 Topics for Middle School Math Projects, page 3
 Probability back to topic list Probability is the study of the likelihood or chance that something will happen.  Probability is measured from 0 (impossible) to 1 (always).  Chances are that you already know something about probability. Be sure your project goes beyond what you have already learned! Pythagorean Theorem  back to topic list This is a special relationship that holds in all right triangles.  The square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (legs).  There are many applications in science and engineering.  See also Trigonometry. Quadratic Equations  back to topic list A quadratic equation is an equation of the second degree--the highest exponent is two.  The standard form of a quadratic equation in one variable is ax2+ bx + c = 0.  A quadratic equation has two solutions or roots.  There are many applications.  You might also investigate the graphs of quadratic equations.  7 Bridges of Konigsberg  back to topic list   This is a very famous problem in topology that was studied by Leonard Euler in the 1730's.  In Konigsberg, Germany, a river ran through the city.  In the center of the river was an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people could cross from one part of the city to the other.  The problem is to cross each of the 7 bridges exactly once. (Konigsberg is now known as Kaliningrad.) See also Topology. Spirals back to topic list A spiral is a curve that begins at a point and traces a line that rotates around and away from the point according to some ratio or function.  Two types of spirals include the Archimedian spiral and the logarithmic spiral.  Statistics back to topic list You may already be familiar with a few ways to represent a "typical score" in a group of data:  the mean, median and mode.  Statistics are used in many areas of the sciences including the social sciences.  Be sure that your project goes beyond what you have already learned in class. See also Math in Sports. Taxicab Geometry  back to topic list The shortest distance between two points is a straight line, right?  Not in taxicab geometry.  Think about a taxi driving you home from school.  It can't take shortcuts through  backyards and it might even have to worry about one-way streets.  This is a type of non-Euclidean geometry. Take a ride to Cynthia Lanius' site!  She has a great article on school-bus geometry since kids usually don't take taxis! Tessellations and M.C. Escher  back to topic list A tessellation is a repeated pattern with no overlaps or gaps.  Tessellations can be made up of polygons but may also include complex shapes.  The Dutch artist M.C. Escher (1898-1972) was famous for his tessellating patterns.  You might create your own pattern using reflections, rotations and slides.  See also Art in Mathematics. Topology back to topic list Topology is one of the "newest" branches of mathematics. It is often described as rubber sheet geometry. Topologists study those properties of shapes that remain the same when the shapes are bent, stretched or twisted.  See also 7 Bridges of Konigsberg, Mobius Strip, Four Color Map Problem.  Trigonometry back to topic list "Trigonometry" comes from two Greek words:  trigon meaning triangle and metra meaning measurement.  It began as the study of the relationships between the sides and angles in a right triangle.  There are six trigonometric functions:  sine, cosine, tangent, secant, cosecant and tangent.  Trigonometry has  many applications including science. See also Pythagorean Theorem. Zeno's Paradox  back to topic list A paradox is a statement that appears to be contradictory.  Here is one description of Zeno's famous paradox.  If you were to walk from your house to the end of the next block, Zeno argued that you could never get there because first you must walk the first half of the block, and then you must walk half of what is left, and so on an infinite number of times. Find more information at www.mathforum.org/isaac/problems /zeno1.html