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Primary School - Grades K-3
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P=Project E=Experiment
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Investigate how a 3-D object changes as it increases in size by measuring and comparing the length of an edge, the surface area, and the volume.
[E]
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Elementary School - Grades 4-6
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P=Project E=Experiment
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Does The Size Of A Circle Affect The Value Of Pi?
[E]
Find number patterns in spirolaterals.
[E]
How the number of the sides in a regular polygon with a fixed perimeter affects its area.
[E]
Which formula is the most accurate for estimating the volume of an M&M candy?
[E]
Test the relationship between the three different dimensions (length, width and height) of a three-dimensional object with a constant volume.
[E]
Prove Pythagorean theorem by using common items such as a fan and a skateboard.
[E]
[E]
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Middle/High School - Grades 7-12
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P=Project E=Experiment
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Pi
Pi Calculation Methods and Practical Application in the Usage of Pi in the Scientific World
[E]
[E]
How Does Particle Density Influence "Monte Carlo" Derivations of Pi?
[E]
[E]
Evaluate the different methods for calculating the irrational decimal place values of the constant Pi? Is any method more accurate or efficient than others?
[E]
[E]
(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.
[E]
A recursive equations for Pi by estimating the area and circumference of a circle in terms of squares and triangles.
[E]
(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.
[E]
The Effect of a Low Precision Computational Environment on Comparative Algorithm Speed for Calculating the Value of Pi
[E]
Miscellany
Fractals and Serpinski Triangle
[E]
[E]
[E]
What is the effect of putting different variable values in the fractal "Mandel's" equation?
[E]
[P]
Determining the Fraction of Lattice Points Visible from the Origin in the Third Dimension
[E]
Circumscribing a Circle about a Triangle Using the Geometry Applet
[E]
Inversion and the Pappus Chain Theorem
[E]
Circles, Tangent Lines and Triangles Proofs with the Geometry Applet.
[E]
[E]
What are Fractals? Make Your Own Fractals.
[E]
[P]
Prove that the sum of the perimeters of the inscribed semicircles is equal to the perimeter of the outside semicircle.
[E]
The Area of the Arbelos
[E]
[E]
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.
[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]
Measuring Height (or Altitude) with an Inclinometer
[E]
Deriving formulas for scaling factor and fractal dimension of self-similar Sierpinski polygonal fractals.
[E]
Make a Mercator Projection
[E]
[E]
Find properties other than those involving matrices and determinants to prove Heron's Formula and Brahmagupta's Formulas.
[E]
[E]
[E]
Research the Pappus Chain Theorem and circle inversion and prove the theorem
[E]
[E]
The Planar Isometries of Polygons and a geometric proof of Langrange's Theorum
[E]
[E]
Does Varying the Ratio of the Two Axes of an Ellipse Affect Packing?
[E]
Investigate Pick's Theorem
[E]
[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]
Follow in the steps of Eratosthenes - measure the Earth's circumference
[E]
Explore which shapes can tile a rectangular grid or infinite plane and understand why.
[E]
[E]
The geometry of close packing spheres
[E]
[E]
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Useful Links
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R=Resource
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Science Fair Projects Resources
[R]
Mathematics Resources
[R]
Citation Guides, Style Manuals, Reference
[R]
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