# .

Menaechmus (b. 380 BC, d. 320) was a Greek mathematician and geometer born in Alopeconnesus (within modern-day Turkey), who was known for his friendship with the renowned philosopher Plato and for his apparent discovery of conic sections and his solution to the then-long-standing problem of doubling the cube using the parabola and hyperbola. There are few direct sources for Menaechmus' work- his work on conic sections is known primarily from a epigram by Eratosthenes, and the accomplishment of his brother (of devising a method to create a square equal in area to a given circle using the quadratrix), Dinostratus, is known solely from the writings of Proclus. Proclus also mentions that Menaechmus was taught by Eudoxus

There is a curious statement by Plutarch to the effect that Plato disapproved of Menaechmus achieving his doubled cube solution with the use of mechanical devices; the proof currently known appears to be solely algebraic.

Menaechmus was said to have been the tutor of Alexander the Great; this belief derives from the following anecdote: supposedly, once, when Alexander asked him for a shortcut to understanding geometry, he replied "O King, for traveling over the country, there are royal road and roads for common citizens, but in geometry there is one road for all" (Beckmann 1989, p. 34). However, this quote is first attributed to Stobaeus ~500 AD, and so whether Menaechmus really taught Alexander is uncertain.

Where precisely he died is uncertain as well- though modern scholars believe that he eventually expired in Cyzicus.

**External links
**

- John J. O'Connor and Edmund F. Robertson. Menaechmus at the MacTutor History of Mathematics archive.

- Article at Encyclopedia Britannica

Ancient Greek and Hellenistic mathematics (Euclidean geometry)

Mathematicians

(timeline)

Anaxagoras Anthemius Archytas Aristaeus the Elder Aristarchus Apollonius Archimedes Autolycus Bion Bryson Callippus Carpus Chrysippus Cleomedes Conon Ctesibius Democritus Dicaearchus Diocles Diophantus Dinostratus Dionysodorus Domninus Eratosthenes Eudemus Euclid Eudoxus Eutocius Geminus Heliodorus Heron Hipparchus Hippasus Hippias Hippocrates Hypatia Hypsicles Isidore of Miletus Leon Marinus Menaechmus Menelaus Metrodorus Nicomachus Nicomedes Nicoteles Oenopides Pappus Perseus Philolaus Philon Philonides Porphyry Posidonius Proclus Ptolemy Pythagoras Serenus Simplicius Sosigenes Sporus Thales Theaetetus Theano Theodorus Theodosius Theon of Alexandria Theon of Smyrna Thymaridas Xenocrates Zeno of Elea Zeno of Sidon Zenodorus

Treatises

Almagest Archimedes Palimpsest Arithmetica Conics (Apollonius) Catoptrics Data (Euclid) Elements (Euclid) Measurement of a Circle On Conoids and Spheroids On the Sizes and Distances (Aristarchus) On Sizes and Distances (Hipparchus) On the Moving Sphere (Autolycus) Euclid's Optics On Spirals On the Sphere and Cylinder Ostomachion Planisphaerium Sphaerics The Quadrature of the Parabola The Sand Reckoner

Problems

Angle trisection Doubling the cube Squaring the circle Problem of Apollonius

Concepts/definitions

Circles of Apollonius

Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center

Results

In Elements

Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon

Apollonius

Apollonius's theorem

Other

Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Cyrene Library of Alexandria Platonic Academy

Other

Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction

Ancient Greece
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