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| Simple v complex depends on the level of understanding http://www.envirolink.org/forum/viewtopic.php?f=8&t=2678 |
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| Author: | Wayne Stollings [ Wed May 31, 2006 6:24 pm ] |
| Post subject: | Simple v complex depends on the level of understanding |
Engineering Procedure Engineering Procedure from an unknown but astute source: Every new engineer must learn early that is it never good taste to designate the sum of two quantities in the form: 1 + 1 = 2 (1) Anyone who has made a study of advanced mathematics is aware that: 1 = ln e and that: 1 = sin2 x + cos2 x further: 2 = n=0Σn=¥ (1/2n) Therefore, Eq. (1) can be expressed more scientifically as: ln e + (sin2 x + cos2 x) = n=0Σn=¥ (1/2n) (2) This may be further simplified by the use of the relations: 1 = cosh y √ (1-tanh2 y) and e = lim z-¥ (I + 1/z)z Equation (2) may therefore be rewritten: ln [lim z-¥ (I + 1/z)z] + (sin2 x + cos2 x) = n=0Σn=¥ (cosh y √ (1-tanh2 y)/ 2n) (3) At this point, it should be obvious that Eq, (3) is much clearer and more easily understood than Eq. (1). They are the same thing! Other methods of a similar nature could be used to clarify Eq. (1) but - these are easily discovered once the reader grasps the underlying principles. |
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| Author: | Grace [ Wed May 31, 2006 7:39 pm ] |
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| Author: | Wayne Stollings [ Wed May 31, 2006 7:41 pm ] |
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| Author: | Grace [ Wed May 31, 2006 7:46 pm ] |
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| Author: | Wayne Stollings [ Wed May 31, 2006 8:34 pm ] |
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| Author: | Grace [ Wed May 31, 2006 8:35 pm ] |
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| Author: | Origam [ Wed May 31, 2006 8:59 pm ] |
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| Author: | Wayne Stollings [ Wed May 31, 2006 9:51 pm ] |
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| Author: | Origam [ Wed May 31, 2006 10:23 pm ] |
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| Author: | Wayne Stollings [ Wed May 31, 2006 10:37 pm ] |
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| Author: | Origam [ Thu Jun 01, 2006 1:00 am ] |
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| Author: | Wayne Stollings [ Thu Jun 01, 2006 7:53 am ] |
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| Author: | Origam [ Thu Jun 01, 2006 8:53 am ] |
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