61. The Crystalline Sphere Universe Of Aristotle Makes A Simple ( aristarchus of samos (c. 310230 BC), Greek astronomer, firstto maintain that the Earth rotates and revolves around the Sun. http://zebu.uoregon.edu/2003/hum399/lec05.html

The crystalline sphere universe of Aristotle makes a simple prediction all the wheels move in the same direction. This means that any planet should always move in the same direction, with respect to the background stars (which are the coordinate system here). Yet, the retrograde motion of Mars was well known at the time. Mars generally moves west to east (right to left) on the background of stars. But every 780 days it goes through period of 83 days during which it moves east to west against the stars, the retrograde motion. The retrograde period is centered around the time when Mars is in opposition - Mars is directly opposite the Sun. Thus, this phenomena could be established as repeatable and realiable after only a decade's worth of observations. Plato gave his students a major problem to work on. Their task was to find a geometric explanation for the apparent motion of the planets, especially the strange retrograde motion. One key observation: as a planet undergoes retrograde motion (drifts westward with respect to the stars), it becomes brighter. Plato and his students were, of course, also guided by the Pythagorean Paradigm. This meant that regardless of the scheme they came up with, the Earth should be at the unmoving center of the planet motions. One student named Aristarchus violated that rule and developed a model with the Sun at the center. His model was not accepted because of the obvious observations against a moving Earth. Ptolemy to the Rescue?

62. Outline Of Cosmology And Astronomy To Aristarchus Spring, 1999. Source Thomas Heath, aristarchus of samos, the Ancient Copernicus,Clarendon Press, Oxford, 1913. Reprinted by Dover, New York, 1981. http://ullman.clarku.edu/~djoyce/ma105/astrocos.html

Outline of Cosmology and Astronomy to Aristarchus Math 105 History of Mathematics, D Joyce. Spring, 1999 Source: Thomas Heath, Aristarchus of Samos, the Ancient Copernicus, Clarendon Press, Oxford, 1913. Reprinted by Dover, New York, 1981. Thales of Miletus (c. 630? - c 550? BC) Statesman, engineer, mathematician and astronomer, one of the "seven wise men." Cosmology: earth floated on water, a disk. Sun, stars, and planets fiery. Perhaps based on Egyptian and/or Babylonian cosmology. Said to have predicted a solar eclipse, but unlikely. Eudemus referred to two written works by Thales: On the Solstice and On the Equinox, since lost. Noted length of four seasons not all the same. Diogenes Laertius says Thales declared the apparent size of the sun and the moon to be 1/720 part of the circle described by it (i.e., 1/2 degree). Recommended sailing by Little Bear (Little Dipper) as the Phoenicians did. Anaximander of Miletus (Anasimandros) (c. 611 - c. 547 BC) Considered first Greek philosopher. Student of Thales. Cosmology: earth at center, a disk with depth 1/3 of breadth floating in air. Believed the stars to be fiery wheels emitting flames through vents, and eclipses occur when the vents are stopped up. Concluded the circle of the sun is 27 or 28 times the size of the earth, and that of the moon 18 or 19 times. Probably brought the vertical sundial (gnomon) to Greeks from Babylonians. Said to be first to draw a map of the inhabited earth. Anaximenes of Miletus (c. 585 - c. 528 BC. Stars on crystal sphere, but planets have their own movements. Sun, moon, stars made of fire. Said eclipses due to obscuring dark bodies.

63. Science - Mathematics: Aristarchus 2) which is 75. Plato mentioned this approximation of 2^(1/2). Skipping a few steps,FEBH 362 or 181. aristarchus of samos goes on to prove that BA 20BC. http://www.archaeonia.com/science/mathematics/aristarchus.htm

ARISTARCHUS A ristarchus was yet another successful Greek mathematician and astronomer . He was one of the first exponents of a heliocentric (not Earth-centered) universe (where the earth goes around the sun). He made pioneering attempts to predict the sizes of the moon and sun ; primitive instruments were the only reasons he was at an error. However, he was definitely correct in predicting the length of a solar year Here is an indicative proof from Aristarchus known as proposition 7 and there has been great interest in it over the years. Prop. 7 says that the distance of the sun from the earth is greater than 18 times , but less than 20 times, the distance of the moon from the earth. This is an improvement over previous estimates. Other mathematicians involved in these estimations were Anaximander (c. 611-545 B.C.), Eudoxus , and Phidas who was Archimedes' father. A is the center of the sun ; B is the center of the earth ; and C is the center of the moon so that the angle ACB is right. ABEF is a square, and AE is a quadrant of the circular orbit produced by the sun. If we put together BF and bisect the angle FDE by BG, so that the angle GBE is equal to 1/4 of R or 221/2 degrees.

64. The Copernican Model: A Sun-Centered Solar System This sequence is commonly called the Copernican Revolution. Been There, DoneThat aristarchus of samos. The idea of Copernicus was not really new! http://csep10.phys.utk.edu/astr161/lect/retrograde/copernican.html

The Copernican Model: A Sun-Centered Solar System The Earth-centered Universe of Aristotle and Ptolemy held sway on Western thinking for almost 2000 years. Then, in the 16th century a new idea was proposed by the Polish astronomer Nicolai Copernicus The Heliocentric System In a book called On the Revolutions of the Heavenly Bodies (that was published as Copernicus lay on his deathbed), Copernicus proposed that the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system . The ordering of the planets known to Copernicus in this new system is illustrated in the following figure, which we recognize as the modern ordering of those planets. The Copernican Universe In this new ordering the Earth is just another planet (the third outward from the Sun), and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction. Retrograde Motion and Varying Brightness of the Planets The Copernican system by banishing the idea that the Earth was the center of the Solar System, immediately led to a simple explanation of both the varying brightness of the planets and retrograde

65. TruePhysics Physics In A New Way. 260 BC, aristarchus of samos, ratio of EarthSun distance to Earth-Moon distancefrom angle at half moon. 260 BC, aristarchus of samos, heliocentric cosmology. http://www.truephysics.com/timeline/timeline500_1.html

66. Bloomfield Science Museum, Jerusalem - Young Scientist - Scientists And Inventor birthdays to such scientists! Birthdate May aristarchus of samos, b.about 310 BC, d. about 230 BC, (Greek) Heavenly Perfection From http://www.mada.org.il/website/html/eng/2_1_1-29.htm

We decided it was unfair to exclude from "Birthday of the Month" scientists whose birthdate is unknown, so from time to time we shall arbitrarily assign birthdays to such scientists! Birthdate May Aristarchus of Samos, b. about 310 BC, d. about 230 BC, (Greek) Heavenly Perfection From ancient times, the "perfection" of the heavens was contrasted with the "chaos" of earth. The myriad stars moved across the sky in stately, unchanging order - marred only by the strange behaviour of the moon and five other heavenly bodies we now call the planets (the other planets are not visible to the naked eye). The strangest behaviour of all was that of "The Red Planet" - Mars - which not only moved across the field of stars at a variable speed but even on occasion reversed its direction ("retrograde motion"). Furthermore, its brightness varied by a large factor. The challenge was to reconcile these observations with the idea, universally held in ancient times, that the Earth was the centre of the Universe. In the fourth century BC, Eudoxus developed a system of spheres centred on the Earth which succeeded in explaining (in principle) the variable motions of the planets and even the retrograde motion of

67. Samos - Cityreview-Suche Translate this page Aristarchus Aryabhata Aryabhata (India about 500 pC) The Aryabhatíya of Aryabhataaristarchus of samos Aristarchus`s Discoveries Archimedes Home Page .. http://suche.cityreview.de/samos.html

Samos Samos: Günstig reisen Buchen Sie hier Ihre Traumreise zu supergünstigen Bestpreisen! http://www.travel24.com Mit Tchibo nach Samos ab 549 Euro Ausgewählte Traumreisen zu Traumpreisen. Familienreisen, Kultur- und Rundreisen, Aktivreisen, Städtetouren oder Kreuzfahrten. Neu: Last Call-Angebote zu sensationell günstigen Preisen. http://reisen.tchibo.de Reiseangebote Samos bei Holiday Land Reiseangebote - Samos bei Holiday Land. Angebote für die Sommersaison 2004 online. http://www.holidayland.de Reise Angebote nach Samos Last Minute Angebote nach Samos. Täglich Last Minute Angebote aller Reiseveranstalter. Abflug auch ab Österreich und Schweiz möglich. Detaillierte Infos zu jedem Reise Angebot. http://www.vistamare.de Samos bei Testsieger Traveltopia von Stiftung Warentest: Informationen über Samos, über 800.000 Flüge weltweit mit vielen Specials, attraktive Lastminute-Angebote, Rabatte auf Mietwagen, günstige Hotels und vieles mehr! http://www.traveltopia.de Samos - Travelocity - Clever buchen und sparen Ob Flug, Hotel, Mietwagen, für Ihren Urlaub finden Sie bei Travelocity die Ideallösung - Travelocity - Clever buchen und sparen! http://www.travelocity-online.de

68. Symposium Poster Guild Hall - 900 am~1230 pm. Daniel J. Mania. Professor TimCarroll, Sponsor. aristarchus of samos and His Heliocentric Theory. http://www.emich.edu/symposium/abstracts2003/mathematics.html

Department of Mathematics Theodore Begeman Professor Ken Shiskowski, Sponsor Coding by the Numbers Codes or Cryptology has been of intense interest in modern times to securely send messages as well as to encrypt data. One of the simplest and hardest to (theoretically) break methods is the PSA algorithm which uses large primes and modular arithmetic. The mathematical software Maple will be used to program the PSA algorithm and to examine its behavior. Poster - Guild Hall - 9:00 a.m.~12:30 p.m. Clarence Johnson, Jr. Professor Ken Shiskowski, Sponsor If Newton had a Computer, What Could He Have Done? The Generalized Newton and Householder's methods for solving equations of the form f(x) = produce wonderful and complicated fractal graphics which provide a great deal of information about each method. The mathematical software Maple will be used to generate these graphics in order to examine local versus global behavior for each method. Poster - Guild Hall - 9:00 a.m.~12:30 p.m. Daniel J. Mania Professor Tim Carroll, Sponsor Aristarchus of Samos and His Heliocentric Theory Copernicus is recognized as the main person that laid the groundwork for our present understanding of our solar system. But up to about 1500 C.E. most people believed in the Geocentric Theory of the Universe as put forward mainly by Ptolemy around 150 C.E. Aristarchus of Samos actually had a Heliocentric Theory almost 300 years before Ptolemy came along and 'proved' his theory with some rigorous mathematics. Aristarchus also performed some interesting calculations involving a few celestial objects.

69. Thousands Of Free Essays At OPPapers.com Born in 270 BC, the Greek astronomer aristarchus of samos, was the firstscientist known to suggest that the earth revolves around the sun. http://www.oppapers.com/read.php?id=33380&idenc=KxyHiuJa

70. General Science 2310 - Greek Astronomy - Aristarchus aristarchus of samos (300 BC) Demonstrated that the sun was much farther away thanthe moon by measuring the time between first and third quarter phases of the http://www.lakeheadu.ca/~physwww/courses/Astro/2310/Ancient/Aristarchus.htm

Last Update : A NCIENT A STRONOMY Greek Early Greek astronomy was characterized by a number of viable geometrical models but not enough observations to choose between them Observational science became part of Greek method with the Alexandrian School, the most famous practitioner was Aristarchus of Samos (300 BC) Aristarchus of Samos (300 BC) Demonstrated that the sun was much farther away than the moon by measuring the time between first and third quarter phases of the moon and noting that it is very nearly exactly half of a month Determined the ratio of the moon's diameter to that of the Earth by measuring the time taken for the moon to cross the Earth' shadow during a lunar eclipse Noted that the moon almost exactly covers the sun during a solar eclipse, deduced that since the Sun is so much farther away it must be much bigger than either the Moon or the Earth First advocate of the Heliocentric Theory (Earth goes round the Sun) All distances and sizes were expressed in terms of the (unknown) size of the Earth To contact the instructor please email to: wwall@gale.lakeheadu.ca

71. Aristarchos Von Samos - Wikipedia Aristarchusof Samos, Oxford, 1913; TL Heath,aristarchus of samos. http://de.wikipedia.org/wiki/Aristarchos_von_Samos

Aristarchos von Samos aus Wikipedia, der freien Enzyklopädie Aristarchos von Samos auch Aristarchus ,(etwa 310 - 230 v. Chr.) war ein griechischer Astronom und Mathematiker. Als er die wechselseitige Beziehung von Sonne und Erde untersuchte, halfen ihm die Vorstellungen Epikurs und Demokrits über die Unendlichkeit der Welt. Er brach mit der Ansicht, die Erde befinde sich im Mittelpunkt der Welt. Ihm drängte sich die Überzeugug auf, die Erde bewege sich um die Sonne. Plutarch berichtet von Kleanthes bis ), dem damaligen Vorsteher der stoischen Schule, dieser sein der Meinung gewesen, Aristarch müsse der Gottlosigkeit abgeklagt werden(1). Die Begründung der Anklage sollte darin bestehen, daß Aristarch für Naturerscheinungen neue Erklärungen suchte. Der Sturz des geozentrischen Weltbildes( Geozentrismus ) und die Ersetzung durch das heliozentrische galt dem Stoiker als Glaubensfrevel, womit sich die Ambivalenz Zenons und sein Anliegen in der Wirkung ausdrückten. Der Gleichmut in den Ansichten hattte hier seine Grenzen gefunden. Er zählt zu den ersten Vertretern des Heliozentrischen Weltbilds , das die Sonne in den Mittelpunkt der Welt rückte. Seine Ideen wurden im

72. Stanford SOLAR Center -- Ask A Solar Physicist FAQs - Answer around 450 BC. It was again suggested by aristarchus of samos, around220 BC, but this idea did not catch on. About 1800 years later http://solar-center.stanford.edu/FAQ/Qsunasstar.html

Who discovered that the Sun was a star? This answer is courtesy of Louis Strous of the National Solar Observatory, Sacramento Peak, NM. Many people's work was needed to prove that the Sun is a star. The first person we know of to suggest that the Sun is a star up close (or, conversely, that stars are Suns far away) was Anaxagoras, around 450 BC. It was again suggested by Aristarchus of Samos, around 220 BC, but this idea did not catch on. About 1800 years later, around AD 1590, Giordano Bruno suggested the same thing, and was burnt at the stake for it. Through the work of Galileo, Kepler, and Copernicus during the 16th and 17th centuries the nature of the solar system and the Sun's place in it became clear, and finally in the 19th century the distances to stars and other things about them could be measured by various people. Only then was it proved that the Sun is a star. For most of human history, almost all people have thought that the Earth was in the center of a giant sphere (or ball, called the "celestial sphere") with the stars stuck to the inside of the sphere. The planets, Sun, and Moon were thought to move between the sphere of stars and the Earth, and to be different from both the Earth and the stars. Anaxagoras

73. Aristarchus aristarchus of samos. Born about 310 BC in Greece Diedabout 230 BC in Greece. Show birthplace location http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/rstrchs.htm

Aristarchus of Samos Born: about 310 BC in Greece Died: about 230 BC in Greece Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Aristarchus was a mathematician and astronomer who is celebrated as the exponent of a Sun-centred universe and for his pioneering attempt to determine the sizes and distances of the Sun and Moon. Aristarchus was a student of Strato of Lampsacus, head of Aristotle 's Lyceum, coming between Euclid and Archimedes . Little evidence exists concerning the origin of his belief in a heliocentric system, the theory was not accepted by the Greeks and is known only because of a summary statement in Archimedes The Sand-Reckoner and a reference by Plutarch. The only surviving work of Aristarchus, On the Sizes and Distances of the Sun and Moon, provides the details of his remarkable geometric argument, based on observation, whereby he determined that the Sun was about 20 times as distant from the Earth as the Moon, and 20 times the Moon's size. Both these estimates were an order of magnitude too small, but the fault was in Aristarchus' lack of accurate instruments rather than in his correct method of reasoning.

74. Pythagoras - Number Burnet10 claims It is probable, at any rate, that this theory started the trainof thought which made it possible for aristarchus of samos to reach the http://www.mathgym.com.au/history/pythagoras/pythnum.htm

Return to MATHGYM Back P YTHAGORAS of S AMOS A Collection of Essays and Lessons for Junior and Senior High School Contents Early concepts of Number and Number Mysticism Figurate Numbers Number Patterns in Music Incommensurables ... Academic Introduction: The Pythagorean view of the universe rested squarely on the belief that Natural (counting) number was the key to the various qualities of mankind and matter. Since in their view everything was composed of number, the explanation for an objects existence could only be found in number. Elsewhere about this time, number existed for utilitarian purposes only, as a device for solving problems in calendar construction, building and commerce. It was the Pythagoreans who saw number as important in itself, the numbers themselves having "personality in a rustic landscape". The distinction was made between logistic (art of computation) and arithmetic (number theory). Kline [6 ] quotes the famous Pythagorean Philolaus (425 B.C.E.), as writing: "Were it not for number and its nature, nothing that exists would be clear to anybody either in itself or in its relation to other things...You can observe the power of number exercising itself ... in all acts and the thoughts of men, in all handicrafts and music." Pythagoras and the early Order initially treated number concretely, as patterns with pebbles, but over time the Pythagoreans developed and refined their concept of number into the same abstract entity which still exists today. Though it is difficult to separate fact from fancy in some of the surviving references to the Pythagoreans, it is generally conceded that they began number theory, and were responsible for the introduction and development of number mysticism in Western Society.

75. Teacher Lesson Plan 14 Heracleides of Pontos http//www.astunit.com/tutorials/greek.htm Tycho Brahe http//www.geocities.com/CapeCanaveral/Hangar/7990/aristarchus of samos http//www http://www.sil.si.edu/exhibitions/chasing-venus/teachers/lessonplan14.htm

Home On the Shoulders of Giants These exercises and lesson plans are designed to accompany and enrich the study and discussion of the June 2004 Transit of Venus. Goal: Students research important astronomers and scientists from the past and make presentations on their achievements. Grade Level: Objectives: Identify and use different documents for research Synthesize information around a theme or topic Develop theme that the advances in science are built on the past achievements and scholarship of many individuals Develop and present the information as part of the theme Subject Area or Standard: History, Creative Writing Materials Needed: Internet access Books and articles Representation of sun on poster board sliced into wedges. Classroom presentation tools Websites: Jeremiah Horrocks http://www.uclan.ac.uk/facs/science/physastr/misc/horrock.htm

76. Lecture 13: Greek Astronomy Early Geocentric Systems Anaximander; Pythagoras, Eudoxus, Aristotle. TheHeliocentric System aristarchus of samos. aristarchus of samos (?310230BC). http://www-astronomy.mps.ohio-state.edu/~pogge/Ast161/Unit3/greek.html

Astronomy 161: An Introduction to Solar System Astronomy Prof. Richard Pogge, MTWThF 9:30 Lecture 13: The Harmony of the Spheres Greek Astronomy Key Ideas: Early Geocentric Systems: Anaximander The Heliocentric System: Aristarchus of Samos Epicyclic Geocentric Systems: Hipparchus of Nicaea Claudius Ptolemy Summary of Celestial Motions Fixed Stars Uniform daily motion about the celestial poles. The Sun Daily motion around the celestial poles (rising and setting). Eastward drift along the Ecliptic over a year, a little faster in winter, slower in summer. The Moon Daily motion around the celestial poles. Eastward motion near the Ecliptic over a month. The Planets Daily motions about the celestial poles. Generally eastward motion near the Ecliptic at different speeds for each planet. Occasional westward "retrograde" motions. Superior Planets are brighter at opposition, fainter at conjunction. Any successful description of the Solar System must explain all these facts. The Geocentric System Geocentric = Earth-Centered.

77. APOD: November 8, 1997 - Aristarchus' Unbelievable Discoveries aristarchus lived on the Greek island of samos, a small island in thecenter of the above picture that can be identified with a good map. http://antwrp.gsfc.nasa.gov/apod/ap971108.html

Astronomy Picture of the Day Discover the cosmos! Each day a different image or photograph of our fascinating universe is featured, along with a brief explanation written by a professional astronomer. November 8, 1997 Aristarchus' Unbelievable Discoveries Credit: Space Shuttle Columbia NASA Explanation: Here lived one of the greatest thinkers in human history. Aristarchus lived on the Greek island of Samos, a small island in the center of the above picture that can be identified with a good map . Aristarchus, who lived from 310 BC to 230 BC, postulated that the planets orbited the Sun - not the Earth over a thousand years before Copernicus and Galileo made similar arguments. Aristarchus used clear logic to estimate the size of the Earth, the size and distance to our Moon , the size and distance to our Sun, then he even deduced that the points of light we see at night are not dots painted on some celestial sphere but stars like our Sun at enormous distances. Aristarchus' discoveries remained truly unbelievable to the people of his time but stand today as pillars of deductive reasoning. Tomorrow's picture: Surveyor Slides Archive Index Search ... USRA NASA Technical Rep.:

78. ARISTARCHUS, OF SAMOS aristarchus, OF samos. ~ n Naxos, but he quarrelled with Megabates, the kersian og mmander, who warned the 7. T aristarchus, of samos, Greek astronomer, flourished about H ~0 BC http://www.1911encyclopedia.org/A/AR/ARISTARCHUS_OF_SAMOS.htm

ARISTARCHUS, OF SAMOS arian and critic, flourished about 155. He settled early in. ti lexandria, where he studied under Aristophanes of Byzantium, 01 horn he succeeded as librarian of the museum. On the accession ci the tyrant Ptolemy Physcon (his former pupil), he found his h e in danger and withdrew to Cyprus, where he died from a -opsy, hastened, it is said, by voluntary starvation, at the age p 72. Aristarchus founded a school of philologists, called after le m Aristarcheans, which long flourished in Alexandria and g~ terwards at Rome. He is said to have written 800 corn- a entaries ilon.e, without reckoning special treatises. He edited h esiod, Pindar, Aeschylus, Sophocles and other authors; but ~I s chief fame rests on his critical and exegetical edition of ti omer, practically the foundation of our present recension. In h ie time of Augustus, two Aristarcheans, Didymus and Arisnicus, undertook the revision of his work, and the extracts p om these two writers in the Venetian scholia to the Iliad t] ye an idea of Aristarchuss Homeric labors. To obtain a 4

79. ARISTARCHUS, OF SAMOS aristarchus, OF samos. ~n Naxos 856). See BergkHinrichs, aristarchus vonsamos (1883) ; Tannery, it ristarque de samos; also ASTRONOMY. ai http://64.1911encyclopedia.org/A/AR/ARISTARCHUS_OF_SAMOS.htm

ARISTARCHUS, OF SAMOS arian and critic, flourished about 155. He settled early in. ti lexandria, where he studied under Aristophanes of Byzantium, 01 horn he succeeded as librarian of the museum. On the accession ci the tyrant Ptolemy Physcon (his former pupil), he found his h e in danger and withdrew to Cyprus, where he died from a -opsy, hastened, it is said, by voluntary starvation, at the age p 72. Aristarchus founded a school of philologists, called after le m Aristarcheans, which long flourished in Alexandria and g~ terwards at Rome. He is said to have written 800 corn- a entaries ilon.e, without reckoning special treatises. He edited h esiod, Pindar, Aeschylus, Sophocles and other authors; but ~I s chief fame rests on his critical and exegetical edition of ti omer, practically the foundation of our present recension. In h ie time of Augustus, two Aristarcheans, Didymus and Arisnicus, undertook the revision of his work, and the extracts p om these two writers in the Venetian scholia to the Iliad t] ye an idea of Aristarchuss Homeric labors. To obtain a 4

80. Aristarchus Van Samos aristarchus van samos. Van aristarchus leven weten we bijna nietsaf. Zelfs zijn datums (310 230 vC) zijn niet nauwkeurig bekend. http://mediatheek.thinkquest.nl/~lla015/biografie/Aristarchus.html

Aristarchus van Samos Vitruvius plaatste hem in een rijtje van mannen die verdienstelijk waren in elk onderdeel van de wetenschap.

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