5 mathematical phenomena that researchers say 'represents the beauty of mathematics'

Mathematics is everywhere in nature, such as 'shell shape,' 'river flow,' and 'galaxy vortex.' Thomas Blitz, a lecturer at the Department of Mathematics and Statistics of the University of New South Wales who loves mathematics since childhood and says that 'beauty is mathematical in itself', says that there are five things that exist everyday 'feeling the connection between mathematics and beauty Is mentioned.

The mystique of mathematics: 5 beautiful math phenomena


◆1: Symmetry (symmetric)

Blitz said in a speech in 2018, and can be explained by mathematics emotions such as 'beautiful and it feel'

spoke . Recent studies have shown that our brains are rewarded for finding 'patterns' such as 'seeing symmetrical things', 'organizing the whole' and 'solving puzzles'. .. And when you find something out of the pattern, such as when you meet something unexpected, your brain receives rewards and you can get pleasure and excitement.

For example, a person feels a symmetrical face to be 'beautiful', but if there is something that breaks the symmetry a little, it adds 'beauty' as a charm.

The same thing can be said for music, and when regular sounds with patterns are combined with unexpected elements, they will be considered as individuality, charm, and depth.

Similar harmonies exist in many mathematical concepts, such as 'patterns and unexpected things,' 'elegance and chaos,' and 'truth and mystery,' says Blitz.

◆2: Fractal
A fractal is one in which the part and the whole are self-similar. The Romanesco vegetable is one of the most common fractals in our daily life, and you can see the same shape repeated as you approach the Romanesco.

Such fractal structures are found everywhere in nature, including snow crystals, river flows, flowers, trees and blood vessels.

The fractal layer found in nature is finite, but conceptually, the fractal layer is infinite. 'When you simulate on a computer, you can't see the end of the fractal no matter how close you are,' Blitz said.

◆ 3:

The 'pi' that you learn in mathematics is a little larger than 3 in a nutshell. Blitz says that π is used when calculating the length and area of the circumference of a circle, but in reality, the concept of π is “more than that”.

'If you look at it naturally, you can find π everywhere. π appears not only in the ones that are connected to the circle, but also in the formulas for things that have nothing to do with the circle, such as probability and calculus.' Despite the most famous number, π seems to be full of mystery.

By definition, π is infinite and we cannot know all numbers. Also, as of 2020, no pattern was found below the decimal point. For this reason, my birthday and phone number also exist somewhere in π.

You can use the following website to find out where your phone number is in π.

Irrational Numbers Search Engine

Π is known to be 50 trillion digits when the article is created. Since no one knows the exact value of π, we can't find the exact area of the circle, but we can approach it. Regarding the number π associated with circles around the world, Blitz said, 'We understand some pi truths, but we do not understand pi itself. This mystery creates beauty.' I said.

◆ 4: Golden ratio
The most famous ratio related to beauty is the golden ratio, which is said to 'place objects in the most wonderful way'.

Since the golden ratio is an irrational number that follows '1.6180339887...', it is usually shown in abbreviated form as '1.618'. The geometrical and visual representation of the golden ratio is shown as a curve and a rectangle as shown below.

“Historically, this ratio has been treated as a benchmark for the “ideal form” in architecture, art, and human figure. I call it the ratio of God. Including Leonardo da Vinci Famous art is based on this ratio,” says Bridge.

The golden ratio is still used in a wide range of fields such as art, design and photography, and in 2014 it became a hot topic as the head of Sega's character Sonic the Hedgehog was also made of the golden ratio.

◆5: Banach-Tarsky Paradox
The Banach-Tarsky paradox is the theorem that 'a sphere can be divided into several parts and then recombined to create two spheres of the same size as the original sphere.' In reality, it is impossible to make a ball at hand into two balls of the same size, but mathematically it is possible, says Bridge, 'in a sense, this is magic.'

The above five mathematical concepts are only part of the beauty of mathematics. “To know a lot of the beauty of mathematics, we need the background knowledge. It requires basic, tedious training for athletes to do push-ups many times, but it's worth it. Yes, we hope that many people will enjoy math more, because there are many hidden beauty here,' said Bridge.

in Science, Posted by darkhorse_log