25 Jun 2012

Farey Fraction Visual Patterns

posted in: Algebra, Fractions Decimals and Percents, GeoGebra, Highlight, Number Theory | 3

The Farey Sequence, \(F_{n}\) is the list of all simplified fractions between \(\dfrac{0}{1}\) and \(\dfrac{1}{1}\) with denominator less than or equal to \(n\). For example,   \( \large F_{5}=\dfrac{0}{1},\dfrac{1}{5},\dfrac{1}{4},\dfrac{1}{3},\dfrac{2}{5},\dfrac{1}{2},\dfrac{3}{5},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{1}{1}\)  

6 Feb 2012

The Tangent is a Tangent!

posted in: GeoGebra, Trigonometry | 13

In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions. I learned the circle definitions of sine and cosine in my junior year of … Read More