Lucian of Samosata and ancient Greek Science Fiction

Λουκιανός Σαμοσατεὺς

Ancient Greek Mathematical Curves


The classic cube doubling, angle trisection and squaring the circle problems.

Trying to solve the classical problems of Antiquity, such as the trisection problem, Greeks discovered different mathematical curves. There was no systematic theory of higher-degree curves in Greek mathematics but Greeks studied many interesting special cases:

  • The Cissoid of Diocles ( c. 100 BC )

Diocles showed that the Cissoid a cubic curve defined by y2 (1+x) = (1-x)3 could be used to duplicate the cube

  • The Spiric Sections of Perseus ( c. 150 BC )

  • The Epicycles of Ptolemy ( c. 140 AD ) used to describe the retrograde motion of Planets in his Earth centric model.

  • Ellipse, Parabola, Hyperbola (Conic Sections) discovered probably by Menaechmus and theory studied in details by Apollonius.

Xah Lee has a very interesting Website that includes also information of Curves among which some have been discovered by ancient Greek mathematicians. I provide the links to the corresponding plane curves. Later I will provide additional information. Also other links are provided.

CURVE

LINKS

Archimedean Spiral

Archimedean Spiral

Conchoid of Nicomedes

Conchoid of Nicomedes

Pappus on Nicomedes' cochloid (conchoid)

Cissoid of Diocles

Cissoid of Diocles

Cissoid and burning mirrors

Spiric of Perseus

Spiric of Perseus

General Conic Sections

Conic Sections

Ellipse

Ellipse

Hyperbola

Hyperbola

Parabola

Parabola

Quadratix of Hippias

A Crowning Achievement: The Quadratrix of Hippias

Quadratrix of Hippias

Pappus on the Quadratrix

Construction from a cylindrical spiral, as the intersection of a plektoid and a plane

Construction from an Archimedes spiral, as the intersection of a plektoid and a plane

Hippopede of Proclus (and Eudoxus)

The Hippopede of Proclus (and Eudoxus)

The Hippopede of Proclus

Philon's Line

The Philon's Line


Derivation of the Formula for the Area of a Circle and the Pythagorean Theorem


LINKS

Vignettes of Ancient Mathematics by Henry Mendell, Cal. State U., L.A.


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