# Computing Square Roots: Part 2: Using Continued Fractions

Posted in Mathematics

## Continued Fractions

Let's start part 2 of our discussion of computing square roots by talking about continued fractions. When we first learn mathematics, we learn to count in the base 10 system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can construct representations of all of the integers using these 10 digits, by arranging them in a different order. So, for example, saying 125 is equivalent to saying …

# Computing Square Roots: Part 1: Using Newton's Method

Posted in Mathematics

## Newton's Method for Finding Roots of Equations

Suppose we have a function $$f(x)$$ and we want to compute values of $$x$$ for which $$f(x)=0$$. These values of $$x$$ are called the roots of $$f(x)$$.

We can compute the roots using Newton's Method, which utilizes the derivative of the function to iteratively compute the roots of the function.

Newton's method begins with an initial guess. It evaluates the derivative …

# CSE 143 Final Project: Hilbert Sort: 3. The Code

Posted in Computer Science

This is the third in a series of three posts detailing the Hilbert Sort problem, its solution, and its implementation. This post deals with the code to solve the Hilbert Sort problem.

# Hilbert Sort: Pseudocode

From our prior post, here is the psudocode for our Hilbert Sort function:

define hilbert_sort( unsorted queue, square dimension ):
create southwest queue
create northwest queue
create northeast queue
create southeast queue
for each point:
if in southwest:
create new point using X -> Y, Y -> X
if in northwest …