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🔗 Philosophy 🔗 Philosophy/Philosophical literature 🔗 Books 🔗 Classical Greece and Rome 🔗 Greece 🔗 Philosophy/Ancient philosophy 🔗 Archaeology

The Derveni papyrus is an Ancient Greek papyrus roll that was discovered in 1962 at the archaeological site of Derveni, near Thessaloniki, in Central Macedonia. A philosophical treatise, the text is an allegorical commentary on an Orphic poem, a theogony concerning the birth of the gods, produced in the circle of the philosopher Anaxagoras. The roll dates to around 340 BC, during the reign of Philip II of Macedon, making it Europe's oldest surviving manuscript. The poem itself was originally composed near the end of the 5th century BC, and "in the fields of Greek religion, the sophistic movement, early philosophy, and the origins of literary criticism it is unquestionably the most important textual discovery of the 20th century." While interim editions and translations were published over the subsequent years, the manuscript in its entirety was first published in 2006.

🔗 Classical Greece and Rome 🔗 Greece 🔗 Theatre

In the theatre of ancient Greece, the eirôn (Ancient Greek: εἴρων) was one of three stock characters in comedy. The eirôn usually succeeded in bringing down his braggart opponent (the alazôn) by understating his own abilities.

🔗 Mathematics 🔗 Classical Greece and Rome

The quadratrix or trisectrix of Hippias (also called the quadratrix of Dinostratus) is a curve which is created by a uniform motion. It is traced out by the crossing point of two lines, one moving by translation at a uniform speed, and the other moving by rotation around one of its points at a uniform speed. An alternative definition as a parametric curve leads to an equivalence between the quadratrix, the image of the Lambert W function, and the graph of the function ${\displaystyle y=x\cot x}$.

The discovery of this curve is attributed to the Greek sophist Hippias of Elis, around 420 BC. Historians of mathematics have suggested that Hippias used it to solve the angle trisection problem, hence its name as a trisectrix. Later around 350 BC Dinostratus used it to solve the problem of squaring the circle, hence its name as a quadratrix. Dinostratus's theorem, used by Dinostratus to square the circle, relates an endpoint of the curve to the value of π. Both angle trisection and squaring the circle can be solved using a compass, a straightedge, and a given copy of this curve; however, they cannot be solved with compass and straightedge alone. Although a dense set of points on the curve can be constructed by compass and straightedge, allowing these problems to be approximated, the whole curve cannot be constructed in this way.

The quadratrix of Hippias is a transcendental curve. It is one of several curves used in Greek mathematics for squaring the circle.