Fibonacci and Pascal Together Again: Pattern Exploration in the Fibonacci Sequence

Abstract

Mathematics is, to a large extent, the study of patterns (Steen 1988). When working with students, it is sometimes beneficial to have them search for patterns where their existence is promising, such as in the Fibonacci sequence or Pascal's triangle. Many of us have explored Pascal's triangle and have seen the Fibonacci sequence within it. However, fewer of us have detected Pascal's triangle buried within the Fibonacci sequence. A small group of preservice teachers made this discovery for themselves. The mathematics required is not above the high school level. Thus high school students can make similar discoveries as they look for and examine the patterns within the Fibonacci sequence. Here is what we discovered.