Polyhedral Waltz

posted in: Geometry, Highlight, SketchUp

Here is a new video Polyhedral Waltz.  I made the animation, and Maurice Page composed the music.   The video shows how Platonic Solids (regular polyhedra) inscribed in the same sphere fit together. If you click on the “cc” button … Read More

Farey Fraction Visual Patterns

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,   $$\large F_{5}=\dfrac{0}{1},\dfrac{1}{5},\dfrac{1}{4},\dfrac{1}{3},\dfrac{2}{5},\dfrac{1}{2},\dfrac{3}{5},\dfrac{2}{3},\dfrac{3}{4},\dfrac{4}{5},\dfrac{1}{1}$$

The Tangent is a Tangent!

posted in: GeoGebra, Trigonometry

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

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