SOLUTION: I would like to know why squaring a+b=c (a2+b2=c2) does not mean that the shortest distance between two points is not necessarily a straight line. How does the power of squaring wo

Question 760292: I would like to know why squaring a+b=c (a2+b2=c2) does not mean that the shortest distance between two points is not necessarily a straight line. How does the power of squaring work?
Thanks
Mel
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
I assume you are talking about using the Cartesian coordinate system with points a, b, c. The a^2 + b^2 = c^2 is an application of the Pythagorean Theorem for right triangles.
Now each point has two values (x, y), so we write the distance between any two points as d = sqrt( (y2 - y1)^2 + (x2 -x1)^2 ).
There are many other coordinate systems where the shortest distance between two points is a curved line (ie Riemann Space).

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