petrophysics writes:
quote:
Without looking it up, prove c^2=a^2+b^2.
Oh, did you ask the wrong person. I am a mathematician, after all.
First, you're misstating the problem. It isn't "a^2 + b^2 = c^2" since that has an infinite number of solutions. Instead, you're referring to something else...perhaps that for a right triangle with legs a and b and hypotenuse c, a^2 + b^2 = c^2. In that case, the classic solution is graphical and thus would be hard to present here. Let me try:
Let a be the longer side of the right triangle with legs a and b and hypotenuse c. Place it flat down. Construct the square C along the hypotenuse c. The square that circumscribes square C has sides that are (a+b) in length.
This creates four equal right triangles at the corners of the circumscribed square with legs a and b and hypotenuse c.
The area of the circumscribed square is, necessarily, (a + b)^2.
It is also the sum of the area of the inner square plus the sum of the four triangles:
c^2 + 4(ab/2)
Thus:
(a + b)^2 = c^2 + 4(ab/2)
a^2 + 2ab + b^2 = c^2 + 2ab
a^2 + b^2 = c^2
But here's the thing: Not even mathematicians go through this every time they try to calculate the sides of a right triangle. We did it once, we showed it to be true, we simply skip to the end when we need it. We do this in science all the time. That's the way most science education is done: Make the student do the work to show how, starting from scratch, you can derive the things everybody already knows. This process not only shows you what it is we already know, it teaches you how to think and how to approach problems. "What is it I am trying to accomplish?" "What do I know?" "How does what I know tell me about where to get where I want?"
Edited by Rrhain, : Error in the second step of the reduction...had an "=" where I needed a "+"
Edited by Rrhain, : And again, correcting the second line...had a "*" where I needed a "+"
Rrhain
Thank you for your submission to
Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
™ Version 4.2
