Similarly, should artists who sample works from public content have to pay royalties? Musicians and artists can claim IP when their works are shared, but what

Similarly, should artists who sample works from public content have to pay royalties? Musicians and artists can claim IP when their works are shared, but what about mathematicians, architects? Do I owe Pythagoras' estate every time I compute A^2 + B^2 = C^2? I want to put French doors in my pantry, who do I make the check out to in order to legally use the design? This man lives comfortably, I'm sure he's not living paycheck to paycheck. He deserves credit for creating the work, but the implication is that he's somehow suffering based on the 'trading'. Life sucks, I'd be pissed too but it's the way things work. Grayson Chance was an internet sensation not too long ago for performing Lady Gaga's music. She didn't try to burn him for most likely stealing the sheet music, she applauded the kid and wished him luck. Relevant, NSFW audio: http://www.youtube.com/watch?v=Cvq3Pf3j61c http://www.youtube.com/watch?v=Cvq3Pf3j61c