subsetHow to divide a set into subsets? To do this, it is necessary to introduce a new unit of measure that is present in some elements of the selected set. Consider an example.
Suppose we have a set of A, consisting of four people. This set is formed on the basis of "people." We denote the elements of this set by the letter "a", the subscript with a number will indicate the serial number of each Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-91632237735293715922019-08-26T23:34:00.002+03:002022-07-21T10:01:32.205+03:00The formation of the setI have already told you that set theory is a herd theory by which shamans try to sort out "sea urchins" of reality. How do they do that? How does the formation of the set actually occur?
Initially, individual elements stand out from reality. After that, a set are formed from some elements that have a common property. Shamans always know in advance how a set they want to show us.
I will show theНиколай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-65248553903693442432019-08-10T18:17:00.004+03:002019-08-26T23:45:29.551+03:00Element of the setIf mathematicians cannot reduce the concept of "set" to other concepts, then they do not understand anything in mathematics. I answer the question: how are the elements of one set different from the elements of another set? The answer is very simple: numbers and units of measurements.
Today everything belongs to some kind of set (as mathematicians assure us). By the way, did you look at yourselfНиколай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-21572901546669528922019-08-09T14:06:00.003+03:002019-08-10T18:42:43.574+03:00Set and multisetThe concepts of “set” and “multiset” are two trump ace in the sleeves of a sharpie, one in each sleeve. The sharpie takes out from the sleeve that trump ace, which is more convenient for him to get. In any case, the sharpie always wins. In the same way, any mathematician will always justify set theory.
There can’t be two identical elements in a set, but if there are identical elements in a set, Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-6794102166699561722019-08-09T00:39:00.003+03:002022-07-19T17:29:14.583+03:00Set theorySet Theory
Set theory is the stone age of mathematics. Only shamans know how to properly form the set. Let's look at set theory from the side and reveal some of the secrets of shamans. To understand the essence of set theory, it is necessary to consider another mathematical concept - a function. The function sets the correspondence between the elements of two sets. Each element from the herd of Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com4tag:blogger.com,1999:blog-3709052452161255816.post-8821958239176250002019-01-12T18:02:00.001+02:002019-01-12T18:03:24.811+02:00Achilles and the tortoise
Achilles and the tortoise
In the fifth century BC, the ancient Greek philosopher Zeno of Elea formulated his famous aporia, the most famous of which is the Achilles and the Tortoise aporia. Here’s how it sounds:
Suppose Achilles runs ten times faster than a turtle, and is a thousand paces behind it. During the time that Achilles has run this distance, the tortoise will crawl a hundred steps Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-72265335763427738512018-02-10T12:42:00.003+02:002018-02-10T12:42:52.241+02:00TrapezoidIn Wikipedia there is a page of a trapezoid. In the drawing it is shown that any trapezoid can be turned into a rectangle.
Trapezoid
Let's look at algebra. These are formulas for calculation of lengths of diagonals of a trapezoid.
Diagonals of trapezoid
We substitute in these formulas data for a rectangle.
Diagonals of rectangle
If to trust these formulas, the rectangle has no Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0