Keynote Address the Dawn of Hydrology and Water Management
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Tunnel of Eupalinos -- Civil Engineering -- Law of Sines Project
Tunnel of Eupalinos -- Civil Engineering -- Law of Sines Project 1 © 2017 NextLesson NextLesson is not affiliated with persons or brands mentioned. Tunnel of Eupalinos -- Civil Engineering -- Law of Sines Project 2 NextLesson is not affiliated with persons or brands mentioned. © 2017 NextLesson Tunnel of Eupalinos -- Civil Engineering -- Law of Sines Project 3 © 2017 NextLesson NextLesson is not affiliated with persons or brands mentioned. One of the greatest engineering achievements of ancient times is a water tunnel, 1,036 meters (4,000 feet) long, excavated through a mountain on the Greek island of Samos in the sixth century B.C. 30 ENGINEERING & SCIENCE NO. 1 The Tunnel of Samos by Tom M. Apostol One of the greatest engineering achievements of for a Project MATHEMATICS! video program, ancient times is a water tunnel, 1,036 meters and realized that the engineering problem actually (4,000 feet) long, excavated through a mountain consists of two parts. First, two entry points have on the Greek island of Samos in the sixth century to be determined at the same elevation above sea Facing page: This 1884 B.C. It was dug through solid limestone by two level; and second, the direction for tunneling map by Ernst Fabricius separate teams advancing in a straight line from between these points must be established. I will both ends, using only picks, hammers, and chisels. describe possible solutions for each part; but first, shows the tunnel running This was a prodigious feat of manual labor. The some historical background. obliquely through the hill intellectual feat of determining the direction of marked as Kastro, now tunneling was equally impressive. -
Glossary Glossary
Glossary Glossary Albedo A measure of an object’s reflectivity. A pure white reflecting surface has an albedo of 1.0 (100%). A pitch-black, nonreflecting surface has an albedo of 0.0. The Moon is a fairly dark object with a combined albedo of 0.07 (reflecting 7% of the sunlight that falls upon it). The albedo range of the lunar maria is between 0.05 and 0.08. The brighter highlands have an albedo range from 0.09 to 0.15. Anorthosite Rocks rich in the mineral feldspar, making up much of the Moon’s bright highland regions. Aperture The diameter of a telescope’s objective lens or primary mirror. Apogee The point in the Moon’s orbit where it is furthest from the Earth. At apogee, the Moon can reach a maximum distance of 406,700 km from the Earth. Apollo The manned lunar program of the United States. Between July 1969 and December 1972, six Apollo missions landed on the Moon, allowing a total of 12 astronauts to explore its surface. Asteroid A minor planet. A large solid body of rock in orbit around the Sun. Banded crater A crater that displays dusky linear tracts on its inner walls and/or floor. 250 Basalt A dark, fine-grained volcanic rock, low in silicon, with a low viscosity. Basaltic material fills many of the Moon’s major basins, especially on the near side. Glossary Basin A very large circular impact structure (usually comprising multiple concentric rings) that usually displays some degree of flooding with lava. The largest and most conspicuous lava- flooded basins on the Moon are found on the near side, and most are filled to their outer edges with mare basalts. -
Alexander the Great (356-323 B.C.E.) by Louis Godbout
Alexander the Great (356-323 B.C.E.) by Louis Godbout Encyclopedia Copyright © 2015, glbtq, Inc. Entry Copyright © 2004, glbtq, inc. Reprinted from http://www.glbtq.com An ancient bust of Alexander the Great. Photograph by Andrew King of Macedonia and conqueror of a kingdom extending from Greece to Persia, Egypt Dunn. and India, Alexander the Great is one of the most fascinating men of all times. He was Image appears under the not only a great soldier, but he was also renowned for his love of his comrade-in-arms Creative Commons Hephaestion. Attribution ShareAlike License. The handsome and courageous Alexander was already, in antiquity, the subject of many histories, some written by people who had known him, most unfortunately lost. The irrefutable achievements of his short life are so extraordinary that they seem almost legendary. It is therefore difficult to distinguish the truth from the many myths that coalesced around such an appealing figure. Alexander's father Philip was himself a brilliant general who had greatly strengthened his kingdom and brought it to dominate the Greek city-states; his dream was to lead them against the Persian Empire, the arch-rival under whose rule Greek colonies on the coast of Asia had fallen. Philip undoubtedly felt very early on that his son, who was born in 356 B.C.E., had exceptional potential, for he hired Aristotle to be the boy's tutor, even though the cost incurred was the rebuilding of Stagira, the philosopher's hometown, which had been razed and its population sold into slavery. Examples of Philip's trust in Alexander's abilities abound. -
9 · the Growth of an Empirical Cartography in Hellenistic Greece
9 · The Growth of an Empirical Cartography in Hellenistic Greece PREPARED BY THE EDITORS FROM MATERIALS SUPPLIED BY GERMAINE AUJAe There is no complete break between the development of That such a change should occur is due both to po cartography in classical and in Hellenistic Greece. In litical and military factors and to cultural developments contrast to many periods in the ancient and medieval within Greek society as a whole. With respect to the world, we are able to reconstruct throughout the Greek latter, we can see how Greek cartography started to be period-and indeed into the Roman-a continuum in influenced by a new infrastructure for learning that had cartographic thought and practice. Certainly the a profound effect on the growth of formalized know achievements of the third century B.C. in Alexandria had ledge in general. Of particular importance for the history been prepared for and made possible by the scientific of the map was the growth of Alexandria as a major progress of the fourth century. Eudoxus, as we have seen, center of learning, far surpassing in this respect the had already formulated the geocentric hypothesis in Macedonian court at Pella. It was at Alexandria that mathematical models; and he had also translated his Euclid's famous school of geometry flourished in the concepts into celestial globes that may be regarded as reign of Ptolemy II Philadelphus (285-246 B.C.). And it anticipating the sphairopoiia. 1 By the beginning of the was at Alexandria that this Ptolemy, son of Ptolemy I Hellenistic period there had been developed not only the Soter, a companion of Alexander, had founded the li various celestial globes, but also systems of concentric brary, soon to become famous throughout the Mediter spheres, together with maps of the inhabited world that ranean world. -
Aristotle (384-322 BCE) [1]
Published on The Embryo Project Encyclopedia (https://embryo.asu.edu) Aristotle (384-322 BCE) [1] By: Haskett, Dorothy Regan Racine, Valerie Yang, Joanna Keywords: Aristotle [2] Epigenesis [3] Aristotle [4] studied developing organisms, among other things, in ancient Greece, and his writings shaped Western philosophy and natural science for greater than two thousand years. He spent much of his life in Greece and studied with Plato at Plato's Academy in Athens, where he later established his own school called the Lyceum. Aristotle [4] wrote greater than 150 treatises on subjects ranging from aesthetics, politics, ethics, and natural philosophy, which include physics and biology. Less than fifty of Aristotle [4]'s treatises persisted into the twenty-first century. In natural philosophy, later called natural science, Aristotle [4] established methods for investigation and reasoning and provided a theory on how embryos generate and develop. He originated the theory that an organism develops gradually from undifferentiated material, later called epigenesis [5]. Aristotle [4] was born in 384 BCE in Stagira, a coastal town in the Chalcidice peninsula of northern Greece. His mother was Phaestis, who came from a wealthy family on the island of Euboea, and his father was Nicomachus, who was a personal physician to King Amyntas of Macedon. Nicomachus boasted of descent from the Asclepiads, who were devotees of Asclepius, the Greek god of healing and medicine. The Asclepiads valued empirical observations, and that culture made Aristotle [4] familiar with biological studies in his early years. Both parents died when Aristotle [4] was young, and he went to live with Proxenus of Atarneus, who was married to Aristotle [4]'s older sister. -
Proud to Be Euboeans: the Chalcidians of Thrace
Proud to be Euboeans: The Chalcidians of Thrace Selene E. PSOMA Περίληψη Οι Χαλκιδείς της Θράκης, όπως αναφέρονται στην αρχαία γραμματεία και τις επιγραφές, ήταν Ευ- βοείς άποικοι στη χερσόνησο της Χαλκιδικής που ζούσαν σε μικρές πόλεις στο μυχό του κόλπου της Τορώνης και στη Σιθωνία. Η Όλυνθος παραδόθηκε στους Χαλκιδείς το 479 και εκείνοι αργότερα δη- μιούργησαν το ισχυρό κοινό των Χαλκιδέων. Οι δεσμοί τους με τη μητρόπολη τεκμαίρονται από το ημερολόγιο τους, την ονοματολογία, το χαλκιδικό αλφάβητο, το ακροφωνικό σύστημα αρίθμησης, καθώς επίσης και από τη νομισματοκοπία. Αυτό το άρθρο εξετάζει όλα τα στοιχεία δίνοντας ιδιαίτερη έμφαση στη νομισματοκοπία. Introduction The ties between Euboean Chalcis and the Chalcidians of Thrace are mentioned by both Aristotle and authors of later date.1 Aristotle, who was born a Chalcidian of Thrace and died in Chalcis, mentions that the Chalcidians of Thrace asked Androdamas of Rhegion to become their lawgiver (nomothetes).2 Rhegion was also a Chalcidian colony, and it was quite common for a colony to ask for lawgivers from one of its sister cities. Another story that Aristotle relates will be discussed at length later. According to Polybius, the Chalcidians of Thrace were colonists of both Athens and Chalcis, and the main opponent to Philip II in Thrace.3 Strabo noted that Eretria founded the cities of Pallene and Athos whereas Chalcis founded those near Olynthus.4 The foundation of these colonies took place when the Hippobotai were rul- ing Chalcis, and the men who led the colonists were among the noblest of their cities. Plutarch mentions the struggle between Chalcidians and Andrians over the foundation of Akanthos in the 7th century BC.5 1. -
In the Kingdom of Alexander the Great Ancient Macedonia
Advance press kit Exhibition From October 13, 2011 to January 16, 2012 Napoleon Hall In the Kingdom of Alexander the Great Ancient Macedonia Contents Press release page 3 Map of main sites page 9 Exhibition walk-through page 10 Images available for the press page 12 Press release In the Kingdom of Alexander the Great Exhibition Ancient Macedonia October 13, 2011–January 16, 2012 Napoleon Hall This exhibition curated by a Greek and French team of specialists brings together five hundred works tracing the history of ancient Macedonia from the fifteenth century B.C. up to the Roman Empire. Visitors are invited to explore the rich artistic heritage of northern Greece, many of whose treasures are still little known to the general public, due to the relatively recent nature of archaeological discoveries in this area. It was not until 1977, when several royal sepulchral monuments were unearthed at Vergina, among them the unopened tomb of Philip II, Alexander the Great’s father, that the full archaeological potential of this region was realized. Further excavations at this prestigious site, now identified with Aegae, the first capital of ancient Macedonia, resulted in a number of other important discoveries, including a puzzling burial site revealed in 2008, which will in all likelihood entail revisions in our knowledge of ancient history. With shrewd political skill, ancient Macedonia’s rulers, of whom Alexander the Great remains the best known, orchestrated the rise of Macedon from a small kingdom into one which came to dominate the entire Hellenic world, before defeating the Persian Empire and conquering lands as far away as India. -
Alexander the Great
© Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. Introduction he reader should be warned that my story (rather than T“study”) is only very marginally devoted to the real Al- exander, but is almost wholly concerned with stories told about him after his death, both about “historical” events and, especially, the fantasy that scholars and poets have woven around him from antiquity down to the present day, from ancient and mediaeval “Romances” to modern film. His name and career have been “used” by authors, histori- ans, and artists, relentlessly. They take us over a very full range of European and eastern literature and art, from Scot- land to China, as well as of geography, since the whole of the Old World was deemed to have been the setting for his ad- ventures, especially Asia. In the latter case, what I write de- pends rather little on personal experience of the eastern areas described (certainly not the imaginary ones, as yet) although I have tourist- travelled Iran, Afghanistan, Uzbeki- stan, Turkmenistan, Pakistan, north India, Ceylon, and China. My principal written sources are those I have abbre- viated, and the many cited in footnotes, and which I have found in the Sackler Library in Oxford or via Abebooks. I should note especially my debt to Richard Stoneman for his many books published on the Romance aspects of the sub- ject over the last twenty- odd years and his comments on what I have written. -
6 X 10. Three Lines .P65
Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A. Huffman Index More information Select index of Greek words and phrases discussed in the text delf»v/delf, 64, 123, 125, 154 galnh, 66, 75, 491, 494–500, 504–05, 515 kanqa, 341 gr, 122–23 ll»triov, 194–95 gewmetrw, 567 nagka©wv, 396 gewmetrik, 232–33, 244 ndocov, 39–40 gewmetrik»v, 244 na©sqhtov, 449 nakmptw, 538 de»menoi, 217–18 naklw, 476–77 dicr»nou , 291 nakÅptw, 322 diagignÛskw, 58–59, 149–51 nalog©a, 179–81, 503, 529–37, 538; toÓ sou, diagnÛmen, xiv, 149 529–37 dignwsiv, 58–59, 149–51 nlogon, 179 digramma, 396, 566 namon, 291 d©aita, partn d©aitan , 300–01 nastrof, 123, 155 diallttw, 215 nepistmwn, 193–94 disthma, 166–67, 169, 181, 458 n»moiov, tn»moia , 436, 441–43 diatrib, 228–32 ntere©dw, 561 dunmenoi, 217–18 ntreisma, 297 dÅnamiv, 446 nt©lhyiv, 451 dusmcanov, 79, 348, 375, 379 nÛmalov, 513–15 nwmal»thv, 513 gg©gnomai, 539 »ristov, 511 e²dov, 93, 123, 226, 238, 250–51, 567; pqeia, 600, 603 (prÛtiston), 122 pantizw, 113, 156 e«kÛn, 601 planv, 542–43 kle©pw, 247 podeiktikäv, 375, 379 mp»diov, 335 p»deixiv, 71, 232, 237–38, mfusw, 113, 160 248–49 n aÉt, 222 podcomai, 503–04 nant©ov, 445 porov, 195 nargv, 71, 233, 236–37, 238, 246–47 pofrssw, 160 narm»zw, 351 riqmhtik, 240–44 xeur©skw, 193, 195, 196–200, 202 rmon©a, tperª tn rmon©an , 565 peiskwmzw, 314, 322 rc, 358, 500, 502, 598 piqumhtik»v, 93 rc kaª mhtr»poliv, 69 p©stamai, 196–200 %rcÅtav, 619 pistmwn, 193–94 stronomik»v, 244 pistthv, 389 aÎxh, 80, 386 pitelw, 72, 237–38, 247, 249 aÉt¼v fa, 55 pitmnw, 587 stÛ, 96 banausourg©a, 380 scatov oÉran»v, 87 638 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A. -
Arxiv:1908.01202V1 [Math.GM] 3 Aug 2019 113 of Π Correct to 6 Decimal Places
SQUARE THE CIRCLE IN ONE MINUTE HÙNG VIÊ. T CHU ABSTRACT. Since squaring the circle was proved to be impossible, mathematicians have picked up a new hobby to square the circle ’approximately’. The most famous work is due to Ramanujan who gave a construction correct to 8 decimal places. In his book Mathographics, Dixon gave constructions correct to 3 decimal places and stated that his method was quite complicated. In this paper, we improve Dixon’s method then give a new construction correct to 9 decimal places, a new record so far. 1. HISTORY Squaring the circle is a problem proposed by ancient geometers who asked whether it was possible to construct a square which has the same area with a given circle using only rulers and compasses. The method is called ruler-and-compass construction or classical construction. Nowadays, we know that this task is impossible, but the problem of squaring the circle had such a long history that many circle-squarers attempted and failed. Because it is possible to approximate the area of a circle with inscribing regular polygons to any degree of precision, and polygons can also be squared, it is reasonable to expect that a circle can be squared. While many Greek mathematicians and philoso- phers including Anaxagoras, Hippocrates of Chios, and Oenopides attempted a solution, mathematicians after the 16th century tried to prove its impossibility. However, it was not until the 19th century that considerable progress was made. In 1837, Pierre Wantzel [5] proved that lengths that can be constructed must be the zero of a polynomial. -
Alexander the Great
LEARNING FROM ARISTOTLE 0. LEARNING FROM ARISTOTLE - Story Preface 1. LEARNING FROM ARISTOTLE 2. THE YOUNG ALEXANDER 3. ALEXANDER'S HOMETOWN 4. ASSASSINATION OF PHILIP II 5. DISCOVERY OF PHILIP'S TOMB 6. ROYAL TREASURES 7. ALEXANDER'S BEQUEST 8. ALEXANDER'S EARLY CONQUESTS 9. CHASING DARIUS III 10. GAUGAMELA AND THE END OF DARIUS 11. ELEPHANTS IN WAR 12. VICTORY IN INDIA 13. GOING HOME 14. ALEXANDER'S DEATH 15. ALEXANDER'S JOURNEY IN PICTURES 16. THE REST OF THE STORY Before Alexander III (later called "The Great") was born in Pella, likely on or about July 20 in 356 B.C., the Persian Empire was the dominant power in that part of the world. Cyrus, who founded the empire, and his successors who followed, including Darius, were intent to keep their conquered lands and subjected people. (A century earlier, some of the Persian-controlled territory had been colonized by Greece.) Philip II (Alexander's father) was also a man of military might and persuasive abilities. During his 23-year reign, he built a formidable army, subdued many Greek city-states, and established a Macedonian kingdom which provided protection for his people. Before his death, he considered invading Persia to further strengthen and solidify his country's position. Wishing his son (then fourteen years old) to study with the best teachers available, Philip sought out Aristotle and invited him to educate Alexander. Scholars believe that Alexander's mother (who reportedly learned to read when she was middle-aged) also favored the selection of Plato's brightest pupil. Aristotle was born in Stageira (located in the current Greek prefecture of Chalcidice [also called Halkidiki], Central Macedonia District, just north of the current village of Stagira). -
Democritus 8
THREE DEMOCRITUS 8 1. His character can be seen from his writing. (DL 9.38) δηλν δεκ ακ των συγγραµµα των ις ην . 2. Men remember one’s mistakes rather than one’s successes. (fr. 265) θρωπι µεµνεαται µαλλν ητω νευ πεπιηµενων . Research into the life and work of Democritus, best known of the Greek atomists, is sadly hampered by the one-sided nature of his extant writings; a fair amount of his ethical work remains, but his scientific theories are known only from secondhand sources.1 The relationship between his work and his biography, therefore, can only partially be recovered, although the secondary sources do, in many cases, amply reveal the biographical mind at work. We begin with his early life. 94 Democritus 95 DATE, TEACHERS, AND PHILOSOPHICAL RELATIONSHIPS Democritus himself gives us some indication of his age and era. In his Lesser World System, Democritus says he was forty years younger than Anaxagoras, giving himself a birth date of about 460–57 BCE. This agrees with the Eightieth Olympiad birth date given by Apollodorus and is generally accepted.2 Democritus is almost universally regarded as a native of Abdera,3 and his father’s name is given as either Hegesistratus, Athenocritus, or Dama- sippus.4 From the biographies, we can infer that, as usual, his father was a man of wealth and influence, further said to have entertained Xerxes (DL 9.34–36). Traditionally, it was through his family friendship that Democri- tus received his early training; the biographers tell us that Xerxes left behind Magi and Chaldaeans who taught Democritus astronomy and theology.