Pi
Pi Calculation Methods and Practical Application in the Usage of Pi in the Scientific World
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How Does Particle Density Influence "Monte Carlo" Derivations of Pi?
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Evaluate the different methods for calculating the irrational decimal place values of the constant Pi? Is any method more accurate or efficient than others?
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(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.
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A recursive equations for Pi by estimating the area and circumference of a circle in terms of squares and triangles.
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(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.
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The Effect of a Low Precision Computational Environment on Comparative Algorithm Speed for Calculating the Value of Pi
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Miscellany
The Algebra and Geometry of Quasicategories
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Arrangements of Minors in the Totally Positive Grassmannian and Sturmfels' Triangulation
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Characterizing the n-Division Points of Genus-0 Curves through Straight Edge and Compass Constructions
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Fractals and Serpinski Triangle
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What is the effect of putting different variable values in the fractal "Mandel's" equation?
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Determining the Fraction of Lattice Points Visible from the Origin in the Third Dimension
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Circumscribing a Circle about a Triangle Using the Geometry Applet
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Inversion and the Pappus Chain Theorem
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Circles, Tangent Lines and Triangles Proofs with the Geometry Applet.
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What are Fractals? Make Your Own Fractals.
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Prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.
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The Area of the Arbelos
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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.
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See how the area changes when a sine function is added to a circular graph.
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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.
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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.
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Determine which regular polygons can be used to tesselate (tile) a two-dimensional plane.
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Study lattice polygons and prove that Pick's Theorem is correct.
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Measuring Height (or Altitude) with an Inclinometer
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Deriving formulas for scaling factor and fractal dimension of self-similar Sierpinski polygonal fractals.
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Make a Mercator Projection
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Find properties other than those involving matrices and determinants to prove Heron's Formula and Brahmagupta's Formulas.
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Research the Pappus Chain Theorem and circle inversion and prove the theorem
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The Planar Isometries of Polygons and a geometric proof of Langrange's Theorum
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Does Varying the Ratio of the Two Axes of an Ellipse Affect Packing?
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Investigate Pick's Theorem
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What would happen if a basic sine function is added to the graph of a circle or an ellipse.
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Demonstrate how parallax works in measuring distances on a small scale, and compare for accuracy the tangent with the radian method.
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Follow in the steps of Eratosthenes - measure the Earth's circumference
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Explore which shapes can tile a rectangular grid or infinite plane and understand why.
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The geometry of close packing spheres
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