University of Connecticut, Storrs,
History, Mathematics, Poem, Collage
In the 5th century BCE, Hippasus of Metapontum discovered the existence of irrational numbers. Metapontum was a Greek city located on the gulf of Tarentum. It was part of Magna Graecia, the coastal area of southern Italy colonized by Greece, which also included the city of Crotona, where Pythagoras (580 - 500 BCE) settled after he left his native island of Samos. In Crotona, Pythagoras established the secret philosophical society known as the Pythagorean Brotherhood. Hippasus was a member of Pythagorean Brotherhood. The society followed strict rules of conduct and a common lifestyle and philosophy.
A fundamental belief of the Pythagorean Brotherhood was that whole numbers underlie all natural phenomena. Whether in music, or astronomy, or philosophy, the central position of "number" was everywhere evident. This belief led them to undertake investigations into the properties of numbers and to the discovery of many interesting mathematical results. Greek mathematics contributed to the discipline its most fundamental principle -- the requirement that mathematical results are validated by proofs. The Pythagoreans were among the first to prove many mathematical truths that were in common usage in the ancient world, like for example, the so-called Pythagoras Theorem. They also discovered and proved numerous new results in geometry and Number Theory. Many of their discoveries were kept secret and when shared with outsiders, they were presented as a common accomplishment of the entire brotherhood.
Hippasus discovered that
square root of 2
The crisis of incommensurable quantities, as the discovery of the irrational numbers came to be called, increased with the realization that Pythagoras Theorem yields an unlimited number of irrational numbers. It fell to Eudoxus of Cnidos (408 - 355 BCE) to resolve the crisis by introducing a theory of proportion that corrected all the invalid proofs. In the end, the discovery of the irrational numbers turned out to be one of the greatest contributions the Pythagoreans made to mathematics.
The poem "Square root of 2"
plays with the imaginary possibility that Hippasus' murder
occurred before he made his discovery public. How did the
future find out about the irrational numbers and their
answer this, use the power of your imagination. The poem's
stanza line count follows the decimal expansion of square root
The collage "Square root of 2" is a square with a diagonal
labeled by the decimal expansion of square root of 2