Problem 1. An Equation x2 + y2 = z2
After looking at the above equation, respond to the following: “What are some answers?
I immediately think about the Pythagorean theorem and finding lengths of the sides of a right triangle (especially after reading through problem #3). But because the variables are not a, b and c this leads me to believe that it might not be what this problem is getting at.
Answers could also be asking for solutions or numbers that make the equation true. You could come up with integer combinations (x = 3, y = 4 & z = 5 for example) or combinations that include irrational numbers (x = 1, y = 2 & z = sqrt 5). When I first was thinking about this I immediately drew these number combinations into triangles.
AFTER THINKING MORE:
I also am thinking about an equation of a circle (although the z should be an r). If we where to graph an equation like this it would be a circle centered at the origin with a radius of z. This answer took me a lot longer to come up with, I think because Pythagorean is so much more of a "major" mathematics theme. Even though I just got done with a unit on Conics right before Christmas, I literally just though of this as I was typing...
[Thanks for reinviting me to your blog - sorry these comments are late!]
ReplyDeleteI had similar thoughts as you on this problem - using the pythagorean theorem. I also struggled with how to answer this problem - i liked your reference to circles though.