April 20, 2008 01:07AM
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Registered: 18 years ago
Posts: 933
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Sqrt 3 comes up in the slope of an equilateral triangle. For example, the profile of the core pyramid inside the Bent pyramid is thought to be close to 60*, i.e., its profile is an equilateral triangle. What is not known is whether its slope was 7:4 or 12:7. It is very difficult to tell these two slopes apart. A 7:4 slope is 60* 15', while a 12:7 slope is 59* 45'.
These two values for sqrt 3 could easily have been discovered by measuring the length of the sides of an equilateral triangle. It would have been found that an equilateral triangle with a height of one cubit would have sides of 12 palms, while an equilateral triangle with sides of one cubit would have a height of 4 palms.
It can also be easily established that 7/4 is slightly greater than sqrt 3, while 12/7 is slightly less than sqrt 3, by a similar amount. Thus, to get a very close approximation to sqrt 3, one would simply take the average of 7/4 and 12/7, and this will give you 97/56. (This is basically an application of Hero of Alexandria's method for generating square roots, discovered in the first century CE.)
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Jim Alison |
April 17, 2008 09:03PM |
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Clive |
April 17, 2008 10:09PM |
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Jim Alison |
April 19, 2008 12:12AM |
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Clive |
April 20, 2008 09:14PM |
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Kanga |
April 20, 2008 09:41PM |
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Clive |
April 23, 2008 07:34PM |
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Kanga |
April 23, 2008 07:58PM |
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Clive |
April 23, 2008 09:29PM |
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Kanga |
April 24, 2008 12:36AM |
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Clive |
April 24, 2008 09:34AM |
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Jon_B |
April 24, 2008 11:59AM |
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L Cooper |
April 24, 2008 02:35PM |
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Jon_B |
April 24, 2008 02:59PM |
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L Cooper |
April 24, 2008 04:37PM |
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Clive |
April 24, 2008 04:12PM |
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Jon_B |
April 25, 2008 02:34PM |
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Clive |
April 25, 2008 07:51PM |
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Jon_B |
April 26, 2008 04:40AM |
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Clive |
April 26, 2008 03:30PM |
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Jon_B |
April 27, 2008 04:45AM |
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Clive |
April 28, 2008 05:26PM |
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L Cooper |
April 27, 2008 09:57AM |
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Jon_B |
April 28, 2008 11:55AM |
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Clive |
April 28, 2008 04:45PM |
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Kanga |
April 28, 2008 08:59PM |
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Clive |
April 28, 2008 09:52PM |
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Kanga |
April 29, 2008 12:18AM |
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Clive |
April 29, 2008 01:07PM |
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fmetrol |
April 18, 2008 04:35AM |
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Dave L |
April 18, 2008 05:39AM |
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L Cooper |
April 18, 2008 06:51AM |
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Dave L |
April 18, 2008 07:05AM |
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L Cooper |
April 18, 2008 08:36AM |
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Dave L |
April 18, 2008 10:03AM |
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Hermione |
April 18, 2008 10:16AM |
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Dave L |
April 18, 2008 10:22AM |
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L Cooper |
April 18, 2008 11:38AM |
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Dave L |
April 18, 2008 12:34PM |
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Graham Chase |
April 19, 2008 04:57AM |
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Graham Chase |
April 19, 2008 05:05AM |
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Jim Alison |
April 19, 2008 08:39AM |
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Graham Chase |
April 19, 2008 10:24AM |
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Jim Alison |
April 19, 2008 01:10PM |
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Graham Chase |
April 20, 2008 02:37AM |
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Kanga |
April 19, 2008 10:30AM |
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Dave L |
April 19, 2008 11:24AM |
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Graham Chase |
April 20, 2008 02:55AM |
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Graham Chase |
April 21, 2008 01:28PM |
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Dave L |
April 21, 2008 01:53PM |
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Graham Chase |
April 21, 2008 03:32PM |
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Dave L |
April 21, 2008 04:13PM |
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Jim Alison |
April 21, 2008 07:02PM |
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Graham Chase |
April 22, 2008 01:54AM |
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Jim Alison |
April 22, 2008 08:03AM |
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Graham Chase |
April 22, 2008 08:56AM |
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Dave L |
April 22, 2008 04:35AM |
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Graham Chase |
April 22, 2008 05:28AM |
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Dave L |
April 22, 2008 07:04AM |
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Graham Chase |
April 22, 2008 07:51AM |
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Dave L |
April 22, 2008 08:51AM |
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Graham Chase |
April 22, 2008 09:16AM |
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Dave L |
April 22, 2008 10:04AM |
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Sirfiroth |
April 19, 2008 10:17PM |
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fmetrol |
April 20, 2008 12:09AM |
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Kanga |
April 20, 2008 01:07AM |
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Kanga |
April 20, 2008 03:40AM |
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MJ Thomas |
April 20, 2008 01:55AM |
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Kanga |
April 20, 2008 04:00AM |
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L Cooper |
April 20, 2008 09:04AM |
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Kanga |
April 20, 2008 06:40PM |
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L Cooper |
April 21, 2008 06:51AM |
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Kanga |
April 21, 2008 08:03AM |
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John Legon |
April 21, 2008 09:41AM |
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L Cooper |
April 22, 2008 06:08AM |
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Jim Alison |
April 22, 2008 07:46AM |
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Graham Chase |
April 22, 2008 08:04AM |
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John Legon |
April 22, 2008 10:34AM |
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MJ Thomas |
April 20, 2008 04:58PM |
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Kanga |
April 20, 2008 07:00PM |
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MJ Thomas |
April 22, 2008 01:06AM |
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Kanga |
April 22, 2008 01:48AM |
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Dave L |
April 20, 2008 05:13AM |
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L Cooper |
April 20, 2008 11:17AM |
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fmetrol |
April 20, 2008 02:17PM |
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Sirfiroth |
April 21, 2008 12:10AM |
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fmetrol |
April 21, 2008 02:34AM |
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lobo-hotei |
April 20, 2008 04:38PM |
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MJ Thomas |
April 20, 2008 05:10PM |
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C Wayne Taylor |
April 20, 2008 05:47AM |
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C Wayne Taylor |
April 22, 2008 05:53AM |
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C Wayne Taylor |
April 22, 2008 07:05AM |
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Hermione |
April 22, 2008 07:10AM |
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C Wayne Taylor |
April 22, 2008 07:41AM |
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C Wayne Taylor |
April 22, 2008 08:20AM |
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C Wayne Taylor |
April 21, 2008 08:32AM |
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poundr17 |
April 23, 2008 08:45AM |
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Jim Alison |
April 22, 2008 10:51PM |
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Kanga |
April 23, 2008 12:25AM |
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fmetrol |
April 23, 2008 03:56AM |
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Jim Alison |
April 23, 2008 08:09AM |
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John Legon |
April 23, 2008 04:10AM |
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Jim Alison |
April 23, 2008 08:18AM |
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L Cooper |
April 23, 2008 01:23PM |
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Clive |
April 24, 2008 04:15PM |
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L Cooper |
April 25, 2008 07:30AM |
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Warwick L Nixon |
April 25, 2008 10:06AM |
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MJ Thomas |
April 25, 2008 02:24PM |
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Clive |
April 25, 2008 01:19PM |
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MJ Thomas |
April 25, 2008 03:50PM |
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stargazer |
April 25, 2008 06:59PM |
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MJ Thomas |
April 25, 2008 07:40PM |
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fmetrol |
April 25, 2008 09:25PM |
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Jim Alison |
April 26, 2008 01:33AM |
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stargazer |
April 26, 2008 08:40AM |
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Clive |
April 26, 2008 06:50AM |
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fmetrol |
April 26, 2008 07:40AM |
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Clive |
April 26, 2008 12:04PM |
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fmetrol |
April 26, 2008 12:34PM |
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Clive |
April 26, 2008 01:40PM |
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fmetrol |
April 26, 2008 01:46PM |
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Clive |
April 26, 2008 10:01PM |
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fmetrol |
April 27, 2008 03:59AM |
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MJ Thomas |
April 26, 2008 09:49AM |
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fmetrol |
April 26, 2008 10:19AM |
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MJ Thomas |
April 26, 2008 10:52AM |
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fmetrol |
April 26, 2008 11:45AM |
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Chris Tedder |
April 26, 2008 10:55AM |
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fmetrol |
April 26, 2008 12:01PM |
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fmetrol |
April 26, 2008 12:30PM |
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MJ Thomas |
April 26, 2008 12:36PM |
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fmetrol |
April 26, 2008 12:41PM |
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fmetrol |
April 26, 2008 12:57PM |
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stargazer |
April 26, 2008 01:23AM |
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MJ Thomas |
April 26, 2008 09:14AM |
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stargazer |
April 26, 2008 09:28AM |
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MJ Thomas |
April 26, 2008 10:17AM |
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stargazer |
April 26, 2008 10:37AM |
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MJ Thomas |
April 26, 2008 11:08AM |
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stargazer |
April 26, 2008 07:36PM |
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Clive |
April 26, 2008 06:34AM |
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MJ Thomas |
April 26, 2008 10:03AM |
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Clive |
April 26, 2008 01:50PM |
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Hermione |
April 26, 2008 01:59PM |
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Clive |
April 26, 2008 10:07PM |
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Hermione |
April 27, 2008 08:26AM |
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Jon_B |
April 27, 2008 10:03AM |
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Clive |
April 28, 2008 06:24PM |
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MJ Thomas |
April 26, 2008 05:24PM |
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Clive |
April 26, 2008 09:56PM |
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MJ Thomas |
April 27, 2008 07:09AM |
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Clive |
April 25, 2008 08:46PM |
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MJ Thomas |
April 26, 2008 09:29AM |
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Warwick L Nixon |
April 26, 2008 11:08AM |
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Clive |
April 26, 2008 02:07PM |
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Warwick L Nixon |
April 28, 2008 11:25AM |