tag:blogger.com,1999:blog-37090524521612558162021-10-16T23:43:35.530+03:00Mathematics For BlondesMathematics is very simple. Mathematicians make mathematics difficult.
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.comBlogger164125tag: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, <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/bl2axykLCoQ" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2021/10/101-cubed-bad-example.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/j1BK_IrY1YA" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2021/07/cube-of-101.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/Dl4AMC5qhtc" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2020/12/plus-on-minus-what-gives.htmltag: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 is<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/1URqmBzolyg" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/11/borsch-trigonometry-addition.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/UUh3USEqMdQ" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/10/mathematicians-lie.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/MwEr6l_Xnbw" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/09/infinite-set.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/YaS0n5a0Ew4" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/08/set-and-subset.htmltag:blogger.com,1999:blog-3709052452161255816.post-91632237735293715922019-08-26T23:34:00.001+03:002019-08-26T23:34:42.004+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 the<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/ytGm3t4ZAwc" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/08/the-formation-of-set.htmltag: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 yourself<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/p70Di7j-mNk" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/08/element-of-set.htmltag: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, <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/oayNW8vHNcI" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/08/set-and-multiset.htmltag:blogger.com,1999:blog-3709052452161255816.post-6794102166699561722019-08-09T00:39:00.000+03:002019-08-09T14:09:07.881+03:00Set theorySet 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 hunters is <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/QkccvxGP94Q" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com4http://www.mathforblondes.com/2019/08/set-theory.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/VlrKa7t2Nzs" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2019/01/achilles-and-tortoise.htmltag: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 <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/AeymPZLgj4o" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2018/02/trapezoid.htmltag:blogger.com,1999:blog-3709052452161255816.post-87042188895371974592017-03-02T11:32:00.000+02:002017-03-03T10:40:28.438+02:00Inverse transformationsLast time we transformed the law of cosines and a Pythagorean theorem to the sum of a line segments. Now we will execute inverse transformations.
Inverse transformations
In inverse transformations I made everything very simply. The minus sign from a formula disappeared. The problem is that we are not able to measure angles correctly. Than differ a angle 0 degrees from a angle of 180 degrees?<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/6XXLYiXB9Ug" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/03/inverse-transformations.htmltag:blogger.com,1999:blog-3709052452161255816.post-12949604877057335842017-02-27T11:08:00.002+02:002017-03-03T10:40:12.516+02:00We use the law of cosinesI was always interested in a question: how the Pythagorean theorem turns into the sum of a line segments? What I speak about? Here you look.
The Pythagorean theorem and the sum of a line segments
In geometry everything is very prime. The first time we draw a right triangle and we write down a Pythagorean theorem. The second time we draw two a line segments and we write down the sum of a line <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/D0fwjIZAPZw" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/we-use-law-of-cosines.htmltag:blogger.com,1999:blog-3709052452161255816.post-30585274591263641772017-02-25T17:01:00.002+02:002017-02-25T17:02:11.075+02:00Law of sinesThe law of sines (sine law, sine formula, or sine rule) is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
The law of sines
Where:
a, b, c - are the lengths of the sides of a triangle;
α, β, γ - are the opposite angles;
T - are the area of triangle;
R - are the radius of the triangle's circumcircle.
How to use this monster? Use dress-making<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/wyUyMRSR-EY" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/law-of-sines.htmltag:blogger.com,1999:blog-3709052452161255816.post-10359455782375693262017-02-13T12:35:00.000+02:002017-02-13T12:35:47.641+02:00Transformations of trigonometric functions
Transformations of trigonometric functions
This table shows how one trigonometric functions can be transformed to other trigonometric functions. Sin, cos, tan, cot, sec, csc - all these functions can be transformed.<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/2_aeO4VOuUA" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/transformations-of-trigonometric.htmltag:blogger.com,1999:blog-3709052452161255816.post-78593054532015287022017-02-10T17:28:00.000+02:002017-02-10T17:28:53.306+02:00Number to the power minus oneWhat to do if number to the power minus one? Write down this number in a fraction denominator. Here several examples with numbers to the power minus one.
Number to the power minus one
Negative exponents of numbers mean that these numbers are in a fraction denominator.
Negative exponents
<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/Z7Ykl2Dt0eA" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/number-to-power-minus-one.htmltag:blogger.com,1999:blog-3709052452161255816.post-6274382550958954502017-02-10T10:14:00.003+02:002017-02-10T10:15:33.640+02:00Trigonometrical circle of a tangentLast time I drew for you a unit circle of cotangent. Now you can look at a trigonometrical circle of tangent.
Trigonometrical circle of a tangent
There is no sense here. There are angles and values of tangents. If you want to understand sense of a tangent and cotangent, look here.<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/m89BdvrvSpU" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com1http://www.mathforblondes.com/2017/02/trigonometrical-circle-of-tangent.htmltag:blogger.com,1999:blog-3709052452161255816.post-4832252783356505882017-02-08T16:38:00.001+02:002017-02-17T01:51:23.992+02:00Trigonometric table
Trigonometric table are crazy
This trigonometrical table is an example of mathematical marasmus. I am touched by exact values of a sine and cosine. No comments.
If mathematicians do not know what is trigonometric functions, let read here. If mathematicians are not able to divide into zero, let study. I like the idea of this table. I do not like its contents. I corrected this <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/vXAIqkHV1_w" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com1http://www.mathforblondes.com/2017/02/trigonometric-table.htmltag:blogger.com,1999:blog-3709052452161255816.post-28503095391438786712017-02-08T00:51:00.001+02:002017-02-08T00:53:17.863+02:00Cotangent 210 degreesToday we will consider a cotangent of 210 degrees. We will draw a unit disk and we will write values of cotangents. Here what turned out.
The unit circle and cotangent
Value of a cotangent of 210 degrees same, as at a cotangent of 30 degrees. We take mathematics in hand and we check. The cotangent is the cosine divided into a sine. Values of a sine and cosine of 30 and 210 degrees can be taken<img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/BPr0TBB-KF0" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/cotangent-210-degrees.htmltag:blogger.com,1999:blog-3709052452161255816.post-29881389006751960422017-02-07T11:46:00.001+02:002017-02-07T11:47:56.866+02:00Signs of trigonometric functionsAll trigonometric functions can have different signs. Signs of trigonometric functions depend on the coordinate system. In mathematician the Cartesian coordinate system is accepted. Four quadrants of a Cartesian coordinate system define signs of trigonometric functions.
Signs of trigonometric functions
You do not speak to mathematicians, but remember. Signs are not property of trigonometric <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/N5z5vTyZN2E" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/signs-of-trigonometric-functions.htmltag:blogger.com,1999:blog-3709052452161255816.post-53798046611689470672017-02-06T13:56:00.002+02:002017-02-06T13:59:26.749+02:00How to divide fraction into fraction?When performing calculations often there is a question: "How to divide fraction into fraction?". Mathematicians rules tell so:
To divide a number by a fraction, multiply that number by the reciprocal of that fraction.
How to divide fraction into fraction?
Transform fraction to division if in numerator and a denominator there are fractions. Be attentive! The numerator and denominator of <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/7vJC38LWtKU" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/how-to-divide-fraction-into-fraction.htmltag:blogger.com,1999:blog-3709052452161255816.post-32800044338097616672017-02-03T16:48:00.000+02:002017-03-03T10:39:39.782+02:00Non-inertial engine of the UFOLast time we considered the fine-molded engine which is used in our technique. The main shortcoming - they do not save the vehicle from influence of inertial forces. Our observations show that the UFO can instantly change speed, can turn at a huge speed at right angle. It breaks the fundamental law of physics - a law of inertia. We consider that it is impossible. If such flights are impossible, <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/p4G8BBwheJU" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com2http://www.mathforblondes.com/2017/02/non-inertia-engine-of-ufo.htmltag:blogger.com,1999:blog-3709052452161255816.post-37725139617913252712017-02-01T19:08:00.001+02:002017-02-01T19:09:13.040+02:00Engines and inertiaBe not surprised to the fact that now we will speak about engines and inertia. This introduction to more fascinating conversation on extra-terrestrials and their UFO. We will speak with engaging of mathematical concepts. But before to discuss extra-terrestrials, let's talk about us and the level of development of our technique.
And so, we will begin with mathematics. The matter is that all our <img src="http://feeds.feedburner.com/~r/MathematicsForBlondes/~4/p2FmULLmyeU" height="1" width="1" alt=""/>Николай Хижнякhttp://www.blogger.com/profile/12714206257364077985noreply@blogger.com0http://www.mathforblondes.com/2017/02/engines-and-inertia.html