Pure Mathematics Project Ideas



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No matter what your favorite card game is, we all wish we could use psychic powers to draw the card we want on our turn. You may not have psychic powers, but you might have the power of probability on your side. Do this experiment and discover how math can help you avoid the words, "Go fish!" One piece of Play-Doh can make many different shapes. Even though you can change the shape by squishing or stretching the Play-Doh, it is still the same size unless you add or take away some of the dough. Try this experiment to test how these changes in size and shape occur in each dimension. In this project, you will make 2-dimensional templates, called nets, that fold up into 3-dimensional (3-D) shapes. By making shapes of different sizes, you will be able to see how 3-D shapes change with size. Which property (or aspect) will change the most: the length of an edge, the surface area, or the volume? Juice boxes are so convenient, just poke the straw in and sip away! It might surprise you how much thought goes into the design and manufacturing of a juice box. Each manufacturer has carefully calculated how big each side should be to hold a certain amount of juice inside. Find out how different brands of juice measure up. Have you ever wanted to take a short cut? How about when doing your math homework? In this experiment you can learn how estimation can save you time doing math calculations. But beware, some estimations are better than others! Can you match this sample size with the best population? How accurate are your estimation skills? Measurements are very important for scientists. It is especially important that the measurements be accurate. Think about how important accuracy is when you want to know if you are taller than a friend of yours, every inch counts! In this experiment, you will investigate how different objects can be measured with accuracy. Are small or large objects more difficult to measure? Who in your family is the best at measuring? Maybe it will be you! It has been said that, "Life is like a box of chocolates—you never know what you're going to get." (Forrest Gump in Forrest Gump, 1994.) In this experiment you can test the "Forrest Gump Chaos Theory" by using M&M's, which are much cheaper than a box of chocolates. What if life is more like a bag of M&M's? Find out in this experiment if some things in life are predictable by using the awesome power of statistics. Have your parents ever found you munching on candy and asked you, "How much candy did you eat?" Instead of saying, "I don't know?" and getting in trouble, wouldn't you rather say, "I ate precisely 10.7 cubic milliliters of candy mom." Make your parents proud of their candy-eating genius child (you) with this simple experiment. People often draw conclusions from a small number of observations, but how easy is it to draw the wrong conclusion? Here is a simple project that shows the importance of making enough observations before making a prediction. This project shows how mathematical probability sometimes contradicts our intuition. Despite the fact that there are 365 days in a year, if you survey a random group of just 23 people there is a 50:50 chance that two of them will have the same birthday. Don't believe it? Try this project and see for yourself. If you've ever wondered how tall that bridge is, or how high your kite was, then this could be a good project for you. You'll learn how you can use the mathematics of right triangles to measure the height of an object with two measurements that you can make on the ground. You're playing Monopoly with a friend, and you've already got Park Place and you really, really want to get Boardwalk. If you're on Pacific Avenue, what are the chances you'll reach your goal? Here's an easy project that will show you how to find out.
If you like to play Tetris then you might like this project. You'll learn something interesting about the mathematics of complex shapes. Science Fair Project image
This a straightforward, but interesting, project in geometry. It is a good first proof to try on your own. You should be able to figure it out by yourself, and you'll gain insight into a basic property of circles. Science Fair Project image
The arbelos is the white-shaded region between the three semicircles in the illustration at right. In this project, you'll prove an interesting method for determining the area of the arbelos. Science Fair Project image
If you like solving challenging puzzles, this could be a good project for you. In this project you'll learn one method for solving Rubik's Cube. Then you'll do your own background research to find other methods for solving the puzzle. Which method works fastest? This project challenges you to figure out how to make geometric patterns with Rubik's Cube. Leaving your cube in one of these positions makes it much more tempting to pick it up and 'fix' it. Can you figure out how to make a checkerboard, or a cube-within-a-cube? Can you make only the center piece a different color from the rest? Can you figure out how to solve the cube from these positions? Do you like to play cards? Here's a project that will get you thinking about strategy in card games and help you become a better card player. The mathematics of tiling patterns or tessellation has applications in crystal structure and materials science. Tiling patterns can also be appealing on their own. In this project you can learn about the geometry of tessellations using congruent, regular polygons.
This is a great project for someone who is interested in both mathematics and art. Spidrons are geometric forms made from alternating sequences of equilateral and isosceles (30°, 30°, 120°) triangles. Spidrons were discovered and named by Daniel Erdély in the early 1970's, and have since been studied by mathematicians and artists alike. This project is a great way to learn about the mathematics and art of tiling patterns. Science Fair Project image
Here's a fun project that combines baseball and math. Major League baseball is played in ballparks that have their own individual quirks when it comes to the exact layout of the field. Fenway Park in Boston has the famous "Green Monster" in left field, Yankee Stadium in the Bronx is notorious for the "short porch" down the right field line, and Coors Field in Denver is at a much higher altitude than any other ballpark. How do these differences affect batting statistics? You'll need to do a little digging to pull the numbers together, but a nice thing about this project is that the experiments are already done, and the data is out there waiting for you. Here's a project that will teach you about math as you follow some of your favorite players or teams. You'll be comparing day-to-day performance with long-term averages, and trying to determine if the "streaks" and "slumps" over shorter time periods are due to random chance or something else. When you've finished, you'll have a better understanding of some important concepts in statistical analysis and baseball. What makes a winning team? Getting all the best players? Good coaches? Good chemistry? This project will show you how you can use math to help you test your hypothesis about what makes a winning team. This is an interesting geometry project that goes back to the time of Archimedes, the famous Greek mathematician. You can combine this mathematical project with computer science and take this ancient problem into the twenty-first century with a dynamic diagram using the geometry applet. If you're the kind of person who has taken apart your Rubik's cube in order to grease the inside parts so it will move more smoothly, this could be a great project for you. We'll show you three sets of move sequences that accomplish specific rearrangements of the cube. Can you devise a way to solve the cube using only these three move sequences?
Although fractal images can be intriguingly complex, fractals are more than just pretty pictures. In this project, you'll explore the mathematical properties of the famous Mandelbrot (illustration at right) and Julia sets. You'll learn about how these images are generated, and about the relationship between the Mandelbrot set and the Julia sets. Science Fair Project image
Here is a challenging problem for anyone with an interest in geometry. This project requires background research to solve it, but it is an excellent illustration of visual thinking in mathematics. Science Fair Project image


Additional Project Ideas

Note: The following project ideas are abbreviated, without notes to start your background research or a procedure for how to do the experiment. You can identify abbreviated project ideas by the asterisk at the end of the title. If you want a project idea with full instructions, please pick one without an asterisk.

Many industries rely on scale models to develop new products and designs. Architects, industrial designers, artists, clothing designers, and car manufacturers all use scale models. Each model is built to a scale that relates the actual object to the model through a ratio. Can you determine a formula for constructing a scale model? You can use your... Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in different types of bank accounts. How much better is a savings account than a checking account? What difference does the interest rate make? Which is... Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced... Block off one-third of a soccer net with a cone, 5-gallon bucket or some other suitable object. Shoot into the smaller side from a set distance, but systematically varying the angle to the goal line. Take enough shots at each angle to get a reliable sample. How does success vary with angle? For a basic project: How do you think your success... Can you remember what the weather was like last week? Last year? Here's a project that looks at what the weather was like for over a hundred years. You'll use historical climate data to look at moisture conditions in regions across the contintental U.S. You'll use a spreadsheet program to calculate the frequency of different moisture conditions... Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial... What do knots, maps, mazes, driving directions, and doughnuts have in common? The answer is topology, a branch of mathematics that studies the spatial properties and connections of an object. Topology has sometimes been called rubber-sheet geometry because it does not distinguish between a circle and a square (a circle made out of a rubber band can... Music has many mathematical elements in it: rhythm, pitch, scale, frequency, interval, and ratio. There are many ways to turn these elements into a science fair project. You can investigate how the scale is based upon a special type of number sequence called a Harmonic Series. Another scale used by Bach, called the "Well-Tempered-Scale" or the... You may know Lewis Carroll as the author of Alice in Wonderland, but did you know that in real life he was a mathematician who studied symbolic logic and logical reasoning? How can math help you solve Lewis Carroll's Logic Game? (Bogomolny, 2006) How are algorithms for solving the game Sudoku similar to solving a logic problem? (Hayes, 2006)... A magic square is an arrangement of numbers from 1 to n2 in an n x n matrix. In a magic square each number occurs exactly once such that the sum of the entries of any row, column, or main diagonal is the same. You can make several magic squares and investigate the different properties of the square. Can you make an... Sunspot activity has been monitored continuously since about 1700. The historical data shows that sunspot activity rises and falls in a roughly 11-year cycle. This project shows you how you can use a spreadsheet program to perform both graphical and statistical analysis to look for patterns in cyclical data. You'll learn how to use a... Here's a project that combines sports and math. You'll learn how to use correlation analysis to choose the best team batting statistic for predicting run-scoring ability (Albert, 2003). You'll also learn how to use a spreadsheet to measure correlations between two variables. Which Team Batting... Math is used by many different types of scientists to model phenomenon and evaluate data from an experiment. By building mathematical models scientists can understand how different physical, chemical, and biological processes are affected by different variables. The most important tools are: making a graph to give a visual representation of the... A fractal is, "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced/size copy of the whole" (Mandelbrot, 1982). There are many different fractal patterns, each with unique properties and typically named after the mathematician who discovered it. A fractal increases in... How do you turn a 2-dimentional piece of paper into a 3-dimentional work of art? Origami, the classical art of Japanese paper folding, is loaded with mathematical themes and concepts. What are the common folds in origami, and how do they combine to create 3-dimentional structure? Can you classify different types of origami into classes based upon...

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