In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)