Dinostratus (Greek: Δεινόστρατος; c. 390 – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle.
Dinostratus | |
|---|---|
| Born | c. 390 BCE |
| Died | c. 320 BCE |
| Nationality | Greek |
| Known for | Quadratrix of Dinostratus Dinostratus' theorem |
| Scientific career | |
| Fields | Mathematics |
Life and work[edit]
Dinostratus' chief contribution to mathematics was his solution to the problem of squaring the circle. To solve this problem, Dinostratus made use of the trisectrix of Hippias, for which he proved a special property (Dinostratus' theorem) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix of Dinostratus as well.[1] Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.[1] Over 2,200 years later Ferdinand von Lindemann would prove that it is impossible to square a circle using straight edge and compass alone.
https://en.wikipedia.org/wiki/Dinostratus
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
Constructible numbers Angle trisection Doubling the cube Squaring the circle Problem of Apollonius
Concepts/definitions
Angle Central Inscribed Chord 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 Intersecting chords theorem Intersecting secants theorem Inverse Pythagorean theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon
Apollonius
Apollonius's theorem
Other
Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines 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
Authority control Edit this at Wikidata
Integrated Authority File (Germany) VIAF 1 WorldCat
In mathematics, a quadratrix (from the Latin word quadrator, squarer) is a curve having ordinates which are a measure of the area (or quadrature) of another curve. The two most famous curves of this class are those of Dinostratus and E. W. Tschirnhaus, which are both related to the circle.
https://en.wikipedia.org/wiki/Quadratrix
In geometry, a strophoid is a curve generated from a given curve C and points A (the fixed point) and O(the pole) as follows: Let L be a variable line passing through O and intersecting C at K. Now let P1 and P2 be the two points on L whose distance from K is the same as the distance from A to K. The locus of such points P1 and P2 is then the strophoid of C with respect to the pole O and fixed point A. Note that AP1 and AP2 are at right angles in this construction.
In the special case where C is a line, A lies on C, and O is not on C, then the curve is called an oblique strophoid. If, in addition, OA is perpendicular to C then the curve is called a right strophoid, or simply strophoid by some authors. The right strophoid is also called the logocyclic curve or foliate.
https://en.wikipedia.org/wiki/Strophoid
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