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CTK Exchange
Dan
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Jun-19-07, 05:47 PM (EST) |
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"Pythagorean Theorem Incomplete?"
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Can someone check this? I'm not very good at cosines and such. I'd greatly appreciate it. For all scalene triangles: if c = hypotenuse, then <(1/90 * angle ab) a^2> + <(1/90 * angle ab) b^2> = c^2 |
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alexb
Charter Member
2039 posts |
Jun-19-07, 08:17 PM (EST) |
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3. "RE: Pythagorean Theorem Incomplete?"
In response to message #2
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>I'm sorry, I meant to say: "the longest leg of the three". OK. >I thought that right triangles were Scalene. First, this is not true. There are isosceles right triangles. Second, this is also irrelevant. What is relevant is the fact that not all scalene triangles are right. |
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alexb
Charter Member
2039 posts |
Jun-19-07, 08:23 PM (EST) |
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4. "RE: Pythagorean Theorem Incomplete?"
In response to message #0
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>if c = the longest side then ><(1/90 * angle ab) a^2> + <(1/90 * angle ab) b^2> = c^2 What is this expression in the brackets? 1/90 * angle ab? Is it the angle between a and b divided by 90? Why? I cannot find a reasonable explanation for those expressions. But you may want to earch for the Cosine Law. |
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Dan
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Jun-19-07, 08:58 PM (EST) |
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5. "RE: Pythagorean Theorem Incomplete?"
In response to message #4
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I figured that a 90 degree angle equals 100% of the side being multiplied. So, when multiplying with a greater angle of 90 degrees, results with a percentage greater than 100. And that excess percentage would contribute to the length of side c. At least I thought so. |
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Ergo
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Jul-04-07, 11:24 PM (EST) |
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7. "RE: Pythagorean Theorem Incomplete?"
In response to message #6
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The essence of mathematics is stating concepts PRECISELY. Until one can specify PRECISELY what s/he means, s/he doesn't (in any meaningful psychological sense) KNOW what s/he means. That's why it's often said )in non-math contexts) that once a question is stated precisely it contains its own answer. Take the time to write, in complete grammatical sentences, in English, the proposition that you are asserting. At that point those able to "do the math" will be able to respond accurately to the hypothesis. (alexb: cf. the start of Polya's algorithm for problem solving) |
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