SUMMERMATH 2002 PATTERNS by Louie Beuschlein Basketball Simulation Say you’re a 60% free throw shooter. Is it possible that you could step up to the.

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Presentation transcript:

SUMMERMATH 2002 PATTERNS by Louie Beuschlein

Basketball Simulation Say you’re a 60% free throw shooter. Is it possible that you could step up to the line and make 9 out of 10? What about only making 3 out of 10? What are the odds that you make at least 7 out of 10?

Kids in a Family Suppose some day you have a family of six kids. What are the odds that you’ll have 3 boys and 3 girls? What are the odds that you’ll have all girls?

Population Patterns Population Clock Will there be a day when our planet will no longer be able to sustain the number of people living on it? Will our population level off? How do populations of animals change in nature?

Want to be a Millionaire? How long do you need to save up in order to become a millionaire? How much do you need to save each year? How does the interest rate affect your wait?

Fractals How can you create your own fractal? How can you use probability and a computer to create a fractal? Could the coastline of Britain really be infinite?

Chaos If a butterfly flaps its wings in China, can that really affect the weather in Champaign-Urbana?

Sonic Booms What happens when a plane breaks the sound barrier? What do sonic booms have to do with the Doppler Effect? What geometry is involved? click plane for movie click horn to hear Doppler Effect

Pizza Geometry Which would rather have, two 8-inch pizzas, or one 16-inch pizza? What if all you really like is the crust? Math can make you a more knowledgeable pizza consumer!

Pendulums L E N G T H M A S S Release Angle What affects the period of a pendulum? Pendulum Link

Pendulum Formula T = 2  L g L g Why doesn’t the formula contain the mass or the release angle? If you made the swing 9 times longer, what would happen to the period? How would a pendulum behave differently on the moon compared to on Earth?  is normally used when dealing with circles. Why do you think it appears in this formula? Why didn’t all of our data points lie exactly on the line? T = period, L = length, g = gravitation field strength

Pendulum Formula T = 2  L g L g T = period, L = length, g = gravitation field strength Here’s the graph of y = x. The graph should look similar to our pendulum graph. The value of y depends on the value of x, so y is called the dependent variable. We can put whatever we want in for x (as long as it’s not negative), so x is called the independent variable. Identify the dependent and independent variable in our formula. What quantities are constant?

Credits fractal: free throw: Michael Jordan: Brady Bunch: Earth: Millionaire: show/who-wants-to-be-millionaire.jpghttp:// show/who-wants-to-be-millionaire.jpg fractal: fractal tree: Mandlebrot:

Credits butterfly: world map: sonic boom: pizza: pizza eating: