41. Background On The Hexagonal Honeycomb Conjecture 6. Loeb Classical Library. In Book V Pappus takes up a topic not mentioned by Euclid,but apparently discussed by the Athenian mathematician zenodorus . http://www.math.pitt.edu/~thales/kepler98/honey/hexagonHistory.html

Background on the Hexagonal Honeycomb conjecture In 1994, D. Weaire and R. Phelan improved on Lord Kelvin's candidate for the least-area way to partition space into regions of unit volume. Contrary to popular belief, even the planar question remains open. -Frank Morgan, Trans. AMS, Vol. 351, No. 5, p1753, 1999. Let T be a tile of unit area such that the plane may be tiled by congruent copies of it. Steinhaus asks if the perimeter length of T is least when T is a regular hexagon. More generally, if the plane is tiled by bounded tiles, not necessarily congruent, but all of a diameter of at least D0, say, does the regular hexagonal tiling minimize the maximum (perimeter length of T)^2/(area of T) taken over all tiles T in the tiling? The 3-dimensional analog of this is likely to be challenging: What is the tile T of unit volume and least surface area that permits a tiling of R^3 by congruent copies of T? -Hallard T. Croft, Kenneth J. Falconer, Richard K. Guy, Unsolved Problems in Geometry (Problem C15). Springer-Verlag, 1991. Bees are not of a solitary nature, as eagles are, but are like human beings... They have three tasks: food, dwelling, toil; and the food is not the same as the wax, nor the honey, nor the dwelling. Does not the chamber in the comb have six angles, the same number as the bee has feet? The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space.

42. Jackson & Li--Ant-eating Jumping Spiders Preycapture techniques and prey preferences of zenodorus durvillei, Z. metallescensand Z. orbiculatus, tropical ant-eating jumping spiders (Araneae http://www.rsnz.org/publish/nzjz/2001/21.php

Search options map New Zealand Journal of Zoology abstracts Prey-capture techniques and prey preferences of Zenodorus durvillei Z. metallescens and Z. orbiculatus , tropical ant-eating jumping spiders (Araneae: Salticidae) from Australia ROBERT R. JACKSON Department of Zoology University of Canterbury Christchurch, New Zealand DAIQIN LI Department of Biological Sciences National University of Singapore Singapore 119260 Abstract Capture techniques and preferences of Zenodorus durvillei (Walckenaer), Z. metallescens (L. Koch) and Z. orbiculatus Keywords Spiders; Zenodorus ; Salticidae; ants; predation; myrmecophagy; prey preferences Received 2 November 2000; accepted 8 May 2001 New Zealand Journal of Zoology, 2001, Vol. 28 0301-4223/01/2803-0299 $7.00/0 (c) The Royal Society of New Zealand 2001 This year's abstracts Journal home page All abstracts Publishing home page ... Topics

43. Hist7 pillaging the Damascenes. zenodorus, whose eparchy Auranitis was givento Herod goes to Rome to protest, but returns unsatisfied. Then M http://www.abu.nb.ca/Courses/NTIntro/InTest/Hist7.htm

The Reign of Herod the Great, King of the Jews (37-4 BCE) 1. Brief Account of Events Said to Have Occurred From 37 until 4 BCE, Testament of Moses [6] for an unflattering description of Herod's reign presented as a prophecy.) 2. Primary Sources 2.1. Reading: Josephus, Antiquities (Translated by W. Whiston) 2.2. Reading: Josephus, War (Translated by W. Whiston) Herod's Palace at Jericho The Herodion Caesarea Maritima The Burnt House ... Map of Herod's Kingdom Oil Lamp from the Herodian Period Silver denarius minted in Alexandria (Egypt) bearing the images of Anthony and Cleopatra on either side (British Museum) 3. More Detailed Account of Events Alleged to Have Occurred with Citation of Sources (*=significant apparent disagreement in sources) Date BCE Events Sources Herod plunders the wealthy of Jerusalem in order to give gifts to Antonius and others; he kills forty-five of the leading members of the Antigonus' supporters. He rewards those who supported him during the siege, in particular the Pharisee Pollion and his disciple Samaias, who advised the people during the siege to open the gates to Herod. (This same Pollion was the one who spoke during Herod's trial, and foretold that, if Herod's life was spared, Herod would one day persecute Hyrcanus and the members of the Synhedrion .) Antonius executes Antigonus in Antioch by beheading him, in order to strengthen Herod's hold on the kingship.

44. Guy Clark Ancient Coins And Antiquities- Roman Provincial Coins RP111. Syria, Chalkis, zenodorus, dated 32/31BC, time of Octavian,AE21x19. Octavian head rt., date before (B Pi Sigma = year 282 http://www.ancient-art.com/romprov.htm

Guy Clark's Ancient Coins and Antiquities Roman Provincial Coins Last update: 27 May 2004 Macedonia, Gaius Publilius, Quaestor, after 146BC, AE21. Athena head rt./Bull feeding rt., BMC76var (has legend of BMC75). Near centered, nice portrait and bull, most legend clear, black patina, about Very Fine....$95 Photo Crete, Knossos(?), L. Lollius, ca 1st Century BC, AE28. Artemis Diktynna head rt./Stag stands rt., L LOL I VS, RPC909. Near centered on large flan, overstruck on unidentified bronze so there are some areas of slight flatness and garbling but not bad, clear portrait, stag and most of rev. legends, brown patina, the exact location of the mint for these is unknown but supposed to be Knossos, RARE, Very Fine....$475 Photo Phoenicia, Aradus, Marc Antony, ca 38/37 BC, AE18. Antony head rt./Bull gallops left, CWM in exergue, RPC I, 4466sim. Centered on slightly small thick flan, nice clear portrait and rev., olive green patina, RARE, about Very Fine....$150 Photo Corinth, Augustus, 27BC-AD14, AE20. Emperor head rt./Caius and Lucius heads face to face, RPC1136. Obv. centered a little high crowding the top of his head, rev. nearly centered, some legend weak, black patina, overall decent with clear portraits, SCARCE, Fine+....$175 Photo This is a coin that may have been circulating in Corinth at the time of the visit of the Apostle Paul and the early church.

45. Guy Clark Ancient Coins And Antiquities- Greek Coins SOLD Photo. GB333. Syria, Chalkis, zenodorus, 3020 BC, AE22x19. Octavianhead rt./zenodorus head left, Lindgren 2136. Near centered http://www.ancient-art.com/greekAE.htm

Guy Clark's Ancient Coins and Antiquities GREEK BRONZE COINS Last update: 03 May 2004 Greek Bronze Coins (I have attempted to scan many of the bronzes to convey a better idea of what they look like. Please note that some have come out with the color off somewhat. I hope to improve this as I learn more about scanning techniques. Few Greek bronzes are of known denomination and so most are designated by a number following AE which indicates the diameter of the coin in millimeters. Thus a coin listed as AE15 is 15mm in diameter. For those who are metrically challenged, there are approximately 24mm per inch.) SPECIAL Miscellaneous Greek Bronze Coins. If, after looking at the selection of bronzes below, you still can't decide where to start, I have a number of miscellaneous Greek bronzes from many areas. These coins will average Fine or better condition with minimal problems such as centering, pitting, etc., so, while not choice specimens, they are not ugly either. These coins can be a good starting point or, if you are only planning to have one representative example, will suffice for an inexpensive type coin. Most are from Syria, Phoenicia, Thrace, Macedonia, and various mints in Asia Minor and date from the 4th to the 1st Century BC. If you order more than one, I will provide variety. Each only ...$14.95 Armenia Armenia, Tigranes II, 95-56 BC, AE13 (Chalcus). King's bust rt./Ear of grain, Nercessian 102ff. Near centered on slightly small flan, top of crown and tip of grain ear slightly off, black patina with light earthen cover, portrait and rev. clear, decent example of the smaller bronzes of his reign, Very Fine.....$85

46. The Antiquities Of The Jews By Flavius Josephus From Nalanda Digital Library - N How Herod Sent His Sons To Rome; How Also He Was Accused By zenodorus And TheGadarens, But Was Cleared Of What They Accused Him Of And Withal Gained To http://www.nalanda.nitc.ac.in/resources/english/etext-project/history/antiqjews/

THE ANTIQUITIES OF THE JEWS By Flavius Josephus Project Gutenberg File Converted into HTML pages by Nalanda Digital Library under Etext Conversion Project (ECP) BOOK-15 CHAPTER 10. How Herod Sent His Sons To Rome; How Also He Was Accused By Zenodorus And The Gadarens, But Was Cleared Of What They Accused Him Of And Withal Gained To Himself The Good-Will Of Caesar. Concerning The Pharisees, The Essens And Manahem. Previous Chapter Next Chapter

47. BOOK 17 FOOTNOTES a very useful note of Grotias, on Luke 31, here quoted by Dr. Hudson When Josephussays that some part of the house (or possession) of zenodorus (ie Abilene http://www.globusz.com/ebooks/Jews/00000045.htm

G lobusz P ublishing BOOK 17 FOOTNOTES Those who have a mind to know all the family and descendants of Antipater the Idumean, and of Herod the Great, his son, and have a memory to preserve them all distinctly, may consult Josephus, Antiq. B. XVIII. ch. 5. sect. 4; and Of the War, B. I. ch. 28. sect. 4; in Havercamp's edition, p. 336; and Spanheim, lb. p. 402405; and Reland, Paleslin. Part I. p. 178, 176. This is now wanting. Pheroras's wife, and her mother and sister, and Doris, Antipater's mother. His wife, her mother, and sister. It seems to me, by this whole story put together, that Pheroras was not himself poisoned, as is commonly supposed; for Antipater had persuaded him to poison Herod, ch. v. sect. 1, which would fall to the ground if he wore himself poisoned; nor could the poisoning of Pheroras serve any design that appears now going forward; it was only the supposal of two of his freed-men, that this love-potion, or poison, which they knew was brought to Pheroras's wife, was made use of for poisoning him; whereas it appears to have been brought for her husband to poison Herod withal, as the future examinations demonstrate. That the making of images, without an intention to worship them, was not unlawful to the Jews, see the note on Antiq. B VIII. ch. 7. sect. 5.

48. Iturea still another was the region of Chalcis, given by Claudius to Herod, grandson ofHerod the Great; and finally the territory of zenodorus, which came into the http://www.ccel.org/s/schaff/encyc/encyc06/htm/iii.xlix.htm

ITHACIUS CLARUS. See P RISCILLIAN , P RISCILLIANISTS ITUREA: A region named in Luke iii. 1 . The name of a people, "the Itureans," is older than "Iturea" as the name of a region, and is to be connected with the Jetur of Gen. xxv. 15 , a son of Ishmael denoting a nomadic stock of the Syro-Arabian desert, whose home, according to the Genesis passage, was in the neighborhood of Teima on the western border of Najd, between Medina and the oasis of Jauf. I Chron. v. 18-22 tells of a victorious campaign of the Hebrews of the East-Jordan land against Jetur and other nomads in pre-exilic times, which shows that Jetur must have changed its place of abode to the neighborhood of the Jabbok; but the mention in Luke iii. 1 can have nothing to do with this passage. Aristobulus I. (105-104 B.C. ) fought the Itureans and annexed part of their territory (Josephus, Ant. XIII., xi. 3), and Strabo (XVI., ii. 10, 18) in Roman times locates them on the plain of Massyas (Marsyas) between Laodicea and Chalcis, i.e., in C?le-Syria (q.v.), and he is corroborated by an inscription of Quirinius (Mommsen in Ephemeris epigraphica

49. Ituraea - International Standard Bible Encyclopedia part of their territory to Judea, 140 BC (Ant., XIII, xi, 3). Dio Cassius callsLysanias king of the Itureans (xlix.32), and from him zenodorus leased land http://www.studylight.org/enc/isb/view.cgi?number=T4735

50. Zenas - International Standard Bible Encyclopedia ZENAS ze -nas (Zenas (Titus 313); the name in full would probably be zenodorus,literally, meaning the gift of Zeus ) 1. A Jewish Lawyer http://www.studylight.org/enc/isb/view.cgi?number=T9357

51. OCEANO Translate this page The Free Site. OCEANO. di zenodorus. Romba l’Oceano. Con mille urla. e deposel’uovo. principio del mondo. e di noi tutti. . zenodorus. =. http://spqr.9cy.com/oceano.htm

FREE WEB SITE HOSTING - 9cy.com Web Hosting Service OCEANO di ZENODORUS Romba l’Oceano Con mille urla Una dea danza al di sopra delle acque Un vento la avvolge Tra le sue spire Come un grande serpente Sempre più stretto Finché la dea si liberò come una colomba E volò lontano ai confini dell’Universo anzi al suo centro e depose l’uovo principio del mondo e di noi tutti. Zenodorus

52. Presentazione Translate this page Pronuncia del latino. MITOLOGIA. La formazione del mondo (Ovidio). MISCELLANEAPOETICA. Bellona (Anonimo Virgiliano). Oceano (zenodorus). STUDIOSI. http://spqr.9cy.com/

cookie_name="pop1"; cook_value="1!!1086147707"; cook_expires="Wed, 02 Jun 2004 03:42:47 GMT"; document.cookie=cookie_name+"="+cook_value+";expires="+cook_expires+";"; FREE WEB SITE HOSTING - 9cy.com Web Hosting Service WEB HOSTING - 1 GIG, 1000 EMAILS, 50 GIG TRANSFER, CGI, PHP, MySQL ONLY $6.95 S P Q R ResPublica Quiritium Romanorum REPUBBLICA DEI QUIRITI ROMANI – GOVERNO IN ESILIO Lupa Capitolina, bronzo,VI secolo a.e.v.: i gemelli sono di età moderna (Palazzo dei Conservatori – Roma) Presentazione Questo sito rappresenta una repubblica virtuale: quella dei “pagani” tradizionali italiani. Per“pagani” tradizionali si intendono quelle persone che seguono una delle religioni politeiste dell’antica Italia. Non è un tentativo di creare una vera nazione virtuale tipo Novaroma, con tanto di votazioni, ecc.(non ne sarei capace), ma un riferimento per i “pagani” tradizionali che si trovano ancora in Italia. In teoria vorrebbe esserlo anche per quelli sparsi nei territori dell’Orbe Romano, ma sarebbero necessarie traduzioni nelle loro lingue natìe alle quali, al momento, non posso provvedere. La Repubblica dei Quiriti Romani non è altro che l’antica Roma repubblicana: ciò non significa però che possano farne parte solo i seguaci della religione romana. Al contrario sono invitati a farne parte tutti i “pagani” tradizionali, rifiutando assurde contrapposizioni tra i popoli della nostra terra, e ricordando che anche nell'Italia antica, se il culto ufficiale dello Stato era romano, quello delle singole città, e ancor di più quello privato, era in parte o in tutto locale.

53. La Domus Aurea Translate this page Verum omnem amplitudinem statuarum eius generis uicit aetate nostra zenodorus Mercuriofacto in ciuitate Galliae Aruernis per annos decem, Hs quater centies http://members.xoom.virgilio.it/AndreaZoia/approfondimenti/domus.aurea2.htm

La Domus Aurea Le meraviglie della Domus Una sala della Domus Aurea All'interno del vestibolum, come riferito da Svetonio, era collocato il colosso che rappresentava Nerone, consacrato al Sole, di cui ci parla anche Plinio ( Nat. Hist. XXXIV, 18 ), riportando anche il nome dello scultore, il greco Zenodoro: XXXIV Verum omnem amplitudinem statuarum eius generis uicit aetate nostra Zenodorus Mercurio facto in ciuitate Galliae Aruernis per annos decem, Hs quater centies centena milia manupretii; postquam satis artem ibi adprobauerat, Romam accitus a Nerone, ubi destinatum illius principis simulacro colossum fecit CXIX pedum longitudine, qui dicatus Soli uenerationi est, damnatis sceleribus inius principis. Mirabamur in officina non modo ex argilla similitudinem insignem, uerum et de paruis admodum surculis quod primum operis instaurati fuit. Ea statua indicauit interisse fundendi aeris scientiam, cum et Nero largiri aurum argentumque paratus esset et Zenodorus scientia fingendi caelandique nulli ueterum postponeretur. La statua bronzea, alta più di 35 metri, raffigurava Nerone con attributi solari e si ispirava, con ogni probabilità, al colosso di Rodi. L'imperatore era rappresentato nudo e con il braccio sinistro piegato per sorreggere una sfera, il destro proteso in avanti. Sul capo portava una corona composta da sette raggi, lunghi ben sei metri ciascuno. Le uniche raffigurazioni che ci rimangano dell'immane colosso sono state ritrovate su alcune monete degli imperatori Gordiano III ed Alessandro Severo.

54. Modele Translate this page A- Price on Request Agrias amydon tryphon aristoxenes SA Peru m 25 Agrias amydontryphon aristoxenes SA Peru m A- 15 Agrias amydon zenodorus flavicellus (yellow http://www.insect-trade.com/Selection/rhopalocera.html

BUTTERFLIES OF THE WORLD Latin names - Continent - Country (Prov.) - Sex - Quality - Price ($US) HESPERIIDAE Amblyscirtes aenus NA USA Arizona m 2 Amblyscirtes aenus NA USA Arizona f 4 Amblyscirtes cassus NA USA Arizona m 2 Amblyscirtes cassus NA USA Arizona f 4 Amblyscirtes eos NA USA Arizona m 3 Amblyscirtes exoteria NA USA Arizona m 1 Amblyscirtes exoteria NA USA Arizona f 4 Amblyscirtes nereus NA USA Arizona m 2 Amblyscirtes nysa NA USA Arizona m 3 Amblyscirtes oslari NA USA Arizona m 2 Amblyscirtes oslari NA USA Arizona f 4 Amblyscirtes vialis NA Canada Quebec m 1 Amenis vashti SA Brasil m 5 Ancyloxypha numitor NA Canada Quebec m 1 Atrytone logan NA USA m A2 1 Atrytone logan NA USA f 4 Atrytone logan NA USA f A- 2 Atrytonopsis lunus NA USA Arizona m 4 Carterocephalus palaemon NA Canada Quebec m 1 Celotes nessus NA USA Arizona m 2 Cogia caicus NA USA Arizona m 3 Cogia caicus NA USA Arizona f 6 Cogia hippalus NA USA Arizona m 3 Copaeodes aurantiaca NA USA Arizona m 1 Epargyreus clarus NA USA m 2 Erynnis baptisiae NA USA m 3 Erynnis baptisiae NA USA m A2 1 Erynnis baptisiae NA USA f 5 Erynnis brizo NA USA m 3 Erynnis brizo NA USA m A- 2

55. Login To BioOne Natta Karsch 1879, two undescribed species of Xenocytaea Berry, Beatty, Prózy ski1998 (formerly called “Euophrys”) and zenodorus orbiculatus (Keyserling http://www.bioone.org/bioone/?request=get-document&issn=0161-8202&volume=028&iss

56. Greek Mathematics rotating about axis of revolution). zenodorus (200140 BC) workedon various geometric optimization problems. He showed that the http://members.fortunecity.com/kokhuitan/greek.html

Era of Greek Mathematics The Greeks are responsible for initial explosion of Mathematical ideas. For several centuries, Greek mathematics reign the mathematical world, with great advances in Number Theory, the Theory of Equation, and in particular Geometry. The first great Greek mathematician is Thales of Miletus (624-547 BC). He brought the knowledge of Egyptian Geometry to the Greeks and discovered several theorems in elementary Geometry. He predicted a Solar Eclipse in 585 BC and could calculate the height of a pyramid, as well as how far a ship is from land. One of his pupils, the Greek philosopher, Anaximander of Miletus (610-546 BC), is considered the founder of Astronomy. Perhaps the most prominent Greek mathematicians is Pythagoras of Samos (569-475 BC). His ideas were greatly influenced by Thales and Anaximander. His school of thought practiced great secrecy and he (and his followers, called Pythagoreans) believe everything in the world can be reduced to numbers. This idea stemmed from Pythagoras' observations in Music, Mathematics and Astronomy. E.g. Pythagoras noticed that vibrating strings produce harmonics in which the lengths of the strings are in ratios of whole numbers. In fact, he contributed greatly to the mathematical theory of music. He had the notion of Odd and Even Numbers, Triangular Numbers, Perfect Numbers, etc. In particular, he is well known today for his Pythagoras Theorem. Although this theorem is known to the Babylonians and Chinese long before Pythagoras, he seemed to be the first person to provide a proof of it.

57. Euclid - Books I-IX 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.org/unlearn/euclid/before/o-commentators.htm

58. Feb 16, 2001, The Benson Collection Part 1 - Chapter 142 Chalcis. zenodorus, c. 3225 BC. Bare head of Octavian right, date around.Reverse Head of zenodorus left, Greek inscription around. RPC 4774. http://www.goldbergcoins.net/catalogarchive/20010216/chap142.shtml

Feb. 16, 2001, The Benson Collection Part 1, Sale 8 (If you have a problem viewing enlarged photos, your browser may be blocking pop-up windows. Check with your IT consultant.) Ancient Coins Greek Coins Lot Aegina. Aegina, c. 525-500 BC. AR Stater (11.9 g). Top view of sea turtle. Reverse: Fine or better. Estimated Value $150-200. Lot Aegina. Aegina, 457-431 BC. AR Stater (12.1 g). Top view of land tortoise with segmented shell. Reverse: Refined skew punch. SNG Delepierre 1535ff. Countermark at middle of shell; sunburst countermark in lower field. An especially refined, handsome depiction of this animal. Attractive toning. A pleasing Extremely Fine. Estimated Value $500-650. Lot Aegina. Aegina, c. 457-431 BC. AR Stater (12.2 g). Top view of land tortoise with segmented shell. Reverse: Skew punch of five compartments. SNG Delepierre 1535ff. Deep old cabinet toning. Choice Very Fine. Estimated Value $350-450. Lot Corinthia. Corinth, c. 350-338 BC. AR Stater (8.4 g). Pegasus flying left, koppa below. Reverse: Helmeted head of Athena left. Old toning with areas of blue iridescence. Struck on compact flan with no visible symbols on reverse. Estimated Value $150-200.

59. Title southern Italy) Zeno of Sidon, Zeno of Sidon Born about 150 BC in Sidon (now Saidain Lebanon) Died about 70 BC in Athens, Greece zenodorus, zenodorus Born http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=Z

60. 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

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Calculus of Variations Isoperimetric Problem 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 such that is a maximum Zenodorus proved that the area of the circle is larger than that of any polygon having the same perimeter , but the problem was not rigorously solved until Steiner published several proofs in 1841 (Wells 1991). Circle Dido's Problem Double Bubble Isoperimetric Quotient ... search Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century.

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