English
On the blue island of Samos, a child named Pythagoras was born. From a young age, he was not the type of person to be satisfied with the answer "that's just the way it is." He traveled to Egypt and Babylonia, learning from priests and astronomers about the secrets of the stars and the shapes of the land.
When he returned and settled in Croton, Italy, he founded a school that was more like a "secret club." His followers were known as Pythagoreans. They believed in one extreme motto: "All is number."
**Discovery in the Blacksmith’s Shop**
One day, legend has it that Pythagoras was walking past a blacksmith's shop. He heard the clanging sound of hammers hitting the anvil. He realized something magical:
* Hammers with proportional weights (for example, a 2:1 ratio) produced harmonious tones (octaves).
* From this, he realized that music, which feels so emotional, is actually governed by rigid mathematical rules.
**The Secret of the Right-Angled Triangle**
However, his greatest legacy emerged when he observed the simplest of shapes: the right-angled triangle.
Long ago, the Egyptians already knew that if you had a rope with knots at intervals of 3, 4, and 5, you could form a perfect right angle. But Pythagoras wanted to prove why this occurred for all such triangles.
Imagine a right-angled triangle. On each of its sides, Pythagoras imagined a square attached. He discovered that the areas of the two squares on the short sides, when added together, were exactly equal to the area of the square on the long sloping side.
In the mathematical language we know today:
a² + b² = c²
**The Tragedy Behind the Numbers**
The story of Pythagoras is not just about formulas. The Pythagoreans so revered order that when one of their members, Hippasus, discovered the existence of "nonsensical" numbers (irrational numbers like √2), the group panicked.
To them, numbers that could not be written as simple fractions were a threat to the perfection of the universe. Legend says Hippasus was "disappeared" at sea for leaking the secret of these imperfect numbers.
**The Legacy of the Maestro**
Pythagoras may have been an eccentric teacher (he reportedly forbade his students from eating beans for spiritual reasons!), but he changed the way humanity views the world. He taught that the universe is not random; there are patterns, there is rhythm, and there is logic that we can calculate.
Every time you see an architect building a perpendicular structure, or GPS navigation determining your location, it is there that the spirit of Pythagoras lives on.
When he returned and settled in Croton, Italy, he founded a school that was more like a "secret club." His followers were known as Pythagoreans. They believed in one extreme motto: "All is number."
**Discovery in the Blacksmith’s Shop**
One day, legend has it that Pythagoras was walking past a blacksmith's shop. He heard the clanging sound of hammers hitting the anvil. He realized something magical:
* Hammers with proportional weights (for example, a 2:1 ratio) produced harmonious tones (octaves).
* From this, he realized that music, which feels so emotional, is actually governed by rigid mathematical rules.
**The Secret of the Right-Angled Triangle**
However, his greatest legacy emerged when he observed the simplest of shapes: the right-angled triangle.
Long ago, the Egyptians already knew that if you had a rope with knots at intervals of 3, 4, and 5, you could form a perfect right angle. But Pythagoras wanted to prove why this occurred for all such triangles.
Imagine a right-angled triangle. On each of its sides, Pythagoras imagined a square attached. He discovered that the areas of the two squares on the short sides, when added together, were exactly equal to the area of the square on the long sloping side.
In the mathematical language we know today:
a² + b² = c²
**The Tragedy Behind the Numbers**
The story of Pythagoras is not just about formulas. The Pythagoreans so revered order that when one of their members, Hippasus, discovered the existence of "nonsensical" numbers (irrational numbers like √2), the group panicked.
To them, numbers that could not be written as simple fractions were a threat to the perfection of the universe. Legend says Hippasus was "disappeared" at sea for leaking the secret of these imperfect numbers.
**The Legacy of the Maestro**
Pythagoras may have been an eccentric teacher (he reportedly forbade his students from eating beans for spiritual reasons!), but he changed the way humanity views the world. He taught that the universe is not random; there are patterns, there is rhythm, and there is logic that we can calculate.
Every time you see an architect building a perpendicular structure, or GPS navigation determining your location, it is there that the spirit of Pythagoras lives on.