Topics for Middle School Math Projects, page 2
4 Color Map Problem back to topic list
This topic explores the smallest number of colors needed to color a map if bordering countries cannot be the same color. In 1976 with the help of a computer, the four color map theorem was proven. See also Topology.
Fractal Geometry back to topic list
Fractals can be anything that contains self-similar images within itself. They have fractional (fractal) dimension. Fractals can often be formed by a repeating process where the new figure is more complicated than the original. The Koch curve is one example. Try this fractal site to start.
Game Theory back to topic list
Game theory is the branch of mathematics and logic that deals with analysis of games (i.e., situations involving parties with conflicting interests). Applications are to complicated games such as cards, checkers, and chess, and real-world problems such as economics, property division, politics, and warfare. Mathematician John Nash (A Beautiful Mind) worked on game theory.
Geodesic Dome back to topic list
A geodesic dome is a structure that roughly approximates a hemisphere. Geodesic domes have been popular in recent years as economical, easily erected buildings and may be constructed from limited materials. The architect R. Buckminster Fuller was an early proponent of geodesics for housing and other functions.
Golden Ratio/Section back to topic list
The golden ratio is a number often found when taking the ratios of distances in simple geometric figures such as the pentagram, decagon and dodecagon. It is also known as the divine proportion, golden mean, and golden section. The golden ratio can be found in ancient and modern art and architecture as well as in music. See also Art & Architecture in Math and Mathematical Patterns in Music.
Logic back to topic list
Logic is the study of reasoning. The value of logic statements may be expressed in "truth tables." Proofs are used in this branch of mathematics.
Magic Squares and Magic Cubes back to topic list
A magic square is a 2-dimensional arrangement of numbers. Every row, column and diagonal must have the same sum. A magic cube is a 3-D extension of a magic square.
Math in Sports back to topic list
Do you have a favorite sport? If you watch any games on tv, you may have wondered how they are able to come up with the statistics so quickly. That is the statistician's job. You might investigate statistics relating to your favorite sport. See also Statistics.
Mathematical Patterns in Music back to topic list
This a good topic for people interested in music. You might explore the golden ratio in music or answers to questions such as "why are there 12 tones in an octave?" Dave Rusin's site, based at Northern Illinois University, has some interesting answers and a link to a bibliography. Be careful! While the study of why some math enthusiasts enjoy music is interesting, that aspect is more appropriate for a psychology or sociology paper. See also Golden Ratio.
Matrices back to topic list
"Matrices" is the plural of matrix (not to be confused with the movie The Matrix). A matrix is a rectangular arrangement of numbers or data in horizontal rows and vertical columns. Each position in the matrix has a purpose. Matrices are often used as tools in problem-solving.
Mobius Strip or Band back to topic list
A one-sided piece of paper! The Mobius strip is formed by making a half twist at the end of a sheet of paper and attaching it to the other end. Try this Topology experiment. Draw a line down the middle of your Mobius strip. Now make a snip and cut down the middle.
Pascal's Triangle back to topic list
Pascal's triangle is an arithmetical triangle that can be used for many things. Two areas of math that it is used in include algebra and probability. More details and a diagram of the triangle can be found at this site. See also Catalan numbers.
Pi back to topic list
Pi is the ratio of the circumference of a circle to its diameter. Two approximations of pi that we use today are 3.14 and 22/7. You might investigate the history of approximations to pi and the methods of calculating pi.
Platonic Solids or Polyhedra back to topic list
Polyhedra comes from "many faces." A polyhedron is a 3-D solid model bounded by plane polygons. There are five regular polyhedra are known as the Platonic Solids: tetrahedron, hexahedron (cube), octahedron, dodecahedron and icosahedron. They can be found in nature. You might wish to build your own solid models as part of your project.
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