## Tuesday, February 21, 2023

### Where 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". My response was: "\$45.000 Price may be revised down". From the point of view of mathematics, the equality 45.000=45.000 is beyond doubt. As soon as I add different units of money to this equality, it disappears.

 Where does math end?

We use numbers to measure money. Numbers are written on coins and banknotes. Have you heard of banknote or a coin with the number "zero"? Zero is not a number. The more I study this question, the more I am convinced of the correctness of my statement.

 Zero dollars

I'm not even talking about the minus sign on money. Through the prism of money, I considered set theory. The result is very interesting.

## Sunday, February 12, 2023

### Why is the sine of 30 degrees equal to 1/2?

The answer to the question "why is the sine of 30 degrees equal to 1/2?" 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

 Equilateral triangle

I have drawn an equilateral triangle with sides equal to one. I so want. The sum of the angles of a triangle is 180 degrees. An equilateral triangle has three 60 degree angles. I don't know trigonometry yet.

## Height of an equilateral triangle

 Height of an equilateral triangle

I drew the height in an equilateral triangle. The height is always perpendicular to the base of the triangle. If the height is drawn through the vertex of such a triangle, it will divide it into two equal right-angled triangles. This is always the case in isosceles triangles. An equilateral triangle is a special case of an isosceles triangle, in which the base is equal to the sides.

What happened as a result? The height divided the angle at the apex into two equal angles 60=30+30, it divided the base into two equal segments 1=(1/2)+(1/2). I still haven't heard anything about trigonometric functions.

## Sine 30 degrees

After that, someone came up with trigonometric functions. I was told that the sine of an angle in a right triangle is the ratio of the opposite leg to the hypotenuse. How do I find the sine value for a 30 degree angle? I just flip the picture 90 degrees and remove all unnecessary.

 Sine 30 degrees

The hypotenuse is equal to one. Any number divided by one does not change. So the length of the opposite leg in my triangle is equal to the sine of the angle of 30 degrees, that is, 1/2.

## Cosine 30 degrees

The cosine of 30 degrees I can easily find from the Pythagorean theorem. We take the Pythagorean theorem in our hands and count.

 Cosine 30 degrees

The cosine of 30 degrees turned out to be equal to the square root of three, divided by two.

Here's how easy it is to calculate. No tables needed.