# Eratosten english

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20-Jun-2015Category

## Education

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### Transcript of Eratosten english

- 1. FOLLOWING IN THE FOOTSTEPS OF ERATOSTHENES Measuring the circumference ofMeasuring the circumference of EarthEarth Slavoljub Miti, teacher Primary School Bubanjski heroji Ni, Srbija

2. ERATOSTHENES 276 BC - 194 BC Greek mathematician, geographer,Greek mathematician, geographer, astronomerastronomer He lived in AlexandriaHe lived in Alexandria devised a simple way to measure thedevised a simple way to measure the circumference of the Earthcircumference of the Earth 3. In Egypt, about 2200 years ago, a papyrus drew attention of a certain Eratosthenes, then Director of the Great Library of Alexandria (a town located on the side of the Mediterranean Sea): it was about a vertical stick which, on the first day of summer (that is to say on June the 21st) and at noon local solar time, did not cast any shadow on the ground (the Sun's rays reach the bottom of a well!). This happened very far from Alexandria, straight to the South, in a town called Syene (now Aswan). However, Eratosthenes noticed from his side that in Alexandria, on June the 21rst also and at the same time, a stick vertically driven in the ground did cast a shadow, even if such a shadow was relatively short. What the hell was this mystery? We invite you to discover it by yourselves. This will lead you pretty far since, as Eratosthenes showed, the key of this mystery will allow you to measure the circumference of the Earth, nothing less! This text give to your studentsThis text give to your students 4. at noon Syene (now Aswan) - the Sun in vertical to the ground - in zenith, and the sun rays come to the bottom of the well, while the shadows of the vertical objects are only around them - the vertical objects do not cast the shadow Alexandria - the Sun is not in the vertical position and the objects cast a very short shadow 5. SyeneAlexandria 6. Why do the length of the shadowsWhy do the length of the shadows different, or why is it a shadow in onedifferent, or why is it a shadow in one case and not in the other?case and not in the other? 7. Eratosthenes used these starting hypotheses :Eratosthenes used these starting hypotheses : the Earth is flat the Sun should be close so the objects of the same height have shadows of different length 1 2 3 8. The Earth is not flat, but has a curved the Sun is far so the Sun rays are parallel while coming to the Earth 1 2 3 Eratosthenes used these starting hypotheses :Eratosthenes used these starting hypotheses : 9. Eratosthenes accepted the second hypothesis:Eratosthenes accepted the second hypothesis: 1 2 3 The Earth is not flat, but it is curved the Sun is far a way so the Sun rays are parallel while coming to the Earth 10. Eratosthenes measured the length of the obelisks shadow, whose height he had known before. According to the length of the shadow and height of the obelisk he calculated the angle which Sun rays form with the vertical. The value of the angle is 7,20 11. Starting from the hypothesis that the Earth is spherical, he draw a picture which can help him to calculate easily the circumference of the Earth. Alexandria Syene 12. The extensions of the verticals in Alexandria (the obelisk) and in Syena (the well) intersect in the centre of the Earth . The angle they form in the Earths centre is equal to the angle which Eratosthenes measured with the shadow of the obelisk in Alexandria 7,20 Alexandria Syene 13. angle 3600 angle of the full circle 50 2,7 360 0 0 = the distance between Syena and Alexandria 800km the length of the circular curve corresponding to the angle of 7,20 kmkm 4000050*800 = circumference of the Earth shadow = 7,20 d=800km 14. The Project Eratosthenes 2200 years later 15. The task To measure the Earth meridian in the same way Eratosthenes did that 2200 years ago 16. How to do it? Determine the local midday - at what time it is the noon in our town - at what time the Sun is in its zenith. Measure the length of the shadow of vertical object at noon. In cooperation with some other remote school calculate the circumference and the diameter of the Earth. 17. the noon is the moment when the Sun reaches the highest point in the sky How to determine the real solar midday? the shadow turns around and changes the length depending on the hour of a day 18. How to determine the real solar midday? plant a stick into the ground and adjust it vertically by a plumbline or a level; 19. late in the morning start measuring the length of the shadows; being close to the noon, the shadow will be shorter and after the noon it will become longer and longer; the shortest measured length will be the shadow at noon; How to determine the real solar midday? 20. (Nish) latitude 430 32 longitude 220 30 21. the direction of the shortest shadow can be determined by a compass - in the relation to the bottom of the stick determine the direction to the North 22. Constructing and application (usage) of the sundial - gnomon: Material: stick or a rod of 1 metre length; a pedestal (a base); a level, a protractor, a compass 23. at noon - measure the length of vertical objects shadow according to the length of the shadow and the height of the sundial (gnomon) determine the value of the angle on a graph paper draw a minimized picture of gnomon and a shadow connect the ends - you will get a right angle triangle that measure the angle by a protractor; Procedure: 24. to determine the value of the angle you can use these web sites http://perbosc.eratosnoon.free.fr/spip.php?article191 http://isheyevo.ens- lyon.fr/eaae/groupspace/eratosthene/help-for- calculations/angle-of-the-sun/ 25. in cooperation with same other remote school calculate the circumference and the diameter of the Earth point A - the school is northwards (to the north) point B - the school is southwards (to the south) angle 1 - the angle measured at school which is in northwards angle 2 - the angle measured at school which is in southwards the angle which is necessary for calculation = 1 - 2 1 2 2 1 BB 26. if the school - partner in the project is situated in the southern hemisphere the angles are added = 1 + 2 1 2 2 1 27. d distance between point and from north to south that the results were more accurate distance should be as higher - at least 3 or 4 degrees of latitude THE DISTANCE BETWEEN THE TOWNS The schools are at the same meridian The schools are not at the same meridian 28. the distance between the towns: two schools are probably not at the same meridian, you should determine the shortest distance between the parallels that go through the towns in which two schools are situated 29. according to the latitudes of the schools, determine the distance in a geographic map or write latitudes in the appropriate fields on these web sites and read the value of the distance http://perbosc.eratosnoon.free.fr/spip.php?article187 http://isheyevo.ens- lyon.fr/eaae/groupspace/eratosthene/help-for- calculations/distance/ 30. http://perbosc.eratosnoon.free.fr/spip.php?article187 http://isheyevo.ens- lyon.fr/eaae/groupspace/eratosthene/help-for- calculations/distance/ write latitudes in the appropriate fields on these web sites and read the value of the distance 31. dO O d 0 0 360 360 = = 2 2 O R RO = = The calculation:The calculation: d - the distance between two towns; O - the circumference of the Earth; - the calculated angle; R - the radius of the Earth. 32. The final measuring at all schoolsThe final measuring at all schools June 21st, at noonJune 21st, at noon Registration is open until the end of DecemberRegistration is open until the end of December 33. http://lamap.inrp.fr/eratos information and instructionsinformation and instructions http://rukautestu.vin.bg.ac.rs//eratosten http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene http://perbosc.eratosnoon.free.fr/ 34. (Nish) (latitude) 430 32 (longitude) 220 30 smitic61@ptt.rssmitic61@ptt.rs fizikazaosnovce678.wordpress.comfizikazaosnovce678.wordpress.com Site of the organization of primary school teachers of physics Nis District: aktivfizicara.wordpress.com