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BluePhyre · 05-15-2010, 05:54 PM

Quote:

Originally Posted by Antarctica!

OOC: As usual, the other posts have been noted. :>

"It is, but even here, maths is necessary. I would hate to think of what would happen to your potions if you did not measure correctly."

"Not so much the light or the view, but... Miss Force, do you know?" The girl had an almost frighteningly excited grin on her face. Risu pointed at her.

"That he did, but I was looking for an exact explanation as to how. Very well." Risu indicated the picture that the quietly humming projector had thrown against the wall behind him.

"The importance is this: Eratosthenes knew the distance compared to a full circle. Which is to say, seven degrees. But he needed a figure to compare those seven degrees against - and that is why he made someone measure the distance between Syene and Alexandria."

He turned back to the class. "To cut a long story short, the king's step counter estimated the distance to be about 5000 stadia, or 835 kilometres. So... seven degrees corresponded to 5000 stadia in Eratosthenes' time. I will spare you the calculations," he smiled thinly at the girl who had spoken up earlier, "but the end result of those calculations was a circumference of the Earth of about 230 thousand stadia."

"You explained it very well," Risu said with a nod. "That's exactly what he did. Now, depending on how long you take one stadium to be, you get greatly differing results. But if you take the value a stadium had in Egypt at that time, about 160 metres, Eratosthenes calculated the circumference of the Earth to an accuracy of only a few percent. Our best estimate today is a little more than 40,000 kilometres at the equator. Eratosthenes arrived at 41,700 kilometres."

He spread out his hands. "Very impressive for an ancient living more than 2000 years ago, and very impressive for someone who used nothing more than a stick, some observations and a tiny bit of maths. Now..." He flicked his wand, and the projector turned off. "We're nearly done, but what were some of the limitations of Eratosthenes' method?"

Phyre listened to the correct answers and sighed, raising her hand to try again. "If any calculations had gone wrong, the entire measurement could be off," she said shakily. "Furthermore, if he had used a different amount as a stadia, then he would have been wrong, and yet credited to this day to be extremely accurate, as accurate as one could be with the technology available at the time. Because of the differing measurement systems and opinions within the same measuring system, his method, while perfected by himself, would not be able to be used by many others of his time. While it's not a limitation on Eratosthenes himself, it would effect his method."

05-15-2010, 05:54 PM	#161 (permalink)
BluePhyre Doxy Join Date: Oct 2009 Location: The Dog Park Posts: 6,390 Hogwarts RPG Name: Casper Duluth III Fourth Year	Whoop!Phyre \|\| ❤LiliAnzaScarNatAmyEmi \|\| Professional Vigilante \|\| The Flying Tomato Quote: Originally Posted by Antarctica! OOC: As usual, the other posts have been noted. :> "It is, but even here, maths is necessary. I would hate to think of what would happen to your potions if you did not measure correctly." "Not so much the light or the view, but... Miss Force, do you know?" The girl had an almost frighteningly excited grin on her face. Risu pointed at her. "That he did, but I was looking for an exact explanation as to how. Very well." Risu indicated the picture that the quietly humming projector had thrown against the wall behind him. "The importance is this: Eratosthenes knew the distance compared to a full circle. Which is to say, seven degrees. But he needed a figure to compare those seven degrees against - and that is why he made someone measure the distance between Syene and Alexandria." He turned back to the class. "To cut a long story short, the king's step counter estimated the distance to be about 5000 stadia, or 835 kilometres. So... seven degrees corresponded to 5000 stadia in Eratosthenes' time. I will spare you the calculations," he smiled thinly at the girl who had spoken up earlier, "but the end result of those calculations was a circumference of the Earth of about 230 thousand stadia." "You explained it very well," Risu said with a nod. "That's exactly what he did. Now, depending on how long you take one stadium to be, you get greatly differing results. But if you take the value a stadium had in Egypt at that time, about 160 metres, Eratosthenes calculated the circumference of the Earth to an accuracy of only a few percent. Our best estimate today is a little more than 40,000 kilometres at the equator. Eratosthenes arrived at 41,700 kilometres." He spread out his hands. "Very impressive for an ancient living more than 2000 years ago, and very impressive for someone who used nothing more than a stick, some observations and a tiny bit of maths. Now..." He flicked his wand, and the projector turned off. "We're nearly done, but what were some of the limitations of Eratosthenes' method?" Phyre listened to the correct answers and sighed, raising her hand to try again. "If any calculations had gone wrong, the entire measurement could be off," she said shakily. "Furthermore, if he had used a different amount as a stadia, then he would have been wrong, and yet credited to this day to be extremely accurate, as accurate as one could be with the technology available at the time. Because of the differing measurement systems and opinions within the same measuring system, his method, while perfected by himself, would not be able to be used by many others of his time. While it's not a limitation on Eratosthenes himself, it would effect his method." __________________