The author guides readers through an investigation of the efficiency of the Euclidean algorithm, leading to a remarkable connection with the Fibonacci numbers.

# Search Results

### Michael A. Jones and Brittany Shelton

This year [2011], July has 5 Fridays, 5 Saturdays and 5 Sundays. This happens once every 823 years.

### Annie Perkins and Christy Pettis

Poems have different rhyming patterns, depending on which lines rhyme with each other. For example, a two-line poem has only two different rhyming patterns. The two lines below that rhyme with each other can be described as an AA rhyming pattern:

### Yu Ren Dong

By supporting culture and integrating reading, teachers help English language learners in their mathematics struggles.

### Thomas Koshy

Fibonacci, Lucas, and the ubiquitous Catalan numbers are delightful sources for experimentation, exploration, and conjecture (Askey 2005; Koshy 2001, 2006, 2008). Pell numbers are another similarly rich source. In this article, I will demonstrate some patterns associated with Pell numbers and then will show how they can be extracted from Pascal and Pascal–like triangles. I will provide a geometric interpretation of Pell numbers and conclude by citing a few opportunities for further exploration.

### Ysbrand de Bruyn

This article explains how infinite geometric series can be used to calculate areas under graphs of simple power functions, a method first used by Fermat in his work on areas under graphs of parabolas.

### Dohyoung Ryang and Tony Thompson

The authors generate a formula for the sum of squares, cubes, and fourth powers and then generalize for any integral power.

### Elaine A. Terry

Gauss's method of computing finite sums involves a pattern that can be generalized into a formula—a great introduction to inductive reasoning.

### Erik Jacobson

Table representations of functions allow students to compare rows as well as values in the same row.

### Ron Lancaster

Students analyze items from the media to answer mathematical questions related to the article. The three clips this month all concern calendar questions surrounding the occurrences of Friday the 13th.