Re: I'd never seen this before

Tina <tbaker27705@xxxxxxxxx> wrote:
Jim, you may wish to google Pythagorean. or you can take my word for
this: it is NOT what you had written and the equation .

sqrt (R^2 + d^2) = R + h

is not true in the general case.

You are probably thinking of

A^2 + B^2 = C^2, where A and B are the two sides forming the right
angle. That, solving for the long side, is

C = sqrt(A^2 + B^2), a far cry from the identity mentioned above.

The two equation are identical.

It's easy to forget these things, but in this case I have not.

You have the equation correct, but have forgotten basic algebra.

The following two equations are identical:

y = x^2
sqrt (y) = x

For the original equation:

Let R = A
Let d = B
Let (R + h) = C

Substituting into my original equation we get:

sqrt (A^2 + B^2) = C

Square both sides of the equation and we get:

(A^2 + B^2) = C^2

The parentheses are now irrelevant, so when removed we have:

A^2 + B^2 = C^2

Substitute back in the original values we get:

R^2 + d^2 = (R + h)^2

QED


See http://en.wikipedia.org/wiki/Pythagorean_theorem




--
Jim Pennino

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