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Posted 09 July 2001 - 03:13 AM
Posted 09 July 2001 - 03:43 AM
Posted 09 July 2001 - 03:44 AM
Posted 09 July 2001 - 04:05 AM
Posted 09 July 2001 - 08:43 PM
Posted 10 July 2001 - 05:19 AM
Posted 11 July 2001 - 02:06 PM
Posted 11 July 2001 - 03:10 PM
Posted 11 July 2001 - 03:26 PM
Posted 11 July 2001 - 03:33 PM
quote:
Original post by Dean Harding
Why did they choose 360 degrees for a complete circle? Does anyone know?
Posted 11 July 2001 - 03:43 PM
Posted 11 July 2001 - 09:45 PM
Posted 12 July 2001 - 03:56 AM
Posted 12 July 2001 - 02:38 PM
quote:
Original post by grhodes_at_work
Radians really do exist, as Beer Hunter said, because of the Taylor series expansions. These particular expansions are called the Maclaurin expansions:
Posted 12 July 2001 - 03:40 PM
quote:
Original post by Timkin
[quote]Original post by grhodes_at_work
Radians really do exist, as Beer Hunter said, because of the Taylor series expansions. These particular expansions are called the Maclaurin expansions:
quote:
Original post by Timkin
...on a similar vein. While it is widely believed that Hipparchus was the founder of trigonometry in the 2nd century BC, it is more than likely that he, like Pythagorus, got his information from more ancient texts (scrolls). As some circumstantial evidence, if you measure the distance around the base of the great pyramid (Pyramid of Khafra) and divide it by its height, you get a number that matches 2*pi to several decimal places. If you perform the same calculation for the Pyramid of the Sun in South America (Tiahanucan (sp?) I think) you get 4*pi. I also seem to recall that the angle subtended by an edge of the Great Pyramid with the base is equal to the unit angle (1 radian). These pyramids were purposefully built to encapsulate these numbers. It is structurally more difficult to build a square based pyramid with these properties than it is to build a uniform sqare based pyramid (45 degree sides).
Posted 12 July 2001 - 03:41 PM
quote:
Original post by Timkin
Radians don''t exist ''because'' of the power series approximation, but rather the power series approximation is possible because of the nature of the radian measure.
It is certainly the case the the unit angle was used long before it was called a radian and long before a Maclaurin series was used to approximate trigonmetric functions of functions of unit angles.
quote:
Original post by Timkin
...on a similar vein. While it is widely believed that Hipparchus was the founder of trigonometry in the 2nd century BC, it is more than likely that he, like Pythagorus, got his information from more ancient texts (scrolls). As some circumstantial evidence, if you measure the distance around the base of the great pyramid (Pyramid of Khafra) and divide it by its height, you get a number that matches 2*pi to several decimal places. If you perform the same calculation for the Pyramid of the Sun in South America (Tiahanucan (sp?) I think) you get 4*pi. I also seem to recall that the angle subtended by an edge of the Great Pyramid with the base is equal to the unit angle (1 radian). These pyramids were purposefully built to encapsulate these numbers. It is structurally more difficult to build a square based pyramid with these properties than it is to build a uniform sqare based pyramid (45 degree sides).
Posted 12 July 2001 - 03:54 PM
quote:
Original post by Timkin
The ''Grooved Ware'' people used (some 5000-10000 years ago) a system of measurement for time, distance and angle that were all based on the same base number set that had 366 ''degrees'' in a full circle, 60 ''minutes'' per ''degree'' and 6 ''seconds'' per ''minute''. Of course, these ''degrees'', ''minutes'' and ''seconds'' were not of the same length as the ones we use, hence the quotes to indicate this.
Posted 12 July 2001 - 08:48 PM
quote:
Original post by grhodes_at_work
Lets not get into an argument about how old the pyramids in Egypt are, though!
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