The Pythagorean theorem, a staple of high school mathematics, is remembered by many as a near-magical formula: (a^2 + b^2 = c^2). This equation states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. While the theorem itself is a cornerstone of geometry, the story of Pythagoras, the ancient philosopher behind the theorem, and his followers reveals a profound narrative about the limits of rational thought.
The Enigmatic Figure of Pythagoras
Annual Subscriptions Save 20% – But Only for These 5 Services
OVID TV Shows Documentary Films Major Platforms Refuse to Stream
Pythagoras, a prominent figure of the 6th century BC, was more than just the mathematician behind the famous theorem. He founded a community that melded science, religion, and philosophy. The Pythagoreans, as his followers were known, held a profound belief in the power of numbers, viewing them as the core essence of the universe. They thought that everything—from the cosmos to music to life itself—could be understood through numerical ratios. They lived by the credo, “the number explains everything.”
Life and Beliefs of the Pythagoreans
The Pythagorean community was distinctive in several ways:
- Vegetarianism: They practiced vegetarianism, which was uncommon at the time.
- Gender equality: They promoted a degree of equality between men and women, which was progressive for their era.
- Spiritual rules: Their life was governed by strict spiritual rules, including a requisite five years of silence for new initiates, during which they could only listen to teachings and were required to renounce material possessions.
Paramount+ Streams Every Star Trek Episode Except These 12
Amazon Prime Student Cuts Streaming Costs in Half
They believed in the eternal nature of the soul, viewing the physical body merely as a temporary vessel.
The Discovery That Shook Their World
The Pythagoreans classified numbers into various types, such as odd, even, perfect, and polygonal, and attributed symbolic meanings to them. Numbers like one, which represented the origin, and three, which symbolized harmony, were integral to their beliefs. However, all these numbers had one thing in common: they were rational, meaning they could be expressed as fractions.
The universe of rational numbers, however, was dramatically challenged by a simple yet profound discovery stemming from the theorem that bears Pythagoras’ name. The diagonal of a square with sides of length 1 measures (sqrt{2}), a number that cannot be expressed as a fraction—making it irrational.
A Secret That Could Not Be Contained
The revelation of the existence of irrational numbers caused significant distress within the Pythagorean community, to the extent that there were attempts to suppress this knowledge. The story goes that one member, Hippasus of Metapontum, dared to reveal this secret. His fate, as legend has it, was to be thrown into the sea for disclosing what was supposed to remain hidden.
This unsettling discovery shook the very foundations of mathematical reason, highlighting that even the rational has its limits. The implications of this finding underscore an enduring lesson: the boundaries of understanding are not always as fixed as they might seem.
In the narrative of mathematics and philosophy, the story of Pythagoras and his theorem is not just about the principles of geometry. It is also a tale of how knowledge and belief systems can be challenged, leading to new paradigms that redefine the limits of rationality and expand our understanding of the universe.
Daniel Harris is a specialist journalist focused on the crossroads of breaking news, extraordinary history, and enduring legends. With a background in historical research and storytelling, he blends timely reporting with timeless narratives, making complex events and ancient myths resonate with today’s readers. Daniel’s work often uncovers surprising links between present-day headlines and legendary tales, offering unique perspectives that captivate diverse audiences. Beyond reporting, he is passionate about preserving oral traditions and exploring how extraordinary stories continue to shape culture and identity.