81. Dyalog APL - Sieve Of Eratosthenes nvec ? .sieve nvec © Sieve of Eratosthenes © eratosthenes of cyrene (¯276¯194)Removes multiples of numbers within the argument vector. Thus sieve 2. http://www.dyalog.com/dfnsdws/n_sieve.htm

nvec „ #. sieve nvec © Sieve of Eratosthenes © Eratosthenes of Cyrene (¯276-¯194) Removes multiples of numbers within the argument vector. Thus sieve 2..¾ returns those primes in the range 2..¾. An illustration of most of the D-function con- structs: left argument defaulting; local definition; guards; tail recursion. Example: sieve 2 to 100 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 See also: to Back to: contents Back to: Dyalog APL Trouble seeing APL font

82. Expt. II-3 Measuring The Size Of The Earth eratosthenes of cyrene (273192BC) masterfully measured the size of the earth.Eratosthenes was born in Cyrene, the capital city of the region west of Egypt http://homepage.mac.com/dtrapp/ePhysics.f/labII_3.html

ie-Physics Experiment II-3 Measuring the Size of the Earth If Aristarchos was correct and the Earth did orbit the Sun, then there should be confirming evidence both here on Earth, and with careful observations of the sky. If the Earth moved, the motion would likely be felt. If the Earth moved the motion would likely cause strong prevailing winds from the direction of motion. But more fundamentally, if the Sun occupied the center position and the Earth orbited the Sun, then the angle between neighboring stars along the ecliptic should change with the seasons. When the Earth was closer to the stars the angle should be larger, but when the Earth orbited farther from the stars the angle between the stars should decrease. The lack of any such observable parallax , the lack of any prevailing winds, and the lack of any other evidence of earth motion led the Greeks to reject Aristarchos' proposal that the Earth orbited the Sun. Eratosthenes of Cyrene (273-192BC) masterfully measured the size of the earth. Eratosthenes was born in Cyrene, the capital city of the region west of Egypt. He was educated in Athens, which was still the educational and philosophical center of the Mediterranean despite the rise of the Roman empire. After distinguishing himself academically, he was recruited by the Ptolemaios to tutor a prince in Alexandria, Egypt. Ten years later he became the chief librarian of the Museum of Alexandria, a job that went beyond supervising the vast collections to include leading for four decades the extensive scientific research sponsored by that institution. While he excelled in many areas, Eratosthenes became one of the greatest geographers of all ages by establishing the mathematical geography of the spherical earth.

83. Eratosthenes eratosthenes was born in cyrene which is now in Libya in North Africa. His teachersincluded the scholar Lysanias of cyrene and the philosopher Ariston of http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Eratosthenes.html

84. Erastosthenes Where were you born, eratosthenes? A I was born in cyrene, which is also wherethis interview is taking place. Q How did you get into mathematics? http://www.3villagecsd.k12.ny.us/wmhs/Departments/Math/OBrien/eros2.html

Erastosthenes Cyrene 215 B.C. Q (me, the interviewer): Greetings WM Times readers! We are pleased to present to you an exclusive interview with the now-legendary mathematician, Eratosthenes, who has developed a method for measuring the earths' circumference through math, without traveling around the world in order to do so. In fact, only a fraction of travel was required. It's great to have this exclusive interview, Eratosthenes! A (Eratosthenes): I am glad to be here. I believe this to be a great discovery and am anxious to share it with the scientific community, as well as the world! Q: Nice to hear that. First, let us start off with a little background information. Where were you born, Eratosthenes? A: I was born in Cyrene, which is also where this interview is taking place. Q: How did you get into mathematics? A: I became very interested in mathematics growing up, and met a friend that soon became my mentor, Archimedes. Challenging my intelligence, he would send me math problems on a regular basis for me to solve. He would later send the solution so I could compare with my own. My intellectual strength grew quickly. Q: Amazing! Any early accomplishments?

85. Eratosthenes--Biography eratosthenes. of cyrene (276194 Bc). eratosthenes . biography . historicalsetting . discovery . reference and links . Math History http://www.albertson.edu/math/History/emacy/Classical/biography.htm

ACI Math Department Eratosthenes of Cyrene (276-194 B.c.) Eratosthenes historical setting discovery reference and links ... Math History Biographical Information Eratosthenes was born in what is now Shahhat, Libya in 276 BC. He learned from a variety of teachers, including Lysanias of Cyrene, Ariston of Chios, and Callimachus of Cyrene. These teachers gave him a wide background of study, from philosophy to poetry to mathematics to astronomy. His discoveries and contributions to mathematics show this diversity as well. After spending a few years studying in Athens, after which he traveled to Alexandria to tutor the son of Ptolemy III Euergetes. When his teacher Callimachus passed away, Eratosthenes took over his job as the librarian at Alexandria. This library was the best of the time, and his appointment to the job was a great honor for Eratosthenes. He held the position until his death in 194 BC. Although Eratosthenes showed great ingenuity and intelligence in his studies, he is not known as one of the elite mathematicians of his time. Much of this is due to the fact that he studied so many subjects that he did not finish many proofs or make significant breakthroughs. His work, however, formed the basis for many scholars who followed him and used his work to achieve greatness.

86. Eratosthenes eratosthenes was born in cyrene, Greece, which is now known as Libya, in SouthAfrica, in 276 BCE It is believed that he starved himself to death in 195 BCE http://www.math.wichita.edu/history/men/eratosthenes.html

Eratosthenes 276-195 B.C.E. It can be said that Eratosthenes is most widely known as a famous Greek mathematician. What most people probably do not know is that Eratosthenes is not only a famous mathematician but also a well known geographer, astronomer and historian. Before I get into a few of his accomplishments, let me tell you a little about his personal history. Eratosthenes was born in Cyrene, Greece, which is now known as Libya, in South Africa, in 276 B.C.E.. It is believed that he starved himself to death in 195 B.C.E. due to the fact that he became blind and could no longer work. As a young man, Eratosthenes studied in Athens. Eventually, he made such a name for himself in his many fields that he caught the attention of the ruler of Egypt, Ptolemy III. Ptolemy III invited Eratosthenes to Alexandria, Egypt for two reasons; to tutor his son and to be the librarian for the great Alexandrian University. Eratosthenes jumped at the chance. At the University, he was able to at most interested him and associate with other scholars. Now on to his accomplishments. . . One of his major accomplishments in mathematics is his creation of a sieve that determines prime numbers up to any given limit. This sieve, which is called, the Sieve of Eratosthenes, is still important today in number research theory. Prime numbers are natural numbers greater than 1 that can be divided without remainder only by itself and by 1. Eratosthenes figured out that if you were to write down all the natural numbers from 2 to infinity and "sieve out" every second number after two (or multiples of two), then move to the next available number (3) and continue to "sieve out" every multiple of 3 and so on, one would end up with a list of prime numbers.

87. BBC - History - Eratosthenes (c.276 BC - C.194 BC) eratosthenes was born in cyrene on the north coast of Africa but educated inAthens, and came to Egypt in his thirties. He was a contemporary of Archimedes, http://www.bbc.co.uk/history/historic_figures/eratosthenes.shtml

@import url('/includes/tbenh.css') ; Home TV Radio Talk ... A-Z Index THURSDAY 1st September 2005 Text only BBC Homepage History Homepage Topics Ancient Resources Interactive Content Reading Room Timelines Historic Figures ... History for Kids Practical History Archaeology Family History History Trails Community Messageboard Newsletter About This Site About the BBC ... Help Like this page? Send it to a friend! Eratosthenes (c.276 BC - c.194 BC) Eratosthenes was born in Cyrene on the north coast of Africa but educated in Athens, and came to Egypt in his thirties. He was a contemporary of Archimedes, who would send him mathematical problems to solve, sending the solutions later in case of difficulties. Eratosthenes was a skilled geographer, astronomer, poet and literary critic. He drew a map of the world as it was then known and calculated the angle of tilt of the earth in space. For forty years he served as a librarian at the famous library of Alexandria, and as a renowned mathematician, he invented a way of finding prime numbers, known as the Sieve of Eratosthenes. Possibly his greatest feat, however, was to measure the size of the Earth. Therefore, if he could measure the distance between the two cities, he could estimate the size of the earth. Luckily he had the use of the Royal Pacers; soldiers trained to pace precisely the same distance in each stride. Counting their strides, he was able to measure the distance between the two cities, approximately 500 miles. As a result he calculated that the circumference of the Earth was 51 multiplied by 500, or 25 500 miles, accurate to within about one per cent of the true figure.

88. Eratosthenes: Definition And Much More From Answers.com eratosthenes (er?tos th?nez) , c.275–c.195 BC, Greek scholar, b. cyrene. A pupilof Callimachus in Athens, he became (c.240 BC) head of the library at http://www.answers.com/topic/eratosthenes

showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Dictionary Encyclopedia WordNet Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Eratosthenes Dictionary E·ra·tos·the·nes ĕr ə-tŏs thə-nēz , Third century B.C. Greek mathematician, astronomer, and geographer who devised a map of the world, estimated the circumference of the earth and the distance to the moon and the sun, and constructed a method for finding prime numbers. Encyclopedia Eratosthenes ĕrətŏs thənēz ) , c.275–c.195 B.C. , Greek scholar, b. Cyrene. A pupil of Callimachus in Athens, he became (c.240 B.C. ) head of the library at Alexandria. Known for his versatility, he wrote poetry and works (most of them lost) on literature, the theater (notably on ancient comedy), mathematics, astronomy, geography, and philosophy; he also drew a map of the known world and evolved a system of chronology. Especially noted as an astronomer, he is credited with measuring the circumference and tilt of the earth and the size and distance from the earth of the sun and the moon. WordNet Note: click on a word meaning below to see its connections and related words.

89. Eratosthenes Van Cyrene eratosthenes (276194 vC) van cyrene was de derde bibliothecaris van Alexandriësbibliotheek. Hij volgde Callimachus, een van zijn leraren, op. http://mediatheek.thinkquest.nl/~lla015/biografie/Eratosthenes.html

Eratosthenes van Cyrene Nadat hij blind werd, pleegde hij zelfmoord door zichzelf dood te hongeren.

90. Eratosthenes He was born circa 276 BC, in the Greek colony of cyrene, North Africa (now Shahhat, eratosthenes also studied under the poet and scholar Callimachus, http://www.grecoreport.com/eratosthenes.htm

Eratosthenes Eratosthenes, a Greek astronomer, mathematician, geographer, scientific writer and poet made a surprisingly accurate estimate of the earth's circumference. He was born [circa] 276 B.C., in the Greek colony of Cyrene, North Africa (now Shahhat, Libya). His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios, who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus, also born in Cyrene. Eratosthenes went on to study in Athens and later settled in Alexandria, Egypt, where he became the director of the Library of Alexandria. In the great Library of Alexandria,* he read that a deep vertical well near Syene (now Aswan), in southern Egypt, was entirely lit up by the sun at noon, once a year (June 21st) [the summer solstice. ed.]. Eratosthenes reasoned that, at this time, the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day, because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth by making two assumptionsthat the earth is round and that the sun's rays are essentially parallel. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equaled the size of the angle at the earth's center between Syene and Alexandria. Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. His result, 250,000 stadia (about 46,250 km) is quite close to modern measurements. [He later altered this figure to 252,000 stadia. ed.]. The formula Eratosthenes used is: D/d =A/a. Where d = distance between Syene and Alexandria, A = 360 degrees assumption of round earth, a = shadow angle of vertical stick, D = to be determined (circumference).

91. Astronomy Throughout History cyrene (now Shahhat, Libya). eratosthenes measures the circumference of the earth eratosthenes. cyrene (now Shahhat, Libya). 276197 BC. Galileo Galilei http://web.haystack.mit.edu/pcr/documents/astronomyhistory.htm

Astronomy throughout History The study of planets, stars, galaxies, and intergalactic and interstellar space falls under the field of astronomy. Thousands of years ago, the earliest civilizations observed the heavens. Because astronomers of the past set the foundation for today's astronomy, it is an interesting journey to take a look through the history of astronomy. How did they figure out how big around the Earth is? Who was the first astronomer to recognize galaxies outside our own? What must've it been like to look through Galileo's first telescope to see the craters on the Moon? Were people stunned when Halley correctly predicted the return of a comet? Archeoastronomy is different than looking at the history of astronomy. It sets to find out just how astronomy fit into a certain culture's life. Were women ever allowed or encouraged to be astronomers in ancient times? Did the builders of Stonehenge incorporate into its structure an eclipse prediction system? How did the Mayan calculate the length of a year with such accuracy without a computer? This section will take you on a journey through time, across the continents and into the lives of people from all times and places. It will touch on the history of astronomy, archeoastronomy and more. Please choose which way you would like to begin your journey:

92. No. 1457: Eratosthene's Diameter Of Earth eratosthenes s 2200 year old calculation of Earth s size. eratosthenes realizedhe could measure the shadow cast by a tower in Alexandria while no http://www.uh.edu/engines/epi1457.htm

No. 1457: ERATOSTHENES'S DIAMETER OF EARTH by John H. Lienhard Click here for audio of Episode 1457. Today, we measure the earth. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. T he Discoverers, Daniel Boorstin's monumental book on human curiosity, tells about the complex task of figuring out the form of our planet. His chapter The Geography of the Imagination helps us understand how slowly Earth revealed itself to us. Two complex ideas, the wheel and the globe, are grooved into our minds from infancy. It was only 5500 years ago that we finally saw how a rotating wheel could produce forward motion. Recognizing that Earth's apparently flat surface bends into the shape of a sphere was even more recent. Some cultures imagined Earth as a disc, some, box-shaped. The Egyptians said it was an egg, guarded at night by the moon. Only 2500 years ago, the Greeks finally decided Earth was a sphere. Plato argued that, since the sphere is a perfect shape, Earth must be spherical. Aristotle used observation. He pointed to the circular shadow Earth casts on the moon during an eclipse.

93. Student Help us to achier our projecy.master project of hellinstic period of Eratosthenesof cyrene (276194b.c(mathematician.goographer.astronomer.poets.so we faced http://www.chiark.greenend.org.uk/pipermail/adns-bugreports/2004/002739.html

student help adel orfi adelorfi at yahoo.com Sat, 31 Jan 2004 02:34:43 -0800 (PST) Previous message: Mail delivery failed: returning message to sender Next message: Returned due to virus; was: Test Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... http://pa.yahoo.com/*http://us.rd.yahoo.com/evt=21260/*http://photos.yahoo.com" Previous message: Mail delivery failed: returning message to sender Next message: Returned due to virus; was: Test Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

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