Unbelievable “multiplication”

There are many conclusions in life that seem ordinary but actually surprise us. For example, in 2001, the American girl Britney found a roll of 1.2 kilometers long and relatively thin toilet paper in a local supermarket. With the help of her parents, she completed the fun of “folding a piece of paper 12 times” for more than 7 hours. Project, and this turned out to be a new Guinness World Record.

If a large enough piece of A4 white paper continues to be folded in half, the thickness after more than forty folds in half is equivalent to the distance between the earth and the moon, and the thickness after 50 folds in half can reach 100 million kilometers-this is the sun and 2/3 of the distance between the earth. Is this beyond your imagination?

Similarly, the story of the king rewarding ministers with grains of wheat on a chess board is similar: Place grains of grain on the chess board, place one grain on the first square, and then the number of grains placed on each square is the same as that of the previous square. 2 times, the king promised to send the minister to fill the chessboard with grains of wheat. This is a problem of summing a geometric sequence. The king soon regretted the facts, because if this went on, the whole country would not be able to deliver enough food. This question is often used to show that the exponential growth rate will far exceed everyone’s imagination. This is the power of “geometric multiplication” in mathematics. In many cases, our first instincts will be wrong, but mathematical calculations can help us recognize the facts.

In the process of exploring the world, mathematics has repeatedly subverted the human worldview. For example, in the era of ancient Greece more than two thousand years ago, people only explored a small part of the world, and the earth seemed boundless and infinite. At that time, the mathematician Eratosthenes used the changes in the shadow length of the poles in the two places to calculate. The perimeter of the earth is calculated, and compared with the current data, the error is only an astonishing 2%. From this we can see that mathematics can help us measure the seemingly unfathomable earth and explore areas beyond our reach.

Mathematician Logan mentioned in his TED speech that mathematics is not a subject of “addition, subtraction, multiplication and division of geometry, algebra, etc.” boring formulas, it is our perception of the patterns, relationships and logic contained in the material world when we observe it.

Mathematical reality woven in the universe

Hidden mathematical laws permeate our entire material world. Some of our senses are captured, but more we need to use mathematics as a magnifying glass to observe its magical beauty, and explore beyond you by looking for a certain connection, structure, law or rule. You can feel the charm of mathematics by understanding the fields beyond your ability.

Mathematics “father of fractals” Mondbrodt proposed in his TED speech that in order to better describe and explain the real nature, we need the concept of “fractal geometry”, which is also called fractal and fractal, which means a Rough or fragmented geometric shapes can be divided into several parts, and each part is the overall reduced shape, with self-similar properties.

Galileo once said: “The law of nature is written in mathematical language, and its representative symbols are triangles, circles and other geometric shapes.” The introduction of fractal geometry helps us understand the complexity of nature.

If your vision is not sharp enough and you still have not found the obvious fractal picture in nature, you may as well compare your own human body. The human body is actually a masterpiece of fractals: such as the surface wrinkles of the brain, the structure of the liver and gallbladder and the small intestine, the urinary system, and the neuron. Distribution, double helix DNA structure and even protein molecular chains have obvious fractal characteristics (with self-similarity and infinite levels).

Fractal geometry in the natural world not only shows the beauty of mathematics, enables the depiction of natural scenery, but also reveals the nature of the world, and also changes the way people understand the mysteries of nature.

Special “language expression”

If there is no existing language, mathematics can also be used to create a special language to describe various patterns. The mathematician Gottfried Leibniz invented the calculus symbol in 1675. This “language” description he created is now widely used. For example, the parabola scene can be expressed by calculus. , Used in the prediction of projectile trajectory in the real world.

Another example of mathematical language expression is the Nemos Braille Math Code, which uses standard six-point Braille cell linear coding mathematics and scientific notation to help the visually impaired to read tactilely and understand the world. These codes are examples of a compact, human-readable markup language, which is used by a large number of systems around the world.

Mathematical expression is not only something that can be seen, it can be touched, but it can also be used for listening. For example, we often see special agents in spy war films using Morse code to send signals. Morse code is a kind of always on and off. The signal codes of, express different English letters, numbers and punctuation marks through different arrangement sequences.

With the development of modern communication tools, Morse code has almost become a patent for amateur wireless enthusiasts, but it once played a huge role in communication and communication a hundred years ago. We can also see mathematical expression vectors that contain a lot of information in our daily lives, such as barcodes and QR codes. What we can see are only different lines or blocks, which have certain coding rules arranged, graphic identifiers used to express a group of information, etc., including a large amount of information such as individuals, commodity categories, transactions, and dates.

Mathematics is a discipline that trains people to explain things from different angles. With the rapid development of the digital field, more and more problems need to be solved by mathematical analysis. It can play a huge role in many fields, so it is very important to learn mathematics well.