Date: April 14, 2011
Creator: Beardslee, Jordan & Cherry, William, 1966-
Description: This presentation discusses research on predictable patterns in continued fractions and decimal expansions. Abstract: A continued fraction is a representation of a number by series of fractions inside fractions, such that the numerator of every fraction is a one. Decimal expansion is another way to express a number. Many times in mathematics when we have two different ways to write the same expression, we look for connections between the two notations. When trying to express a number, we encounter an interesting anomaly between continued fractions and decimal expansions. A randomly chosen number, with a predictable decimal pattern, will have an unpredictable continued fraction. Furthermore, a randomly chosen continued fraction, with predictable partial quotients, will have an unpredictable decimal expansion. However, there are those few exceptions, one of which the author is studying in depth. It is a binary sequence closely tied with the Fibonacci numbers, a series of numbers that often occur in nature. Through the author's research, the author hopes to find an understanding to this aforementioned anomaly and bridge continued fractions and decimals. In this presentation, the author will show where predictability lies and furthermore where there is chaos still to be settled.
Contributing Partner: UNT Honors College