Where, how and when to use polynomials?

Question

Mathematics

Hello. I am studying now in the 7th grade, I really like programming, having read all sorts of different books, I still apparently learned the lesson in time for myself that mathematics is needed. The only problem is that the knowledge that I do not understand how to apply is hard for me. Now we go through monomials and polynomials. Well, I understand how to solve them, but I just don’t understand why they are needed. Yes, it's only 7th grade, but still. One of the options, they will be needed further when solving complex problems from further classes, but can polynomials themselves be used in programming?

Answer 1

I'm not sure I understand what it means to "solve polynomials" (simplify them, or what?). Nevertheless:
Imagine that you need to connect several points with a smooth curve. What for? For beauty, not a broken line) Here are the points in the format (x, y): (0.0), (1.1), (2.0), (3.1), here is the solution . This is one of an infinite number of solutions, among others it is distinguished by the fact that it is a polynomial of the minimum degree that satisfies the condition. This is very good - the processor can multiply and add much faster than, say, sines, and, therefore, you can very quickly calculate the height of a point on a curve for any X.

Answer 2

You would also ask why numbers or subtraction are needed (after all, this is the same addition). For example, you need to add many different multiplied variables to different powers. You can stupidly manually write the appropriate code, or you can simply use the polynomial formula.

Answer 3

For example, polynomials (polynomials) are used for polynomial hashing, and they can also be quickly multiplied using the fast Fourier transform.
So if your data is represented as polynomials, you can multiply them quickly, which can be very useful.

Answer 4

If you are wondering how fast computers calculate functions (sine, logarithm...), then it is possible that this is an approximation by Chebyshev polynomials .