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Check out the lessons below if you need a refresher on trigonometry topics. Derive a formula to find the perimeter and area of a Koch snowflake. [E] See how the area changes when a sine function is added to a circular graph. [E] Prove that the area of an arbelos is equal to the area of a circle whose diameter is the altitude of a right triangle drawn to the hypotenuse, which is inscribed in a semicircle. [E] Find three or more different ways to tile the plane (i.e. an infinite two-dimensional surface) with spidron-based shapes as the tiling elements. [E] Determine which regular polygons can be used to tesselate (tile) a two-dimensional plane. [E] Study lattice polygons and prove that Pick's Theorem is correct. [E] Deriving formulas for scaling factor and fractal dimension of self-similar Sierpinski polygonal fractals. [E] Find properties other than those involving matrices and determinants to prove Heron's Formula and Brahmagupta's Formulas. [E] [E] [E] Does Varying the Ratio of the Two Axes of an Ellipse Affect Packing? [E] What would happen if a basic sine function is added to the graph of a circle or an ellipse. [E] Demonstrate how parallax works in measuring distances on a small scale, and compare for accuracy the tangent with the radian method. [E] [E] Explore which shapes can tile a rectangular grid or infinite plane and understand why. [E] [E]

Pages: 92

Publisher: Harper (1928)

ISBN: B00086P920

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