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Zenodorus: more detail

140 Bc: 140 Bc Births, 140 Bc Deaths, Tigranes the Great, Su Wu, Huo Qubing, Gaius Julius Caesar, Lucius Licinius Crassus, Zenodorus

Two new charaxinae from Panama and the Canal Zone (Nymphalidae) (Bulletin of the Allyn Museum) by Lee D Miller, 1971

Eugene Le Moult's Prepona types (Lepidoptera: Nymphalidae, Charaxinae) (Bulletin of the Allyn Museum) by Richard Irwin Vane-Wright, 1974

lists with details

Index Of /~history/Mathematicians
html 20Jan-2003 1753 9.6K Zhukovsky.html 20-Jan-2003 1753 11K Zeuthen.html 20-Jan-20031753 11K Zermelo.html 20-Jan-2003 1753 15K zenodorus.html 20-Jan
http://www.gap-system.org/~history/Mathematicians/?C=N&O=D
TLG: TLG Date Sorting
(3 BC?/AD 1). When it is simply impossible to suggest a date, the wordIncertum has been used instead, as for zenodorus Trag. Incertum
http://www.tlg.uci.edu/help/Doc004.html

Extractions: Last Revised: 2000-5-12 The following defines the sorting order for dates in the TLG Canon as used on the TLG CD ROMs and online databases. Thesaurus Linguae Graecae: Canon of Greek Authors and Works. 3rd edn. Oxford: Oxford University Press. pp. xix-xx.) Arabic numerals in cardinal form indicate the century of an author's floruit . A dash between numerals indicates that the author's floruit spans the two centuries. Thus, the date given for Strabo Geogr. is 1 B.C.-A.D. 1, based upon the approximate dates of his sojourns in Rome (44-35 B.C., again ca. 31 B.C., and a third time in 7 B.C.), Egypt (25 until ca. 19 B.C.), and Amasia (ca. 7 B.C. until his death sometime after A.D. 21.) When no firmer evidence can be adduced, a virgule between numerals is used to suggest the earliest and latest possible dates. Thus, the date given for Alciphron Rhet. et Soph. is A.D. 2/3, meaning that the earliest possible date for his letters (though purportedly written by Athenian fishermen, farmers, parasites, and courtesans of the fourth century B.C.) is the second century and the latest is the third. When only a terminus ante quem is discernable, or at least logically to be assumed, this is indicated by, for instance
Dynamic Caterpillar Event-based Database: Preface
If you note that there are 400+ records of Pyrrhopyge zenodorus (Hesperiidae) caterpillarsfrom Vismia baccifera and only 5 from Vismia ferruginea, please
http://janzen.sas.upenn.edu/caterpillars/preface.htm

Extractions: Authors' preface to http://janzen.sas.upenn.edu/caterpillars/database.htm (5 December 1999): http://www.acguanacaste.ac.cr ). We began this inventory in 1978, and since then many institutions and persons have participated and contributed to its content and structure. The content of the core FileMaker Pro (FMP) database was initially derived from field notebooks in 1988. After that, the data was field notebooked and subsequently computerized at the end of the year (1988-1999). From 1999-2000 onward, the data is being progressively more directly computerized without a hard copy intermediate. Currently in FMP 4.0, as the years pass it will migrate to new structures, applications and their versions, and platforms. A lengthy methodological document for the inventory databases will be placed on this site by 31 January 2000. We feel that misuses of data, layouts and searches are less likely if time is invested in this document. The methodological essay on the inventory process itself should be read as its companion piece. We suggest that these databases be used in the positive sense. The inventory is by its nature a work in indefinite progress, and this is reflected in the databases. If you want a photograph of a last instar
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3. The subject of isoperimetric figures was a favourite one with Pappus,who wrote a recension of zenodorus' treatise on the subject 37 .
http://www.headmap.com/book/euclid/before/o-commentators.htm

Extractions: [p. 19] That there was no lack of commentaries on the Elements before the time of Proclus is evident from the terms in which Proclus refers to them; and he leaves us in equally little doubt as to the value which, in his opinion, the generality of them possessed. Thus he says in one place (at the end of his second prologue) âBefore making a beginning with the investigation of details, I warn those who may read me not to expect from me the things which have been dinned into our ears ad nauseam (diatethrulªtai) by those who have preceded me, viz. lemmas, cases, and so forth. For I am surfeited with these things and shall give little attention to them. But I shall direct my remarks principally to the points which require deeper study and contribute to the sum of philosophy, therein emulating the Pythagoreans who even had this common phrase for what I mean âa figure and a platform, but not a figure and sixpence In another place he says: âLet us now turn to the elucidation of the things proved by the writer of the Elements, selecting the more subtle of the comments made on them by the ancient writers, while cutting down their interminable diffuseness, giving the things which are more systematic and follow scientific methods, attaching more importance to the working-out of the real subject-matter than to the variety of cases and lemmas to which we see recent writers devoting themselves for the most part.â
.Old Roman Coins For Special Collectors: Greek - Greek East
The second countermark is known on the second issue of Ptolemy fromChalkis. A similar countermark is known for coins of zenodorus.
http://www.oldromancoins.com/ggeast1.htm

Extractions: Seleukid Kingdom, Antiochus IV Æ45, (drachm), 175-164 B.C., (60.81g) Antioch Mint, Laureate head of Zeus-Ammon right, dotted border. / BA S I L E W S ] ANTIOXOY ØEOY E R IØANOY S Eagle standing right, on thunderbolt, no control mark. SNG Israel 978; CSE 117; SMA 58 (976). F / Good F, brown patina, edge flaw, closed cracks, two reverse centering marks, scratch at 10:00 on reverse.
Isoperimetric Problem -- From MathWorld
zenodorus proved that the area of the circle is larger than that of any polygonhaving the same perimeter, but the problem was not rigorously solved until
http://mathworld.wolfram.com/IsoperimetricProblem.html

Extractions: Find a closed plane curve of a given perimeter which encloses the greatest area . The solution is a circle . If the class of curves to be considered is limited to smooth curves, the isoperimetric problem can be stated symbolically as follows: find an arc with parametric equations for such that (where no further intersections occur) constrained by References Bogomolny, A. "Isoperimetric Theorem and Inequality." http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml Isenberg, C. "The Maximum Area Contained by a Given Circumference." Appendix V in The Science of Soap Films and Soap Bubbles. New York: Dover, pp. 171-173, 1992. Steinhaus, H.
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way to enclose and separate two regions of prescribed volume in ${\mathbb R}^3$.\end{abstract} \maketitle \section{History} Archimedes and zenodorus (see \cite
http://www.mpim-bonn.mpg.de/external-documentation/era-mirror/2000-01-006/2000-0
Herod The Great: 37-4 BC
To show appreciation, Herod built a temple for Augustus at zenodorus. He reducedmore taxes for those displeased with his emphasis on GrecoRoman culture.
http://campus.northpark.edu/history/WebChron/MiddleEast/HerodGreat.html
130
(180 BC 125 BC) Hipparchus, (1225-1260) Jordanus, (1470-1530) La Roche.(200 BC - 140 BC) zenodorus, (1235-1316) Llull, (1471-1528) Dürer.
http://www.sanalhoca.com/matematik/matematikci1.htm

Extractions: sanal hoca Ana Sayfa Kimya Matematik Fizik ... E-Posta ( 130 - 190 ) Theon of Smyrna (1013-1054) Hermann of R. (1364-1436) Qadi Zada ( 130 BC - 70 BC ) Geminus (1019-1066) Sripati (1390-1450) al'Kashi ( 150 BC - 70 BC ) Zeno of Sidon (1031-1095) Shen (1393-1449) Ulugh Beg ( 200 - 284 ) Diophantus (1048-1122) Khayyam (1401-1464) Cusa ( 240 - 300 ) Sporus (1070-1130) Abraham (1404-1472) Alberti ( 290 350 ) Pappus (1075-1160) Adelard (1412-1486) Qalasadi ( 300 360) Serenus (1092-1167) Ezra (1412-1492) Francesca ( 335 - 395 ) Theon (1114-1185) Bhaskara (1423-1461) Peurbach ( 370 - 415 ) Hypatia (1114-1187) Gherard (1424-1484) Borgi ( 60 AD - 120AD ) Nicomachus (1168-1253) Grosseteste (1436-1476) Regiomontanus ( 65 AD - 125AD ) Heron (1170-1250) Fibonacci (1445-1500) Chuquet ( 70 AD - 130AD ) Menelaus (1195-1256) Sacrobosco (1445-1517) Pacioli ( 78 AD - 139AD ) Heng (1200-1280) Albertus (1452-1519) Leonardo ( 85 AD - 165AD ) Ptolemy (1201-1274) Tusi (1462-1498) Widman (160 BC - 100 BC) Theodosius (1202-1261) Ch'in (1465-1526) Ferro (1680BC-1620BC) Ahmes (1219-1292) Bacon
Faculty :: Fred C. Albertson
1991. Articles zenodorus's Colossus of Nero, Memoirs of theAmerican Academy in Rome 46 (2001) 95118. Three Palmyrene
http://www.people.memphis.edu/~artdept/falbertson.html
.Z. Alphabet
Translate this page 5 - un empereur grec. Zenobia, ae, f. Zénobie (nom de femme). zenodorus, i,m. Zénodore (sculpteur grec). Zenonianus, a, um de Zéon (l'empereur).
http://perso.wanadoo.fr/prima.elementa/Dico-z.htm
Pappus
He compares the areas of figures with equal perimeters and volumes of solids withequal surface areas, proving a result due to zenodorus that the sphere has
http://www.stetson.edu/~efriedma/periodictable/html/Pu.html

Extractions: Our knowledge of Pappus's life is almost nil. It appears that he was born in Alexandria and lived there all his life. A reference to Pappus in Proclus's writings says that he headed a school there. Pappus's major work in geometry is Synagoge , a collection of mathematical writings in 8 books thought to have been written in around 340. Obviously written with the object of reviving the classical Greek geometry, it covers practically the whole field. It is, however, a handbook or guide to Greek geometry rather than an encyclopaedia. It was intended to be read with the original works rather than to enable them to be dispensed with. Book 1 covered arithmetic and is now lost. Book2 is partly lost, but the remaining part deals with Apollonius's method for dealing with large numbers. The method expresses numbers as powers of 10,000. Book 3 is divided by Pappus into four parts. The first part looks at the problem of finding two mean proportionals between two given straight lines. The second part gives a construction of the arithmetic, geometric and harmonic means. The third part describes a collection of geometrical paradoxes which Pappus says are taken from a work by Erycinus. The final part shows how each of the 5 regular polyhedra can be inscribed in a sphere. Book 4 contains properties of curves including the spiral of Archimedes and the quadratrix of Hippias and includes his trisection methods. In Book 5 he discusses the 13 semiregular solids discovered by Archimedes. He compares the areas of figures with equal perimeters and volumes of solids with equal surface areas, proving a result due to Zenodorus that the sphere has greater volume than any regular solid with equal surface area. He also proves the related result that, for two regular solids with equal surface area, the one with the greater number of faces has the greater volume.
Circle
good understanding of the problem. In this knowledge, he followeda book of zenodorus (180 BC) 6) . Some relations of the circle
http://www.2dcurves.com/conicsection/conicsectionc.html

Extractions: Because of its symmetry the circle is considered as the perfect shape. It is the symbol for the total symmetry of the divine (sic!). The Greek scholar Proclus (500 AC) wrote: "the circle is the first, the simplest and most perfect form". As Christian symbol it represents eternity, and the sleeping eye of God (Genesis 1:2). her curve is round, unlike the line. More rational the circle can be described as the ellipse, where the two foci coincide. Or as the collection of points with equal distance to a (center) point. At the top of this page we see the polar equation of a unity circle with radius 1 and as center the origin. This definition - which gives the essence of the circle - was already formulated by Euclid (300 BC) in book III of his 'Elements'. That's why you can draw the curve with a pair of compasses. The circle's form remains intact while turning, what makes her very useful as lid for closing jars. And also for a watch with turning hands. The diameter of a screw is a circle too. But the greatest advantage mankind did get from the insight that for a wheel of a cart not the square, but the circle is the best form. So the study of the circle goes back beyond recorded history.
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A Greek mathematician named zenodorus (200 BC) discovered that regularpolygons (polygons with congruent sides) enclosed the greatest area.
http://www.mps.k12.nf.ca/mathematics/Grassroots/Tessellations/tess1.htm

Extractions: By: Anthony Bailey Maurits Cornelis Escher, master artist and creator of tessellations, was born in Leeuwarden, Netherlands in 1898. After an aborted attempt to become an architect, Escher studied graphic art at the School for Architecture and Decorative Arts in Harlem. Over the years and throughout his travels, he created a number of fascinating landscapes, portraits, and geometric designs, but the work for which he is most famous, his tessellations, were his main occupation. The tile tessellations are the tessellations you see every day. These types are found on floors or ceilings or wherever you can put some tiles and also bricks. Quilts are also common they are shown on blankets. An example of a quilt is To make a tessellation you will need: 1.A small amount of heavy duty paper, like tag board. Any paper will work but the more fragile the paper the more carefully you will have to be. 2.A large sheet of paper, where you will put your final design. 3. Sharp Scissors. The more detailed the design the shaper the scissors must be. 4.Tape. Any kind of tape will workclear scotch tape works well.
As últimas Do Mundo Da Matemática
Archimedes and zenodorus (see K, p. 273) claimed and Schwarz S proved thatthe round sphere is the leastperimeter way to enclose a given volume in R3.
http://www.mat.uc.pt/~jaimecs/ult/ult.html

Extractions: Paul Erdos morreu dia 20/9/96 -1 is now the Largest Known Prime December 6, 2001 > Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc.
Preponini
amydon amydon Hewitson SUBS Agrias amydon philatelica DeVries, 1980 SUBS Agriasamydon tryphon Fruhstorfer, 1925 SUBS Agrias amydon zenodorus Hewitson, 1870
http://www.zoologi.su.se/research/wahlberg/Nymphalidae/Preponini.htm
Collection Resources - Butterflies - Nymphalidae - Charaxinae
Agrias aedon narcissus Staudinger 1888 Agrias amydon tryphon Fruhstorfer 1925 Agriasamydon zenodorus Hewitson 1870 Agrias beata beata Staudinger 1888 Agrias
http://www.nhm.org/research/entomology/butterflies/nymphalidae/charaxinae.html
Lacus_en
Nero also placed in his palace a colossal bronze statue of himself (120 feet high,work of zenodorus), whose face was later modified many times to represent
http://www.the-colosseum.net/architecture/lacus_en.htm

Extractions: LACVS Once there was a lake ... The site of the Colosseum is in fact a depression among the hills of Rome: the Palatine on its south-western side, the Velia on the western side, the last slopes of the Esquiline hill, also called Colle Oppio (now a park) on the northern side and the Celio on the Eastern side. Venezia to the Colosseum cutting through the forums of old Rome. Mussolini demanded a straight road from Piazza Venezia to the Colosseum, and that was the end of the Velia. Right: Granet, The Palatine Hill The valley collected the waters, which created a marsh or a lake, depending on the season. The small lake was fed by the waters of the Rio Labicano, a stream flowing down the Labicana valley, more or less along modern day Via Labicana. The stream can still be seen underground when visiting the Church of St. Clemente in Via di San Giovanni . There you can descend about 30 feet under modern ground level and walk on the cobblestones of old Roman alleys, enter shops and houses, visit a Mithraic temple and listen to the soothing sound of running water. The stream is still there and the water runs clear and fast, enclosed inside a conduct built in the 19 th century in order to drain the underground of the Basilica.
Chapter 13, From Dan To Beersheba - J.P. Newman
Subsequently passing into the hands of the tyrant zenodorus, the province ultimatelyreverted to a descendant of Lysanias, bearing the same name, and who was
http://www.dabar.org/Newman/Ch13.htm

Extractions: At the death of Herod the Great his kingdom was divided into three parts, over which his sons reigned. With his accustomed precision and accuracy, St. Luke not only recognizes this historic fact, but defines the territory of each division. To Archelaus was assigned Idumea, Judea, and Samaria, which embraced all that portion of Palestine from the Jordan to the Mediterranean, and from Beersheba to the northern border of Esdraelon. Ancient Idumea included that district of country lying south of Judea, and extending from the southern end of the Dead Sea to the Gulf of Akabah; but the Idumea of the Herodian era embraced only the northern section of the Desert of Tih, together with several towns of Southern Palestine, with Hebron as the capital city. Though subdued by the warlike Maccabees, and by them subjected to the rule of Jewish prefects, the Idumaeans of this latter period rose to favor under Caesar, who appointed Antipater procurator of aIl Judea, and subsequently his son, Herod the Great, became ''King of the Jews." To Herod Antipas was allotted all Galilee, together with the district of Perea, which includes that part of Palestine east of the Jordan to Arabia, and south of Pella to Machaerus, and which in the New Testament is called the "coasts of Judea beyond Jordan."
Frank Morgan
Thousands of years after zenodorus proved that a planar soap bubble should beround, mathematicians are still stumped by optimal shapes in nature and in
http://www.bgsu.edu/departments/math/Ohio-section/Meetings/Spring98/morgan.html

Extractions: Thousands of years after Zenodorus proved that a planar soap bubble should be round, mathematicians are still stumped by optimal shapes in nature and in geometry. Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His three texts all have current new editions: Geometric Measure Theory: a Beginner's Guide 1995, Calculus Lite 1997, and Riemannian Geometry: a Beginner's Guide, 1998. Morgan went to MIT and Princeton, where his thesis advisor, Fred Almgren, introduced him to minimal surfaces. He then taught for ten years at MIT, where he served for three years as Undergraduate Mathematics Chairman, received the Everett Moore Baker Award for excellence in undergraduate teaching, and held the Cecil and Ida Green Career Development Chair. He spent leave years at Rice, Stanford, and the Institute for Advanced Study. He served on the NSF Math Advisory Committee from 1987-90, on the AMS Council from 1994-97, and as chair of the Hudson River Undergraduate Mathematics Conference in 1997. In January, 1993, he received one of the first MAA national awards for distinguished teaching. In 1995 he represented mathematics research at the exhibition for Congress by the Coalition for National Science Funding. He received the Allen High School Distinguished Alumni Award and an honorary doctorate from Cedar Crest College.

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