How did Eratosthene first determine the size of the earth?
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Eratosthenes knew that on the summer solstice at local noon on the Tropic of Cancer, the Sun would appear at the zenith, directly overhead — though Syene was in fact slightly north of the tropic.\n\nHe also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 7° south of the zenith at the same time. Assuming that Alexandria was due north of Syene- Alexandria is in fact on a more westerly longitude- he concluded that the distance from Alexandria to Syene must be 7/360 of the total circumference of the Earth.\n\nThe distance between the cities was known from caravan travellings to be about 5,000 stadia.\n\nThere were some errors in this calculation although today we can use his method using correct measurements. Syene is not exactly on the Tropic of Cancer, and is not directly south of Alexandria; nor is the Sun at infinite distance. (Eratosthenes knew the latter, but we are not told he corrected for it.) More seriously, angles in antiquity could be measured only to degrees or quarter-degrees, and measurement of overland distances was worse. He established a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion he used is no longer known (the common Attic stadion was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The circumference of the Earth around the poles is now measured at around 40,008 km. Eratosthenes' method was used by Posidonius about 150 years later.
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Carpenters used to use the width of their thumb as a measurement of one inch.  That is where the phrase came from.
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Pythagoras (of Samos, born about 569-82 BC - died about 507 BC) was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it. \n\nIn any right triangle, the area of the square whose side is the hypotenuse (the long side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse, the adjacent and opposite in sine, cosine and tangent workings). \n\nIf we let c be the length of the hypotenuse and a and b be the lengths of the other two sides, the theorem can be expressed as the equation\n\nThis equation provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found.\n\nI was taught this in a long jumpo sand pit, with 25 billard balls.\nmy old teacher, Mr Chadwick, made a line of 5 balls, and this was the hypotenuse. he then drew in the rest of the triangle. he squared the 5 balls, by making a square of 5 by 5 balls, (25 in all).\n\nthen he put balls on the other lines. three fitted onto the short side, and four onto the next side. he then squared the two other sides. 3 x3 and 4 x 4 (9 and 16, when added together = 25. \n\nhe showed me that 27 years ago, It was amazing, and the reason I am now a teacher.
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ok here goes.  the technical scientific name for the shape of the earth which is generally accepted by the scientific community is\n\nOblaite Spheroid \n\nthe earth is not round nor is it flat or pure sphere \n\nit is an oblate spheroid.  however  if you were to either reduce the size of the earth to that of a billiard ball or alternatively increase the size of a billiard ball to that of the earth you would find that even for all its imperfections the earth is actually closer to a perfect sphere than anything man can make. also it would be much Smoother. the planet sized billiard ball would have mountain ranges 100's of times taller than our highest and valleys much lower than our lowest.  \n\nwhy things, i assume you mean cities and such, are not round is that a sphere or spheroid cannot be divided on the surface or otherwise by spheres or circles without intersecting them there would always be some space where the curves pull away from eachother.  you could put a smaller sphere in the empty space but that would only cause the spaces remaining to be smaller and more numerous down to infinity. unless you overlap the spheres /circles but then they arent circles anymore and it would be a waste of space.  \n\nthat all is assuming the world were in fact perfectly smooth which it isn't given things like topography geography and the like. shperes are not the most efficient shapes on earth.  at least not for all applications in fact they can sometimes be the least efficient. \n\nnow some places are and or were circularly built around a central point however usually this was not an economically/ financually/ geophisically  feasable option. again for reasons like coastlines rivers mountains etc.\n\nhope i answered your question withouth boring you to tears\n\nas for the bible saying the earth is flat that isnt true and he needs to read his bible more though he is correct the sun and the rest of the universe does revolve around the earth that at least i believe is biblical though i cant off the top of my head remember exactly where i think not in genesis though\n\nooh and rokon everything in the bible was written by GOD  the bible IS the UNERRANT WORD of GOD
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The largest known prime, as of September 2006, is 2^32,582,657 − 1 (this number is 9,808,358 digits long); it is the 44th known Mersenne prime. \n\nErastothenes didn't discover any particularly large primes but did invent the first sieve method for finding primes, now known as the Erastothenes sieve. He's better known for being the first person to calculate with reasonable accuracy the size of the Earth.
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It was Eratosthenes.  He measured the exact distance between Syene in southern Egypt and Alexandria. He measured the altitude of the noontime sun in both locations and found it was 0 degrees in Syene and 7 degress in Alexandria.  Using the difference in zenith angle and geometry, he could estimate the circumference of the earth.
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I feel the question should be what is the circumference of earth -\nIt is -\nThe average radius of the Earth is 3,959 miles (6,374 kilometers).\nThe equitorial diameter of the Earth (distance from one side of the Earth to the other at the equator) is about 7,926 miles.\n\nThe ratio of the circumference to the diameter of a circle (circumference/diameter) \nis written as the symbol pi. \nPi is approximately 3.141592.\n3.14159265\n3.1415926535\n\nTherefore, to determine the circumference from the diameter given above:\nequitorial diameter x 3.141592 = equitorial circumference\n| |\n7,926 x 3.141592 = 24,900\n| |\nThe earth has a circumference of approximately 24,900 miles.\n\n\nMore precisely the circumference of the earth (or distance around earth)\nat the equator is 24,902 mi / 40,076 km. \n\nso the answer is 24,902 miles or 40,076 kms.
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The Bible noted that the earth is a sphere and sits on "nothing" more than 2800 years ago. So Jesus did not have to restate the facts. Jesus did note that the Rapture would happen at the speed of light and that it would happen at the same time. Matthew 24:40-44 speak of the gathering of the church that will take place in one single event. Notice that there are three differnet periods of time, evening, morning, afternoon. This is only possible with a sperical earth with inhabitants in every hemisphere.\n\nIsaiah 40:22\nIt is [God] who sits* above the sphere** of the earth\n\nJob 26:7\nHe stretcheth out the north over the empty place, and hangeth the earth upon nothing.\n\nHow far has our sins been removed from us when we ask God to forgive us? Note the psalm below would make it finite if the circle of the earth were flat. If it is sperical with a pole, then east and west are directional with no end.\n\nPsalm 103:12\nAs far as the east is from the west, so far has He removed our transgressions from us.\n\nThe Hebrew record is the oldest, because Job is one of the oldest books in the Bible. Historians generally [wrongly] credit the Greeks with being the first to suggest a spherical earth. In the sixth century B.C., Pythagoras suggested a spherical earth.\n\nEratosthenes of Alexandria (circa 276 to 194 or 192 B.C.) calcuated the circumference of the earth "within 50 miles of the present estimate."\n\n__________________________________________________\n\n*Hebrew "yashab" - meaning dwells or inhabits. dwells above the circle of the earth - ie inhabits the heavens.\n\n**Hebrew "khoog" - meaning circle in 2 dimensions and sphere in 3 dimensions. Note: a flat disk wheel (owphan) or circle (cabiyb) are used elsewhere in scripture, but are not sphere (khoog).
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All the dimensions given in Plato's account of Atlantis are approximately 10 times the size of Crete.  Its distance from Egypt is about 10 times the distance of Crete, too, and the date of its destruction is 10 times longer ago than the volcanic eruption and tidal wave which probably destroyed Minoan Crete in 1500 BC.\n\nIt is very plausible that when Solon got this story from an Egyptian priest, he mistranslated the numbers, and Plato just copied them, which would have put Atlantis beyond the pillars of Hercules instead of just south of Greece.
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Most probably when He created the Heavens... The first day. Because i think the heavens includes its dwellers( at that point in time) too.
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history of PI~~\nthe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιμετρος (perimetros), meaning 'measure around' in Greek
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Before they had GPS, altimeters, and satellites to measure altitudes, they estimated the height of a mountain using trigonometry.  If the distance to the mountain can be estimated or determined, the height of the mountain can be calculated from the angle between looking straight and looking up at the top of the mountain.  \n\nThe link in sources gives an example.
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Ptolemy, Aristotles, Thales, Pythogoras and various others had at different times claimed that the earth was round for a varied number of reasons.\nArchimedes was the first one to physically prove that the Earth is round.
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Pluto, which was discovered in 1930, is but a dot of light in even the largest Earth-based telescopes. Pluto is 2/3 the size of Earth's moon but 1,200 times farther away, which makes viewing surface detail as difficult as trying to read the printing on a golf ball located thirty-three miles away.
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Here is a link of Eratosthenes experiment. You will understand it well looking at the drawing. In resume, he had to measure two shadows at the same time (obviously done with another person) in two distant places. He knew the angles and knew the distances between the points, so he could deduce the earths circumference.\nHis measurement gave a result between 36,700 and 46,900 kms, while the true circumference is  about 40,000 kms.\n\n\n---additin--\nForgot to paste the link, here it is\nhttp://www.juliantrubin.com/bigten/eratosthenes.html
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Before the birth of Christ there was records supporting the theory. The early Greeks and Romans wrote about the shape of earth. Like so much of the early learning's the words were ignored, misplaced, and ridiculed until the 1400's at which time early seaman of that century wrote about the earth being round and map makers drew it that way.
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Well as far as a formula i can't help you there. i just happen to own a program that allows me to draw perfect shapes of any size and diminsion them accordingly (auto CADD). and at the top of your 300 ft house, or where ever it is that your measuring from the horizon at sea level is a tad over 21 miles away (21.20389 to be analy exact). first you must know the the earths circumfrance (i know i can't spell) which is 20,890,637 ft, next you have to know the distance you are away from the earth (which you do, 300 ft). now you have to know the formula for finding a line that intersects your hieght and crosses tangentally across the earths surface. know you have your triangle and apply the Pythagorean theorem. you have an answer.