Abstract: Everyone is familiar with 3^2 + 4^2 = 5^2, though not so familiar is 20^2 + 21^2 = 29^2. Can we find more examples of consecutive squares that sum to a square? How about 1^2 + 2^2 + 3^2 + ... + 24^2? Everyone can readily check 1^2 + 2^2 + 2^2 = 3^2. Can we find more examples of this pattern of three squares summing to a square? I have recently looked at a number of questions about sums of squares, and I will discuss some of the insights and methods in this seminar.