#0, Pythagorean Theorem Incomplete?
Posted by Dan on Jun-19-07 at 05:47 PM
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 + = c^2
#1, RE: Pythagorean Theorem Incomplete?
Posted by alexb on Jun-19-07 at 07:25 PM
In response to message #0
>For all scalene triangles:
>
>if c = hypotenuse, then Scalene triangles do not have a hypotenuse.
#2, RE: Pythagorean Theorem Incomplete?
Posted by Dan on Jun-19-07 at 08:13 PM
In response to message #1
I'm sorry, I meant to say: "the longest leg of the three". I thought that right triangles were Scalene. Thanks for the reply!
#3, RE: Pythagorean Theorem Incomplete?
Posted by alexb on Jun-19-07 at 08:17 PM
In response to message #2
>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.
#4, RE: Pythagorean Theorem Incomplete?
Posted by alexb on Jun-19-07 at 08:23 PM
In response to message #0
>if c = the longest side then> + = 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.
#5, RE: Pythagorean Theorem Incomplete?
Posted by Dan on Jun-19-07 at 08:58 PM
In response to message #4
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.
#6, RE: Pythagorean Theorem Incomplete?
Posted by alexb on Jun-19-07 at 09:02 PM
In response to message #5
I suggest you do one of two things, or both:1. Secure a calculator, a ruler and a protracter, draw a few scalene triangles, and see if you formula holds even approximately. 2. Look up the Law of Cosines, or the Cosine Law and think whether you can bridge between it and your formula.
#7, RE: Pythagorean Theorem Incomplete?
Posted by Ergo on Jul-04-07 at 11:24 PM
In response to message #6
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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