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Topic: Pappus


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In the News (Sun 16 Jun 19)

  
  Bryn Mawr Classical Review 2002.03.31
She argues persuasively that Pappus attempts in this book to present himself as the key representative or authority in a discipline, mathematics, which he regards as superior to philosophy because it proves what philosophers take for granted, paradigmatically, that the sphere is the largest of all regular polyhedra with the same surface area.
Pappus defines mechanics as the science of the rest and motion (both natural and contrary to nature) of bodies in the universe, and distinguishes the theoretical part which embraces the mathematical and natural sciences from the practical part which involves craft.
As Cuomo shows, Pappus' account of mechanics serves to incorporate previous views of what mechanics is in such a way that their differences are at once recognized and mitigated, thus allowing him to present himself as a leading proponent of a science with a tradition that goes back to Archimedes and includes Ptolemy.
ccat.sas.upenn.edu /bmcr/2002/2002-03-31.html   (1741 words)

  
 PAPPUS OF ALEXANDRIA - LoveToKnow Article on PAPPUS OF ALEXANDRIA   (Site not responding. Last check: 2007-11-03)
Pappus himself refers to another commentary of his own on the AvandX~jz.ua of Diodorus, of whom nothing is known.
Incidentally Pappus describes the thirteen other polyhedra bounded by equilateral and equiangular but not similar polygons, discovered by Archimedes, and finds, by a method recalling that of Archimedes, the surface and volume of a sphere.
Pappus then enumerates works of Euclid, Apollonius, Aristaeus and Eratosthenes, thirty-three books in all, the substance of which he intends to give, with the lemmas necessary for their elucidation.
18.1911encyclopedia.org /P/PA/PAPPUS_OF_ALEXANDRIA.htm   (1458 words)

  
 Pappus   (Site not responding. Last check: 2007-11-03)
Pappus of Alexandria is the last of the great Greek geometers and one of his theorems is cited as the basis of modern
Again Pappus refers to a friend who was also a philosopher, named Hierius, but other than knowing that he encouraged Pappus to study certain mathematical problems, we know nothing else about him either.
That Pappus wrote on Geography is stated in the Suda and a work which claims to be written by Moses of Khoren in the fifth century seems to be largely based on Pappus's Geography.
www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Pappus.html   (2100 words)

  
 [No title]   (Site not responding. Last check: 2007-11-03)
Pappus speaks poetically of the divine mission of the bees to bring from heaven the wonderful nectar known as honey, and says that in keeping with this mission they must make their honeycombs without any cracks through which honey could be lost.
Inasmuch as Pappus showed that of two regular polygons having equal perimeters the one with the greater number of sides has the greater area, he concluded that bees demonstrated some degree of mathematical understanding in constructing their cells as hexagonal, rather than square or triangular prisms.
Pappus the Alexandrine has left us an account of its hexagonal plan, and drew from it the conclusion that the bees were endowed with ``a certain geometrical forethought''.
www.math.pitt.edu /~thales/kepler98/honey/hexagonHistory.html   (1827 words)

  
 Opinion & Analysis   (Site not responding. Last check: 2007-11-03)
To add to the complexity, Pappu the electrician turned out to be a better carpenter than Pappu the carpenter, and so he ended up executing most of the woodwork while the original Pappu carpenter sulked on the sidelines.
When the cook called Pappu the peon in for tea, all the Pappus took advantage of their name and had a cuppa.
Pappu was my pet name when I was young, but then the name just stuck.” Suddenly he had a bright idea to get out of this Pappu conundrum.
www.business-standard.com /common/storypage.php?storyflag=y&leftnm=lmnu5&leftindx=5&lselect=2&chklogin=N&autono=188829   (582 words)

  
 Stylized demonstration of the dual of Pappus' theorem
Furthermore, it's in fact a stylized reformulation of the dual to Pappus theorem.
Indeed, that dual theorem asserts that for two triplets of concurrent lines, the joints of some of their intersections concur.
The situation is curious: a result in projective geometry that knows not angles nor distances is obtained by means of analytic geometry in which the notions of angle and distance play a central role via the Pythagorean theorem.
www.cut-the-knot.org /Curriculum/Geometry/PappusDual.shtml   (386 words)

  
 PAPPUS OF ALEXANDRIA - Online Information article about PAPPUS OF ALEXANDRIA
Theodosius I. Suidas says also that Pappus wrote a commentary upon the same work of Ptolemy.
Diocletian (A.D. 284—305), that Pappus wrote during that period; and in the absence of any other testimony it seems best to accept the date indicated by the scholiast.
Pappus himself refers to another commentary of his own on the 'AvaXrlµua of Diodorus, of whom nothing is known.
encyclopedia.jrank.org /PAI_PAS/PAPPUS_OF_ALEXANDRIA.html   (2256 words)

  
 Pappus' Theorem
Pappus of Alexandria was a Greek mathematician who lived around the end of the third century AD, although the exact date is uncertain.
In addition, Pappus gave some apparently original results, such as the proposition that is commonly called "Pappus' Theorem" involving a hexagon inscribed between two lines.
About 1300 years after Pappus wrote the Collection, an interesting generalization of Pappus' Theorem was discovered by Blaise Pascal based on the ideas of Girard Desargues.
www.mathpages.com /home/kmath542/kmath542.htm   (780 words)

  
 No Title
As an independent contribution Pappus formulated the volume of a solid of revolution, the result we now call the The Pappus - Guldin Theorem.
Bees, then, know just this fact which is useful to them, that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material in constructing each.
Pappus also discusses the three and four lines theorem of Apollonius.
www.math.tamu.edu /~don.allen/history/pappus/pappus.html   (1400 words)

  
 Pappus' Theorem
The dual of Pascal's theorem has been proven by Charles Julien Brianchon (1783-1864) in 1810 and is known as Brianchon's theorem.
From the broad geometric view point the simplest reply is that the nature of Pappus' theorem is projective.
(Pappus' theorem is generalized by a theorem of Pascal.
www.cut-the-knot.org /pythagoras/Pappus.shtml   (1280 words)

  
 Conic Sections in Ancient Greece
While Pappus of Alexandria was a competent mathematician and geometer, we are interested here in his work as a mathematical commentator and historian of mathematics.
Like Pappus, he had access to original documentation of the mathematics of the Classical and Hellenistic eras that is no longer available.
Pappus says that Euclid wrote about the basic theory of conic sections, targeting his propositions to prepare readers to analyze the solid loci of Aristaeus (Heath, 1961, p.
www.math.rutgers.edu /~cherlin/History/Papers1999/schmarge.html   (5833 words)

  
 pappus   (Site not responding. Last check: 2007-11-03)
Closely associated with Desargues Theorem is the wonderful theorem of Pappus.
Pappus' Theorem (projective plane version) states that given the three points A, B, and C on line l and A', B', and C' on line m that if segments AB' and A'B meet at R, BC' and B'C meet at P, and CA' and C'A meet at Q then P, Q, and R are collinear.
It turns out that one can introduce a coordinate system for a geometry where the coordinates are drawn from a field provided that Pappus' Theorem holds.
www.york.cuny.edu /~malk/mycourses/math244/pappus.html   (410 words)

  
 Archimedean Solids (Pappus)
Below is a translation from the fifth book of the "Collection" of the Greek mathematician Pappus of Alexandria, who lived in the beginning of the fourth century
The earliest surviving manuscript of this work dates from the tenth century and is identified as Codex Vaticanus Graecus 218.
This manuscript gives the first known mention of the thirteen "Archimedean solids", which Pappus lists and attributes to Archimedes.
www.mcs.drexel.edu /~crorres/Archimedes/Solids/Pappus.html   (425 words)

  
 UW-Stevens Point- Freckmann Herbarium: KEY TO TRIBES OF WISCONSIN COMPOSITAE - Tribe 2
   Stems branched or unbranched and leafy or subscapose; achenes truncate or tapered, rarely short-beaked; pappus pale yellow, red-brown, tannish or white; involucral bracts uni- or biseriate.
 Pappus of 5 to numerous outer scales alternating with 5 to numerous scabrous hairs; plants scapose or sub-scapose, branched or not branched; corolla yellow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
 Pappus of numerous minute scales; plants profusely branched; corolla blue, rarely pink or white. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
wisplants.uwsp.edu /Composites/tribe_2.htm   (1423 words)

  
 UW-Stevens Point- Freckmann Herbarium: KEY TO TRIBES OF WISCONSIN COMPOSITAE - Tribe 11   (Site not responding. Last check: 2007-11-03)
  Leaves alternate; plants from a stout taproot or enlarged corm; achenes 10-ribbed; pappus of plumose or barbellate bristles; phyllaries weakly or strongly ribbed.
  Pappus barbellate, not plumose, the lateral cilia 3-6 times the diameter of the bristle.
  Pappus plumose, the lateral cilia 15 or more times the diameter of the bristle; heads cylindrical; phyllaries mucronate to acuminate, the margins ciliate.
wisplants.uwsp.edu /Composites/tribe_11.htm   (459 words)

  
 Untitled Document
We are able to learn that Archimedes' discovered the 13 semiregular polyhedra, which are today known as "Archimedian solids." He also include alternate proofs and supplementary lemmas for propositions from Euclid, Archimedes, Apollonius, and Ptolemy.
Pappus' treatise includes new discoveries and generalizations not found in early work.
It is not known whether or not the problem originated with Pappus, but it has been suggested that possibly it was known earlier to Heron.
jwilson.coe.uga.edu /EMT668/EMAT6680.2000/Burrell/Essay3/Essay3.html   (627 words)

  
 Plants of Southern California: Stephanomeria diegensis
Even when the connection of the pappus and the seed was maintained during collection, by the time I removed the samples from the film canisters in which they were stored, the pappus from every fruit had detached from the seed and collected into a roundish ball.
The plumosity of the pappus was consistent from nearly every sample, ranging from ~75% to ~90% for the vast majority of the pappus, with a few samples at ~70% and a few at ~95%.
Thus a pappus that is 90% plumose is plumose for the upper 90% of its length, and is a simple naked bristle in the bottom 10% of its length.)
tchester.org /plants/analysis/stephanomeria/diegensis.html   (3908 words)

  
 Pappus of Alexandria
Pappus discusses the honeycomb conjecture: Any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal grid.
Pappus refers to the problem and other optimization problems in his fifth book.
In synthesis, by reversal we assume what was obtained last in the analysis to have been achieved already, and, setting now in natural order, as precedents, what before were following, and fitting them to each other, we attain the end of the construction of what was sought.
www.mlahanas.de /Greeks/Pappus.htm   (886 words)

  
 PORPHYRY (ROCK) - LoveToKnow Article on PORPHYRY (ROCK)   (Site not responding. Last check: 2007-11-03)
Thus, in view of the ancillary relation in which Pappus's lemmas generally stand to the works to which they refer, it seems incredible that the first seven out of thirty-eight lemmas should be really equivalent (as Chasles makes them) to Euclid's first seven Porisms.
Again Chasles seems to have been wrong in making the ten cases of the four-line Porism begin the book, instead of the intercept-Porism fully enunciated by Pappus, to which the " lemma to the first Porism " relates intelligibly, being a particular case of it.
It is a fact tha Lemma 31 (though it makes no mention of a conic) correspond exactly to Apollonius's method of determining the foci of a centra conic (Conies, iii.
2.1911encyclopedia.org /P/PO/PORPHYRY_ROCK_.htm   (2645 words)

  
 Pappus   (Site not responding. Last check: 2007-11-03)
A reference to Pappus in Proclus's writings says that he headed a school there.
He writes well, shows great clarity of thought and the this is a work of very great historical importance in the study of Greek geometry.
Other works which could have been written by Pappus include one on music and one on hydrostatics.
www.stetson.edu /~efriedma/periodictable/html/Pu.html   (455 words)

  
 Families of Conics
The configuration of Pappus is obtained by taking two distinct lines, any three distinct points on one line and any three distinct points on the other (subject to the condition that none of the six points lies at the point of intersection of the two lines).
Label the three points on the first line A, C, and E, and the three points on the second line by B, D, and F. We use the notation X=AB.DE to mean that X is the point of intersection of the lines AB and DE.
In the case of a Pappus configuration, there are an additional six conics which, interestingly, meet by two pairs of three in points on the original base lines of the Pappus configuration.
mathforum.org /dynamic/submissions/familyofconics   (755 words)

  
 Pappus' Theorem Main Page   (Site not responding. Last check: 2007-11-03)
Pappus' Theorem is a major result in projective geometry.
I have discovered a construction involving several interlocking applications of Pappus' theorem that has several very nice properties that make it an interesting construction to study.
I found that this construction is best understood by thinking about it as a dynamical system in projective three space that is related to the geometry of the twisted cubic.
www.math.umd.edu /~wphooper/pappus   (236 words)

  
 10
The pappus may be absent or present as a crown of stiff bristles at one end.
Habitat and Distribution: Indigenous to the Mediterranean region and introduced to North America in California as a seed contaminant; adventive in New Mexico along roadsides and in disturbed ground of farms and cropland [Chaves, Otero counties].
Comments: Russian knapweed and yellow starthistle are toxic to horses, producing a neurological disorder known as "chewing disease." The disease is characterized by an acute inability of the animal to eat or drink, and resembles Parkinson's disease in humans.
web.nmsu.edu /~kallred/herbweb/newpage26.htm   (4426 words)

  
 Pappus of Alexandria --  Encyclopædia Britannica
Other than that he was born at Alexandria in Egypt and that his career coincided with the first three decades of the 4th century
More results on "Pappus of Alexandria" when you join.
Most of his other treatises were lost, although their titles and a general indication of their contents were passed on by later writers, especially Pappus of Alexandria (fl.
www.britannica.com /eb/article-9058349   (799 words)

  
 Flowering Plant Families, UH Botany   (Site not responding. Last check: 2007-11-03)
The pappus is of fine, soft, often pure white capillary hairs.
Note white, capillary pappus and head with well developed series of equal, laterally connate phyllaries and a few scattered small phyllaries at base of involucre.
Note the white capillary pappus, the more or less connate series of equal primary phyllaries and a few scattered basal, somewhat abortive ones.
www.botany.hawaii.edu /faculty/carr/senecioneae.htm   (302 words)

  
 Pappus Configuration for Circles   (Site not responding. Last check: 2007-11-03)
When the six the starred points, A* through F* are all the same point, the point at infinity, then all the circles are straight lines, and the configuration reduces to the standard Pappus configuration of Euclidean and projective geometry.
Thus, the hyperbolic version of Pappus configuration is a special case of the inversive version.
Thus, the elliptic version of Pappus configuration is also a special case of the inversive version.
aleph0.clarku.edu /~djoyce/java/round/pappus.html   (269 words)

  
 References for Pappus   (Site not responding. Last check: 2007-11-03)
A Rome, Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste (Rome, 1931).
E étienne and J Roels, Deux aspects particuliers du problème des moyennes dans Pappus d'Alexandrie, Rev.
L Passalacqua, The Collections of Pappus : editorial polemics and circulation of manuscripts in the correspondence of Francesco Barozzi with the Duke of Urbino (Italian), Boll.
www-history.mcs.st-and.ac.uk /history/References/Pappus.html   (181 words)

  
 An Introduction to Pappus' Theorem   (Site not responding. Last check: 2007-11-03)
Pappus' Theorem was discovered by Pappus of Alexandria in the 4th century AD, and has extraordinarily beautiful properties that makeit one of the nicest constructions to study in projective geometry.
Pappus' Theorem states that the three points we just constructed, Z
Above is an interactive applet that demonstrates Pappus' Theorem.
www.math.umd.edu /~wphooper/pappus/intro   (137 words)

  
 Conics and the Pappus configuration
A Steiner conic associated with the configuration of Pappus.
In this paper, we show a family of six conics connected with the Configuration of Pappus.
In the second part of this paper, we show the connection between the above six conics and 12 Steiner conics that are connected with the configuration of Pappus.
www.math.uwaterloo.ca /~ljdickey/conics   (1224 words)

  
 The Columbia Encyclopedia, Sixth Edition: Pappus @ HighBeam Research
He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his Mathematical Collection (8 books; date conjectural).
Pappus' other works include a commentary on Ptolemy's Almagest.
Our archive contains millions of documents from thousands of sources and goes back over 23 years.
www.highbeam.com /library/doc0.asp?DOCID=1E1:Pappus&refid=ip_encyclopedia_hf   (140 words)

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