Surprising Uses of the Pythagorean Theorem

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41

Kalid,

You might want to make it clear that you’re restricting your discussion to squares, since the statement

The area of any shape can be computed from any line segment squared.

is not true for rectangles.

42

Actually, I think I see what you mean. (Sorry, I’m commenting as I read. Maybe I should write down my comments and not say them until I’m finished reading, huh?)

43

I would like to see a derivation of mccoyn’s result of c = a * sqrt(1 + b^2 / a^2) being equivalent to c = a^2 + b^2, if anyone has one.

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Hi John, thanks for the comments! No worries about the inline comments, it’s interesting seeing the thought process. Yep, rectangles can still follow the rule constant * side squared, but that constant will be different for each shape. In the case of a square, the constant is 1 (it is a different way to look at it).

The second result
c^2 = a^2 + b^2
c^2 = a^2 * (1 + b^2/a^2) [rearrange right side]
c = a * sqrt(1 + b^2/a^2) [square root of both sides]

Now, the physical meaning of this is interesting. It basically gives you a constant [sqrt(1 + b^2/a^2)] that maps you distance in the “a” direction to relative distance in the “c” direction.

There’s more details here if you like:

http://betterexplained.com/articles/rescaling-the-pythagorean-theorem/

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@ritesh: Glad you enjoyed it!

46

Thanks Kalid,Superb work,its crystal clear to understand.

47

Thanks Naresh!

48

why do we use the pythagorean theorem??? (plz answer)

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@Teresa: Hi, there’s several uses of the Pythagorean theorem mentioned in the article.

50

i dont get it

51

Can anyone explain the uses of Pythagorus theurom?(please can you answer this question)

52

In the section on proving the Pythagorean Theorem (Intuitive Look at the Pythagorean Theorem), I am unsure why the Area = F*hypotenuse^2. Can you please explain? I tried to use the A= 1/2bh equation and substitute one of the sides with h = sqrt(hyp^2 - B^2) but could not come back to the F * hyp^2.

Thanks,
Ashley

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I Think This Is Good . But I Need Something That Could Be More/Better Explained !

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@Ashley: Hi, that equation

Area = F*hypotenuse^2

refers to the fact that any triangle can have an equation formula like this. The amount of F will change on the shape though.

Area = 1/2 b * h

is a more useful equation because it works for every type of triangle. But the first one gets at the idea that the area of any shape is essentially based on the hypotenuse squared (or any side squared, for a different F). For squares, area is 1 * side^2, or 1/16 * perimeter^2. In both cases, it’s “some number time a measurement squared”.

Hope this helps!

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[…] Geometry: Pythagorean uses, Pythagorean distance, degrees vs radians […]

56

thats all bakvass…

57

Thank you very much ! It’s the best thing I’ve found about Pythagoras… :smiley:

58

Could u please explain me the concept of Area factor. Im really not getting it. With respect to various shapes how can i associate it with the given figure.

59

Could u please explain me the concept of Area factor. Im really not getting it. With respect to various shapes how can i associate it with the given figure.

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got something new to know about pythagoras