tag:blogger.com,1999:blog-37090524521612558162023-09-24T01:38:02.687+03:00Mathematics For BlondesMathematics should be done by blondes - they don't know how to lie.Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.comBlogger183125tag:blogger.com,1999:blog-3709052452161255816.post-41877502120976785842023-05-22T10:54:00.006+03:002023-08-25T22:56:42.477+03:00Negative numbers: subtractionMathematicians tell us that there are positive and negative numbers. Only then do they talk about the absolute value of the number (the modulus of the number). I don't trust mathematicians. Are there negative numbers in nature? What do the plus and minus signs mean in math? We'll try to figure this out.
Negative numbers appear in arithmetic when a larger number is subtracted from a smaller one. Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-76294221263596170852023-04-14T11:28:00.003+03:002023-05-01T15:08:10.321+03:00Аverage percentageAverage percentage
On Reddit, a person asked an interesting question about percentages:
Help with explaining negative compounding
Hey guys, not a maths teacher and I need to teach a concept related to work where something is negatively compounded.
For example:
Of a 1000 items 20% are rejected, leaving 800. At the next stage of those 800 30% are rejected, leaving 560. At next stage of the 560 Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-51645274617945370332023-03-12T11:11:00.008+02:002023-03-12T11:12:58.618+02:00 Sine and cosine tableThis is the most unusual table of sines and cosines. The idea to make such a table came to me in the process of writing these articles:
Why is the sine of 30 degrees equal to half one?
What is the sine of 60 degrees?
Sine and cosine of 45 degrees
I strongly recommend that you read these articles. Then you will know how easy it is to calculate the values of sine and cosine yourself. I Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-44538778548498508402023-03-11T11:29:00.007+02:002023-05-01T15:00:49.779+03:00Sine and cosine of 45 degreesWe have already considered what the sine of 30 degrees is and what the sine of 60 degrees is equal to. Now we will see how to find the sine and cosine of 45 degrees and why they are equal.
Last time we considered an equilateral triangle. Now we will consider an isosceles right triangle. A very rare beast in a herd of triangles. Mathematicians have known it for many thousands of years, and it is Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-10215164956214773212023-03-03T12:37:00.003+02:002023-05-01T15:00:13.663+03:00What is the sine of 60 degrees?Before we look for the answer to the question: "What is the sine of 60 degrees?", I strongly recommend reading the post "Why is the sine of 30 degrees equal to half one?".
Height of an equilateral triangle
I again take an equilateral triangle with a side equal to one. I draw height.
Height of an equilateral triangle
After that, I will not turn anything. I'll just remove half of the drawing.
Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-31734311073475504262023-02-21T23:44:00.003+02:002023-05-01T14:59:45.409+03:00Where does math end?I was offered to sell my Russian site for 45.000 rubles. This prompted me to a very interesting question: "Where does mathematics end?". And here's my answer: "Math ends where money begins". Try any mathematical theory to apply to money and you will learn a lot of interesting things about this theory.
I love math trolling. The sentence contained the phrase: "The price may be revised upwards". MyНиколай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-9783428471147249552023-02-12T19:43:00.006+02:002023-08-25T22:34:15.270+03:00Why is the sine of 30 degrees equal to half one?The answer to the question "why is the sine of 30 degrees equal to half one?" can be searched in the history of mathematics. These are ancient Mesopotamia, ancient Greece and other ancient civilizations. I am not an expert in this area. Obviously, knowledge has evolved from simpler to more complex. I will show you the most obvious answer to this question as I see it.
Equilateral triangle
Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-86709243346844415772022-11-26T19:40:00.004+02:002023-08-25T22:46:29.636+03:00Sums 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-2163769157463417442022-11-22T22:55:00.005+02:002023-08-25T22:44:54.854+03:00Shift 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-55315289881704093942022-11-12T13:20:00.004+02:002023-08-25T23:00:28.494+03:00Trigonometry 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com2tag:blogger.com,1999:blog-3709052452161255816.post-68905384492996489452022-08-13T18:44:00.006+03:002023-08-25T22:43:37.952+03:00Mathematical 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-82276317371245498662022-08-12T21:54:00.002+03:002023-08-25T22:40:42.267+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-33460500031920867212022-08-11T15:43:00.006+03:002023-08-25T22:39:44.417+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-80575954922078127722022-08-11T13:56:00.009+03:002023-08-25T22:38:58.483+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-68850949607480453492022-08-08T13:55:00.009+03:002023-08-25T22:36:51.856+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 theНиколай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-88952592903158614332022-07-28T23:42:00.012+03:002023-08-25T22:36:12.410+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-19794654607665230262022-01-29T09:59:00.002+02:002023-05-01T14:26:13.736+03:00Squaring the circle>Squaring 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-9266210000484013672022-01-01T13:54:00.005+02:002023-08-25T23:01:34.817+03:00Signs 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-81254316264060291072021-10-30T11:17:00.008+03:002023-05-01T14:21:34.307+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 the Николай Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-62252429144254144802021-10-16T13:36:00.006+03:002023-08-25T23:02:31.940+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-1033670902470691322021-07-25T23:09:00.004+03:002023-05-01T14:02:43.269+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-4455710431902987432020-12-20T09:43:00.008+02:002023-08-25T23:03:26.988+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-71941561144321239912019-11-02T21:42:00.005+02:002023-08-25T23:05:31.667+03:00Borsch 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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-18738790356828253162019-10-19T15:59:00.003+03:002023-05-01T13:50:21.323+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0tag:blogger.com,1999:blog-3709052452161255816.post-77066566158309216242019-09-29T15:17:00.003+03:002023-05-01T13:44:59.398+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 Хижняк, Nikolaj Khizhnjakhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0