08/09/2020

Check out 5 mathematical phenomena to inspire you.

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Fascinating, magical, and capable of generating feelings of joy and enthusiasm in our brains. These are some of the characteristics that Thomas Britz attributes to mathematics. "It's not just seen as beautiful. Beauty is also mathematics. The two are interconnected," assures the researcher from the University of New South Wales, in Australia.

In an article published by the university , the mathematician lists five phenomena that demonstrate the allure of science. Check it out and be inspired!

1. Symmetry

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Symmetry is considered beautiful, but a break in the perceived pattern can also be quite interesting. Symmetrical faces, for example, can be pleasing and beautiful. But a feature that subtly breaks this pattern also contributes to the feeling we have about something being enchanting.

Many mathematical concepts exhibit a harmony between pattern and surprise, elegance and chaos, truth and mystery. “The same idea can be seen in music. Standardized and ordered sounds with a touch of the unexpected can trigger personality, charm, and depth,” Britz points out.

2. Fractals

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Self-referential patterns that repeat themselves, to some extent, on smaller scales can be seen in a variety of phenomena and living beings. Snowflakes, river networks, trees, lightning strikes, and even blood vessels. The closer we look at fractals, the more repetitions of them can be seen.

In the environment, patterns are limited. But in theoretical mathematics, fractals can reproduce infinitely if simulated by computers. "You'll never reach the end," the researcher emphasizes.

3. Pi

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Primarily used to deal with circles, the constant can also be observed in places in nature or in mathematical formulas that have nothing to do with circumferences. Currently, 50 trillion digits of Pi are known, but no standard has yet been found in its decimal places.

“What’s the deal with this strange number that somehow unites all the circles in the world?” Britz asks. “There’s some hidden truth in Pi, but we don’t understand it. This mystique makes everything even more beautiful.”

4. Golden ratio

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Also called the "divine proportion," it is considered the most aesthetically pleasing form an object can have. It can be represented geometrically by a golden rectangle or a golden spiral.

A reference point for ideal form in architecture, art, or the body, the golden ratio has been used throughout history and is still explored by artists, designers, and photographers.

5. Banach-Tarski Paradox

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By dividing a ball in 3D space into specific parts, there is a way to reassemble the parts to create two balls. The Banach-Tarski paradox proposes that, when the two new balls are created, they will both have the same weight as the first.

Although it's not possible in real life, mathematically speaking the theorem works and, for Britz, "that's magic".