Proof of the Pythagorean theorem using Dimensional analysis

[elimist]

hello,

in the Wikipedia page for http://en.wikipedia.org/wiki/Dimensional_analysis#Proof_of_the_Pythagorean_theorem" how do we know that area = "largest edge² • f (angle1, angle2)"? Isn't it just as reasonable to say something like area= (largest edge/40000)² • f (angle1, angle2) ?

 

[HallsofIvy]

Yes, it is. However, just taking that "40000" into the function, f, gets you right back to the original form. They are only saying that the area is equal to the largest edge, squared, times some function of the two angles. Since that function is left undetermined, constants don't matter.