Geometry & Trigonometry
Science Fair Projects
Ideas and Sample Projects by Grade Level

P=Project   E=Experiment
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]
P=Project   E=Experiment
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]
Middle / High School - Grades 7-12
P=Project   E=Experiment

### 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

Is Mathematics Discovered or Invented? [E]
Tetrahedral Shoelace Algorithm: Calculating Volume of Irregular Solids [P]
Predicting the Interference Pattern from a Double and Triple Slit Experiment with Geometry [E]
The Algebra and Geometry of Quasicategories [E]
Arrangements of Minors in the Totally Positive Grassmannian and Sturmfels' Triangulation [E]
Characterizing the n-Division Points of Genus-0 Curves through Straight Edge and Compass Constructions [E]
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]

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]
R=Resource
Science Fair Projects Resources [R]
Citation Guides, Style Manuals, Reference [R]

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