Emotion triggered by the series of the Fibonacci series

Everywhere is full of the wind of mathematics, let it blow more violent, although it will blow me without a trace.

I love mathematics in general, but I have learned how powerful it is.

 

Mathematics, mathematics, from arithmetic, to analytic ry, to calculus, and then to composite mathematics, discrete mathematics, probability theory, and, there seems to be many different mathematical branches behind.

I remember that mathematics in high school is just a task, and only mathematics is the most interesting among so many disciplines. The order of going home to do homework every day is the first in mathematics, after all the mathematical assignments are completed, it is the physical chemistry or something. If it is not 12 o'clock, it will recite English words for reading. However, I have never read Chinese, modern, and modern texts. I have never read them, read them in early morning, and have never heard of them.

In junior high school, mathematics has always been my favorite, but I still don't understand what the role it plays? I have never been tired of calculating the slope and intersection of various cone curves. But where can it be used? I didn't think about it at the time. I just learned it in a confused way, and I didn't think so much about it. I thought if I really had to worry about it and didn't find a good reason, I certainly won't study mathematics any more. Maybe I am a real person.

After college, I don't seem to have an impression of the limit derivation, series, Calculus, Calculus, discrete mathematics, composite mathematics, probability theory, and so many things. I'm sorry to say that I forgot, Or I'm sorry to say that I have never heard of these classes because I have never handed in my homework. I just went to class with my ears. People who are confused are terrible. They seem to have lost interest in everything. It is indeed terrible.

Now I want to talk about Mathematics very important. If you are learning computer J!

There are too many reasons, from The 0th digit string in the introduction to computer science and technology, mutual conversion between decimal, binary, octal, and hexadecimal; to the curve drawing function in the GDI plot, what are the rectangles, rectangles, arcs, and strings? These are the basic images that are often encountered in Word Drawing. Then, we can analyze the algorithms that truly reflect the power of mathematics, such as quick sorting algorithms, why is Bubble Sorting slow? Why is it fast? When you rethink this problem with the knowledge of probability theory, everything is so clear. Bubble Sorting traverses n elements every time, it only removes an element that does not need to be compared for the next comparison, and the efficiency is only 1/n. However, it quickly sorts every n elements traversal, it removes half of the elements for the next comparison, and the efficiency is 1/2. It is self-evident that the comparison is fast or slow. Suddenly, the knowledge of probability theory jumped to the front. When you really use the knowledge you learned, you find that there is no fixed formula in the book, and it is not a man-made question that fixed the answer, everything comes from practice, and the useful things are gradually extracted from practice.

 

I accidentally opened the book "Introduction to algorithms", but did not read much, but saw the Fibonacci series. Ha, familiar and unfamiliar name, famous series. If I remember correctly, there will be a Ackerman series, which is also well-known. Describe the Fibonacci series in mathematical language, which is simple and refined and recursive:

 

F (n) = 0 if n = 0

1 If n = 1

F (n-1) + f (n-1) if n> = 2

The value of one item is equal to the sum of the first two items. Let's take a look at the rabbit breeding issues, what monkeys eat peach issues, and what steps they take are all directed at Fig. It is nothing more than to evaluate the value F (n) of the nth item of the Fibonacci ). Recursive programming? What is the recursive down-to-up method? When you look at the several properties of the Fibonacci series:

1.

2. F (n) is an integer equal to or greater than the value.

If you use recursive algorithms that increase exponentially, your computer will not be able to survive for hundreds of years;

If you use down-to-up, first calculate F (0), F (1), F (2 )... And so on, finally finding F (n) is also a good way, three variables, three molding, a variant control iteration when to stop, huh, huh, I clearly want F (N). Why do you need to obtain the Fibonacci series between F (0) and F (n) multiple times ??? Naturally, this approach is not the best. So it's still mathematical mathematics. Mathematics can make you, if you have the ability to control the wild horse of mathematics. If you have learned linear algebra, you are naturally not familiar with matrices.

Haha ///

 

In the algorithm, linear algebra is connected again.

Mathematics is everywhere in the algorithm. Mathematics is everywhere in the computer.

This is especially true in computer graphics, which involves a lot of 3D geometric knowledge. One of the most common problems involved should be dealing with the process of rotating a 3D model in any straight line. Of course, there are other methods to deal with it, such as the magic of using a matrix to rotate the 3D model around the coordinate axis, there is still a lot of knowledge about trigonometric functions in it, but the trigonometric functions here are not difficult and more useful than the questions of trigonometric functions compiled by senior high school students, so that you can continue to learn them with confidence.

 

 

Mathematics is the soul of a computer, but the soul needs to attach to the physical body. The physical body is actually what we can see in various computer programming languages. Although the soul is still great, but less practical, and the body is separated from the soul, it is like walking dead, no meaning. For me, the soul must also be attached to a powerful body, and a strong body needs a great soul for guidance. The perfect combination of body-soul is the real computer, not purely theoretical, because it is not for computer science students and is not biased towards code machines, because that is not a computer science student willing to do. We must be the perfect combination of the body and the soul. There must be no fewer people, or we will not be ourselves.

 

Note: the day after tomorrow, the teacher will read the paper, but I cannot write a word. There are still more than 20 pages to write, and the idea is completely blocked. However, this blog post is easy to write. There is nothing to write in the paper, and it is written as a suicide note.

 

 

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