Epicycle The geometry of epicycles was perfected by hipparchus of rhodes at some time around125 BC, 185 years after the birth of Aristarchus of Samos, the inventor of http://linuxcommand.org/man_pages/epicycle1.html
Extractions: XScreenSaver(1) XScreenSaver(1) epicycle - draws a point moving around a circle which moves around a cicle which... epicycle [-display host:display.screen ] [-root] [-window] [-mono] [-install] [-noinstall] [-visual viz ] [-colors N ] [-foreground name ] [-color-shift N ] [-delay microseconds ] [-holdtime seconds ] [-linewidth N N N number number ] [-harmonics N ] [-timestep number probabil- ity number number The epicycle program draws the path traced out by a point on the edge of a circle. That circle rotates around a point on the rim of another circle, and so on, several times. The random curves produced can be simple or complex, convex or concave, but they are always closed curves (they never go in indefinitely). You can configure both the way the curves are drawn and the way in which the random sequence of circles is generated, either with command- line options or X resources. -display host:display.screen
A Chronology Of Interpolation 150 BC hipparchus of rhodes uses linear interpolation in the construction of tablesof the socalled chord-function (related to the sine function) for the http://imagescience.bigr.nl/meijering/research/chronology/
Extractions: It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. G. W. Leibniz, Historia et Origo Calculi Differentialis ca. 1714). Translation as in J. M. Child, "Newton and the Art of Discovery", in Isaac Newton 16421727: A Memorial Volume , W. J. Greenstreet (ed.), G. Bell and Sons, London, 1927, pp. 117-129. ca. 300 BC and earlier: Babylonian astronomers use linear and higher-order interpolation to fill gaps in ephemerides of the sun, moon, and the then-known planets, written down in cuneiform tablets as shown here. For explanations and more details, see O. Neugebauer
Lecture 6: Motions Of The Stars Halley in 1718 for three bright stars Sirius, Aldebaran, and Arcturus, by comparinghis measurements of their positions to those of hipparchus of rhodes (300BC http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit1/motions.html
Extractions: The great distances to the stars means that their apparent motions across the sky are very small during a human lifetime. Proper Motions Apparent angular motion of nearby stars with respect to more distant stars. These reflect the true motion of the stars relative to the Sun through space. Proper motions are Cumulative The effect of proper motions build up over time... The longer you wait, the greater the apparent angular motion is Modern measurement of proper motions: Example: Consider a star with a proper motion of 0.1 arcsec/year:
History Of Constellation And Star Names This article and Part II of such, published 1988/1989, comprise a study of theCommentary on the Phainomena of Aratus and Eudoxus by hipparchus of rhodes.. http://members.optusnet.com.au/~gtosiris/page6.html
Extractions: An Annotated Bibliography Of Studies of Occidental Constellations and Star Names to the Classical Period Compiled by Gary D. Thompson Go to: Star Maps References With Extensive Bibliographies Return To Site Contents Page Star Maps Books/Pamphlets: Grasshoff, Gerd. (1990). The History of Ptolemy's Star Catalogue. [Note: Based on the author's doctoral thesis. See the (English-language) book review by James Evans in Journal for History of Exact Sciences, Volume 43, Pages 133-144.] Knoel, E[?]. (1877). "The Chronology of Star Catalogues." (Memoirs of the Royal Astronomical Society, Volume 43, Pages 1-74). [Note: Comprehensive.] Stott, Carole. (1991). Celestial Charts: Antique Maps of the Heavens. Warner, Deborah. (1979). The Sky Explored: Celestial Cartography 1500-1800. [Note: Excellent.] Whitfield, Peter. (1995). The Mapping of the Heavens. [Note: At times uncritical and unreliable.] Articles/Entries: Berggren, J[?]. [Len]. (1991/1992). "Ptolemy's Maps of Earth and the Heavens: A New Interpretation." (Archive for History of Exact Sciences, Volume 43, Pages 133-144). Dambis, A[?]. and Efremov, Yu. (2000). "Dating Ptolemy's Star Catalogue Through Proper Motions: the Hipparchan Epoch." (Journal for the History of Astronomy, Volume 31, Part 2, May, Pages 115-134).
The Origin Of The Zodiac It would appear it was the Greek astronomer hipparchus of rhodes (2ndcentury BCE)who first redefined the the boundaries of the 12 signs so that the vernal http://members.optusnet.com.au/~gtosiris/page9a.html
Extractions: Essays Relating To The History Of Occidental Constellations and Star Names to the Classical Period The Origin of the Zodiac by Gary D. Thompson Return To Site Contents Page The Origin of the Zodiac The myth of a prehistoric 12-constellation zodiac (of equal divisions) is not yet extinguished. The suggestion that the zodiac was originally established as an intended scheme of 12 constellations and 12 equal divisions some 6000 years ago (or even earlier) is untenable. The fact that these ideas have been effectively disposed of seems to be ignored in publications addressed to the jury and not the bench. There is no evidence that the Greek scheme of 12 zodiacal constellations existed anywhere prior to its evolvement in Greece circa 500 BCE. The Assyriologist Peter Jensen was the first to show, in his book Die Kosmologie der Babylonier (1890), that the Greek zodiac (and zodiacal constellation names) was adapted (with few changes) from the (newly developed) zodiacal scheme of the Babylonians. The tide of claims up to the early 20th-century for the great antiquity of the zodiac (made by many historians, astronomers and Assyriologists) have been definitively discredited by an understanding of relevant Mesopotamian cuneiform sources. (Nineteenth-century arguments made frequent (misplaced) use of mythology and symbolism i.e.
Appendix 1 A generation later, Greek astronomer hipparchus of rhodes (c190125)compiled the first star catalog of about 850 stars. His follower http://www.visualstatistics.net/Visual Statistics Multimedia/mathmatical_foundat
Extractions: The mathematics pertains to numbers, space, time, and logic. The number sense probably developed from the ordinal concepts of greater than, equal, and less than. Combined with the time sense that some events precede and some events follow the others, numbers were arranged along a scale where some numbers precede and some numbers follow the others. During the time of Pythagoras, about 500 B.C., it was observed that certain numbers, called the Pythagorean triplets, describe the right triangles. For example, the original Pythagorean triplets 3, 4, and 5, associated with the height, the width, and the hypotenuse of a right triangle illustrate the Pythagorean theorem, that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This was one of the first connections made between numbers and geometrical properties of objects and thus the foundation of the visual statistics was laid. The Pythagoreans also noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers. They attempted to build a geometric model of these ratia in the sky where the motions of planets, within the celestial spheres were thought to produce a harmony called the music of the spheres.
OBSERVATORY hipparchus of rhodes, the founder of modern astronomy, by repeating observationsmade at Alexandria, discovered the precession of the equinoxes, and http://12.1911encyclopedia.org/O/OB/OBSERVATORY.htm
Extractions: OBSERVATORY. Up to a comparatively recent date an " observatory " was a place exclusively devoted to the taking of astronomical observations, although frequently a rough account of the weather was kept. When the progress of terrestrial magnetism and meteorology began to make regular observations necessary, the duty of taking these was often thrown on astronomical observatories, although in some cases separate institutions were created for the purpose. In this article the astronomical observatories will be chiefly considered. Up to about 300 B.C. it can scarcely be said that an observatory existed anywhere, as the crude observations of the heavens then taken were only made by individuals and at intervals, employing the simplest possible apparatus. Thus, according to Strabe. The instruments employed in observatories have of course changed considerably during the last two hundred years. When the first royal observatories were founded, the principal instruments were the mural quadrant for measuring meridian zenith distances of stars, and the sextant for measuring distances of stars inter Se, with a view of determining their difference of right ascension by a simple calculation. These instruments were introduced by Tycho Brahe, but were subsequently much improved by the addition of telescopes and micrometers. When the law of gravitation was discovered it became necessary to test the correctness of the theoretical conclusions drawn from it as to the motions within the solar system, and this necessarily added to the importance of observations. By degrees, as theory progressed, it made greater demands for the accuracy of observations, and accordingly the instruments had to be improved. The transit instrument superseded the sextant and offered the advantage of furnishing the difference of right ascension directly; the clocks and chronometers were greatly improved; and lastly astronomers began early in the I9th century to treat their instruments, not as faultless apparatuses but as imperfect ones, whose errors of construction had to be detected, studied and taken into account before the results of observations could be used to test the theory. That century also witnessed the combination of the transit instrument and the mural quadrant or circle in one instrument—the transit or meridian circle.
PSIGate - Physical Sciences Information Gateway Search Results of astronomy is provided with links to further information on selected key astronomers(Thales, Eratosthenes of Cyrene, hipparchus of rhodes, Euclid, Plato http://www.psigate.ac.uk/roads/cgi-bin/tempbyhand.pl?query=1034259138-24564
TITLE Although it is possible to use the Armillary for making observations (Eratosthenes204BC catalogued more than 700 stars, and hipparchus of rhodes (150125BD http://world.std.com/~leep/cat003/armil.htm
Extractions: ARMILLARY SPHERE An Armillary Sphere is a model of the celestial sphere based on the Ptolemy theory of the universe with the earth being stationary at the centre. The celestial sphere is imagined as a sphere with the stars fixed onto its interior and the earth at its centre. Although we now know this to be inaccurate, it does not effect the working of the Armillary Sphere since to an observer on Earth the motion of the Sun and Stars appears the same. It is a refinement of the earlier solid celestial spheres developed by Greek scientists such as Archimedes. Being solid made it difficult to imagine the position of the Earth at the centre, consequently these spheres developed a more skeletal appearance, consisting of a series of rings and becoming known as Armillary Spheres, presumably from the Latin word 'armilla' meaning bracelet. Although it is possible to use the Armillary for making observations (Eratosthenes 204BC catalogued more than 700 stars, and Hipparchus of Rhodes (150-125BD) determined distance from the Earth to the Sun and produced a complete star catalogue for his latitude) in practice this is difficult. However with the advent of stereographic projection the Armillary led to the development of the more accurate and useful anaphoric clock and the Astrolabe.
Scientific American: Netting The Deep Sky 20 arc minutes. It was made around 150 BC by hipparchus of rhodeshe probably used a tabletop brass dial. Around 1600 Tycho Brahe http://www.sciam.com/article.cfm?articleID=000C5A0F-31A7-1C75-9B81809EC588EF21
Reflections Vol20, No3, Aug 95 His better known successor, the ancient Greek astronomer hipparchus of rhodes,invented a magnitude system of stellar brightness in the second century BC. http://hsc.csu.edu.au/pta/mansw/reflections/vol21no1coupland.htm
Extractions: Indices, logarithms, and exponential functions are widely used in scientific applications of mathematics as they provide models for a variety of physical situations. We think this can provide motivating examples in the teaching of these topics. In the workshop at the conference, we first investigated some activities based on everyday situations that could be used as starting points. We also provided some information that may go beyond the current school syllabus in mathematics, but which provides interesting background knowledge for teachers. Investigations that use indices and exponential functions I. Could you be related to a famous historical figure? n the number of - grandparents you have, and g the number of generations back they are? How many years ago do you think your - grandparents were alive? Find out where they were probably living and the population of that part of the world at that time. You may be related to someone famous! You may even be related to the person sitting next to you! II The disappearing function x is the number of shakes, and
Spice Maps Background His work in astronomy was largely based on the ideas of hipparchus of rhodes (threehundred years earlier) who proposed divicding the length and breadth of the http://ias.berkeley.edu/orias/spice/textobjects/moreonmaps.htm
Extractions: (Berthon, p. 19) Map B Herodotus had travelled extensively throughout the Mediterranean and collected information about Asia. Beyond India lay unknown and uninhabited deserts..."for the Indians live the furthest towards the east and the sunrise of all the Asians with whom we are acquainted or of whom we know by hearsay. Eastwards the country of the Indians is a sandy desert." (Wheatley, p. 124) "I cannot help but laughing at the absurdity of all the mapmakersthere are plenty of themwho show Ocean running like a river round a perfectly circular earth, with Asia and Europe of the same size." Herodotus said of the three known continents (Europe, Asia, and Africa) "Europe is as long as the other two put together, and for breadth is not, in my opinion, even to be compared with them."
Extractions: Full Review "The Extraordinary Journey of Pytheas the Greek" is somewhat misnamed. Pytheas was an actual person, born Massalia (present day Marseilles), a Greek colony, in the 4th century BCE. His own account of his travels, "On the Ocean," is no longer extant. Cunliffle relies on all that is left of it, that is, in excerpts recorded in the works of such classical writers as Strabo, Pliny the Elder, and a host of others, some well-known, others as almost obscure as Pytheas himself. Pytheas claimed to have sailed to England and "walked the breadth of it." He could not measure longitude, but had a crude way of measuring latitude by measuring the sun's height at noon on the summer solstice (or subtracting the days until the solstice) with a surveying staff called a "gnomon." The idea of parallel lines of latitude would not developed for another couple centuries by one Hipparchus of Rhodes who used Pytheas' measurements in plotting places in the far north. Pytheas also had a crude way of measuring distance by sea using a rule of thumb as to how far a ship could travel per day.
Mathem_abbrev Heisenberg, Werner Heraclides of Pontus Heron of Alexandria Herschel, CarolineHerschel, John Higman, Graham Hilbert, David hipparchus of rhodes Hippias of http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm
Extractions: Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive.
Astronomy 9 (Spring 2000): Handout 10 6. hipparchus of rhodes (190120 BC) Great Greek astronomer; Synthesized Babylonianand Greek data with new Greek geometrical models from Appollonius http://www.jonathanbaker.org/courses/ay9/week4/handout10/
Extractions: UC Berkeley, Spring 2000 Cosmology in Ancient Greece: Aristotle and Greek Astronomy Aristotle (384-322 BC) Aristotle applies his physics to the cosmos Basic Earthly elements: air, earth, fire, water Terrestrial and celestial physics are very different! Two types of ``natural'' motion (a) Earth: linear, straight-line, finite motion (air and fire go up, water and earth go down) (b) Heavens: perfect, eternal, circular motion
The Ptolemaic Universe little acceptance. 190 120 BC, hipparchus of rhodes developer oftrigonometry; records catalogues of stellar positions. 85 - 165 http://www.astro.soton.ac.uk/~trm/PH421/notes/notes/node10.html
Extractions: Next: The Copernican Revolution Up: Historical Introduction Previous: Historical Introduction The earliest useful observational records of the sky were made by the Babylonians. Their work was taken up by the Greeks following the conquests of Alexander the Great. It is from the Babylonians via the Greeks that we inherit our system our system of time and angle measurements. Babylonian records of solar and lunar eclipses have proved useful in measuring the rate of slowing of the Earth's rotation. The Babylonians were interested in predicting celestial phenomena with accuracy; the Greeks added to this a philosophical interest in the workings of the Universe. Starting with Aristotle, they developed the idea of a fixed Earth at the centre of the Universe with the planets, Sun, Moon and stars rotating around it. Note that although some did believe that the Earth was flat, it is not clear
Ancient Astronomy-Main Page One final method of determining the distances and sizes of the Sun and Moonwas used by hipparchus of rhodes about 50 years after Aristarchus. http://brahms.phy.vanderbilt.edu/~rknop/classes/a250/wahlig/
Extractions: Measuring Distances in Ancient Astronomy Foundations of Ancient Astronomy Circumference of the Earth Relative Distances to Sun and Moon Relative Sizes of Sun and Moon ... References and Links Astronomy has sometimes been called the world's first science. Since the beginnings of human history, mankind has used astronomical objects both as tools for improving daily life and as inspiration for systems of belief. Many different cultures claim that the celestial realm is inhabited by God or gods and that it has profound impact on their daily lives. More practically, astronomical events help us to predict the seasons, create calendars that keep track of past events, and navigate on both land and sea. In the last millennia BC, astronomy became a science of methodical records, changing paradigms, and the first complex geometrical calculations. It is this scientific approach that has led to the "Cosmic Distance Ladder," a series of increasingly large measurements that have allowed us to get a handle on the size, structure, beginnings, and possible endings of our universe. Despite modern-day interest, measurements of distance in the universe were not foremost in the minds of the first astronomers. In ancient times, long before the development of geometry, the telescope, or modern systems of measure, astronomy was a tool used to predict food events like the ripening of local plants or the migration patterns of animals. A group might starve if they had no method of predicting the changes in the seasons. Consider, especially, cultures like that of the ancient Egyptians, whose entire economy depended on the annual flooding of the
Astronomical Games: June 2001 But that's a matter for another essay.). A partial step forward was made by thegreatest astronomer of antiquity, hipparchus of rhodes (c. 190120 BC). http://astro.isi.edu/games/kepler.html
Extractions: and ideas are the other. Victor Hugo, A SEMI-RECENT survey [ ] showed that about a quarter of American adults believe that the Sun goes around the Earth. You can imagine the uproar that rose up in educational institutions around the country. (Actually, it was pretty subdued, and if you were of a cynical bent, you could draw some pretty depressing conclusions about what higher education thinks of the American mandatory educational system. But let's not get into that.) How is it possible that so many Americans could believe such a thing? Well, they believe it for the same reason that the ancient Greeks and everyone else up to about the 16th century believed it. All you have to do is look up, and if you have the common sense God granted the garden snail, it is plain to see that the Sun goes around the Earth. After all, astronomers claim the Moon goes around the Earth, and no one laughs at them for that Granted, appearances were not all that mattered to the Greeks. They had their theory, too. Aristotelian physics held that the Earth was all that was base and ignoble, and it therefore sank to the very center of the universe. The celestial objects, howevereverything up in the skywere good and noble, and therefore light and airy, and they all travelled in great circular arcs around the lowly center, maintaining a cordial distance at all times.
Telescopes And Observatories Using these instruments, hipparchus at rhodes (150 BC) produced the first starcatalog, measured precession and developed the magnitude system of stellar http://zebu.uoregon.edu/~js/ast222/lectures/lec01.html
Extractions: Astronomical Instruments The elegant rings and bands of an armillary sphere (below) symbolize the astronomy of the past. The armillary sphere takes its name from the Latin armilla , meaning a bracelet or metal ring. With the Earth located at the center, the rings trace out what an observer sees in the night sky without a telescope. The outer band, that supports the device, shows the observers horizon and the meridian. Inside these bands is a cagelike assembly of rings that rotate to display the durinal motion of the stars. The zodiac is represented by a broad band marked with the 12 signs. Locating stars and measuring their positions precisely is no simple task. One of the earliest astronomical instruments is the quadrant, shown below, which measures a stars altitude above the horizon. A quadrant acquires its name by its ability to measure within a quarter circle. Using spherical trigonometry, the zenith distance could then be used to calculate a stars celestial longitude and latitude. Quadrants made of metal allowed finer intervals to be ruled for more precise measurements. The astrolabe was a sophisticated time-telling instrument of late antiquity. It was an all-in-one tool for calculating the position of the Sun (thus, local time) and various stars. The typical astrolabe has a rotating cutaway disk, called the rete, that represents the heavens as they revolve around us. Labeled points represent stars, the solid band is the zodiac. A plate, or tympan, is fixed beneath the rete and is inscribed with altitude and azimuth coordinates for the particular latitude where the astrolabe is used. Since the astrolabe displays the coordinates of various bright stars, it can also be used to determine the time at night when the Sun is not visible. Astrolabes were of particular interest to the ancient Muslim culture since it provided the direction to Mecca for daily prayers.
