Summary: Beyond Sums of Squares
In this chapter, we examine some optional (but amazing) additional questions and directions the sums of squares can take us.
- Gauss reimagined many questions. His introduction of Gaussian integers, a complex-valued analogue to our integers is not just related to sums of squares, but provides its own interesting questions, such as those of what complex prime numbers might look like in Fact 14.1.5.
- The next section includes brief discussion of the topics surrounding three amazing facts – Lagrange’s four square theorem, Fermat’s Last Theorem, and the Hilbert-Waring Theorem.
- We prepare to think about other sum questions that could be interpreted geometrically in Section 14.3.
In keeping with its overall feel, the Exercises have more programming exercises than usual, and some exploration.
