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Pappus of Alexandria (; Greek ) ( c. 290 – c. 350 ) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection ( c. 340 ), and for Pappus's Theorem in projective geometry.
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Pappus and Alexandria
The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of Alexandria.
In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century that Apollonius " spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought.
* 320 – Pappus of Alexandria, Greek philosopher, observes an eclipse of the sun and writes a commentary on The Great Astronomer ( Almagest ).
* Pappus of Alexandria, Greek mathematician
* Pappus of Alexandria, Greek mathematician ( d. c. 350 )
He was called Menelaus of Alexandria by both Pappus of Alexandria and Proclus, and a conversation of his with Lucius, held in Rome, is recorded by Plutarch.
* October 18 – Pappus of Alexandria, Greek philosopher, observes an eclipse of the sun and writes a commentary on The Great Astronomer ( Almagest ).
Alexandria, being the center of the Hellenistic world, produced a number of great mathematicians, astronomers and scientists such as Ctesibius, Pappus and Diophantus.
Commentaries on the Almagest were written by Theon of Alexandria ( extant ), Pappus of Alexandria ( only fragments survive ), and Ammonius Hermiae ( lost ).
( This theorem is also known as the Pappus – Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria.
The first geometrical properties of a projective nature were discovered in the third century by Pappus of Alexandria.
As affine geometry deals with parallel lines, one of the properties of parallels noted by Pappus of Alexandria has been taken as a premise:
Pappus of Alexandria made implicit use of concepts equivalent to the cross-ratio in his Collection: Book VII.
A close friendship developed between Simson and Stewart, in part because of their mutual admiration of Pappus of Alexandria, which resulted in many curious communications with respect to the De Locis Planis of Apollonius of Perga and the Porisms of Euclid over the years.
The Suda ( a 10th century Byzantine Greek encyclopedia of known inaccuracy ) states that Pappus was of the same age as Theon of Alexandria, who flourished in the reign of Emperor Theodosius I ( 372 – 395 AD ).
Pappus himself mentions another commentary of his own on the Ἀνάλημμα ( Analemma ) of Diodorus of Alexandria.
* Pappus of Alexandria Encyclopædia Britannica.
* The Hutchinson Dictionary of Scientific Biography ( Helicon Publishing, 2004 ) " Pappus of Alexandria ( lived c. AD 200-350 ) Greek mathematician, astronomer, and geographer whose chief importance lies in his commentaries on the mathematical work of his predecessors.
pt: Pappus de Alexandria
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The theorem is attributed to Pappus of Alexandria and Paul Guldin.
Pappus and Greek
* The Greek mathematician Pappus demonstrates geometrically the property of the center of gravity.
Ancient Greek mathematicians such as Pappus of Alexandria were aware of this property, but the Dandelin spheres facilitate the proof.
Pappus and c
This works out as October 18, 320 AD, and so we can finally say that Pappus flourished c. 320 AD.
In mathematics, Pappus's hexagon theorem ( attributed to Pappus of Alexandria ) states that given one set of collinear points A, B, C, and another set of collinear points a, b, c, then the intersection points X, Y, Z of line pairs Ab and aB, Ac and aC, Bc and bC are collinear.
Pappus and .
Hipparchus also gave an estimate of the distance of the Sun from the Earth, quoted by Pappus as equal to 490 Earth radii.
Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis ( Almagest ) of Claudius Ptolemy.
According to Pappus, " Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics.
" The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
These included notable thinkers such as Euclid, Archimedes, Eratosthenes, Herophilus, Erasistratus, Hipparchus, Aedesia, Pappus, Hypatia, Aristarchus of Samos, and Saint Catherine.
( Book X of Euclid's Elements is described by Pappus as being largely based on Theaetetus's work.
The focus – directrix property of the parabola and other conics is due to Pappus.
Pappus states that the spiral of Archimedes was discovered by Conon.
He continued his studies in Strasbourg, under the professor of Hebrew, Johannes Pappus ( 1549 – 1610 ), a zealous Lutheran, the crown of whose life's work was the forcible suppression of Calvinistic preaching and worship in the day, and who had great influence over him.
Additional properties of fundamental importance include Desargues ' Theorem and the Theorem of Pappus.
Pappus Law: If the red lines are parallel and the blue lines are parallel, then the dotted black lines must be parallel.
Each of these was divided into two books, and — with the Data, the Porisms, and Surface-Loci of Euclid and the Conics of Apollonius — were, according to Pappus, included in the body of the ancient analysis.
Since Pappus gives somewhat full particulars of its propositions, this text has also seen efforts to restore it, not only by P. Fermat ( Oeuvres, i., 1891, pp. 3 – 51 ) and F. Schooten ( Leiden, 1656 ) but also, most successfully of all, by R. Simson ( Glasgow, 1749 ).
Pappus and –
A different date is given by a marginal note to a late 10th century manuscript ( a copy of a chronological table by the same Theon ), which states, next to an entry on Emperor Diocletian ( reigned 284 – 305 AD ), that " at that time wrote Pappus ".
In mathematics, physics, and logic, Pappus ' centroid theorem ( also known as the Guldinus theorem, Pappus – Guldinus theorem or Pappus ' theorem ) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.
Pappus present with bristles 6 – 11 mm long.
Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius – Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte – Coxeter graph, the Dyck graph, the Foster graph and the Biggs-Smith graph.
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