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Find number patterns in spirolaterals.
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How the number of the sides in a regular polygon with a fixed perimeter affects its area. R Which formula is the most accurate for estimating the volume of an M&M candy? R Test the relationship between the three different dimensions (length, width and height) of a three-dimensional object with a constant volume. R Prove Pythagorean theorem by using common items such as a fan and a skateboard. R R |
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PiHow Does Particle Density Influence "Monte Carlo" Derivations of Pi? R R Evaluate the different methods for calculating the irrational decimal place values of the constant Pi? Is any method more accurate or efficient than others? R R (1) An upper bound recursive equation for Pi using regular polygons circumscribed about a circle to approximate its circumference. (2) An Algebraic Polynomial of which one root is Pi itself. R A recursive equations for Pi by estimating the area and circumference of a circle in terms of squares and triangles. R (1) An expression for Pi using the concept of centripetal acceleration, (2) investigate the nature of the Pi Associates. (3) expressions for Pi by approximating the areas of definite integrals. R The Effect of a Low Precision Computational Environment on Comparative Algorithm Speed for Calculating the Value of Pi R
MiscellanyInversion and the Pappus Chain Theorem R Circles, Tangent Lines and Triangles Proofs with the Geometry Applet. R R What are Fractals? Make Your Own Fractals. R S Prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle. R The Area of the Arbelos R R Fractals: 1. Derive a formula to find the total length of all the branches of a tree. 2. Derive a formula to find the perimeter and area of a Koch snowflake. R See how the area changes when a sine function is added to a circular graph. R 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. R 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. R Determine which regular polygons can be used to tesselate (tile) a two-dimensional plane. R Study lattice polygons and prove that Pick's Theorem is correct. R Measuring Height (or Altitude) with an Inclinometer R Deriving formulas for scaling factor and fractal dimension of self-similar Sierpinski polygonal fractals. R Make a Mercator Projection R R Find properties other than those involving matrices and determinants to prove Heron's Formula and Brahmagupta's Formulas. R R R Research the Pappus Chain Theorem and circle inversion and prove the theorem R R The Planar Isometries of Polygons and a geometric proof of Langrange's Theorum R R Does Varying the Ratio of the Two Axes of an Ellipse Affect Packing? R Investigate Pick's Theorem R R What would happen if a basic sine function is added to the graph of a circle or an ellipse. R Demonstrate how parallax works in measuring distances on a small scale, and compare for accuracy the tangent with the radian method. R R Follow in the steps of Eratosthenes - measure the Earth's circumference R Explore which shapes can tile a rectangular grid or infinite plane and understand why. R R The geometry of close packing spheres R R |
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Science Fair Projects Resources
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Mathematics Resources R Citation Guides, Style Manuals, Reference R |
