checking our Hypothesis

To the left are the graphs of all three equations with even exponents. Our original equation, x2+y2=1, is green, x4+y4=1 is red, and the newest equation, x24+y24=1, is blue.

As we can see it looks as though our hypothesis was correct. The graph of x24+y24=1 still has round corners, but is certainly more square-like than the other two graphs.

To the right are the graphs of all three equations with odd exponents. Our original equation, x3+y3=1, is green, x5+y5=1 is red, and the newest equation, x25+y25=1, is blue.

As we can see it looks as though our hypothesis was correct. The graph of x25+y25=1 is still a line with a round portion, but is certainly more leveled off and ledge-like than the other two graphs.