Transcript Document
SUMMERMATH 2002 PATTERNS by Louie Beuschlein 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? Basketball Simulation 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? Kids in a Family 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? Population Patterns • 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? Want to be a Millionaire? • 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? Fractals If a butterfly flaps its wings in China, can that really affect the weather in Champaign-Urbana? Chaos click plane for movie • What happens when a plane breaks the sound barrier? • What do sonic booms have to do with the Doppler Effect? click horn to hear Doppler Effect • What geometry is involved? Sonic Booms Math can make you a more knowledgeable pizza consumer! • Which would rather have, two 8-inch pizzas, or one 16-inch pizza? • What if all you really like is the crust? Pizza Geometry What affects the period of a pendulum? Release Angle MASS Pendulum Link Pendulums T = 2 L g T = period, L = length, g = gravitation field strength • 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? Pendulum Formula T = 2 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 6 negative), so x is called the 5 independent variable. 4 Identify the dependent and 3 independent variable in our 2 1 formula. What quantities 0 are constant? 0 5 10 15 20 25 30 Pendulum Formula fractal: http://wyvern.hants.sch.uk/sierpinski.htm free throw: http://www.playersc.com/NBAJAM64.html Michael Jordan: http://www.htc.net/~nilknarf/Jordan.html Brady Bunch: http://www.bradymaniac.com/intro.html Earth: http://www.msss.com/earth/earth.html Millionaire: http://www.usatoday.com/life/gallery/gameshow/who-wants-to-be-millionaire.jpg fractal: http://www.sscnet.ucla.edu/history/csstm/fractal.jpg fractal tree: http://www.laubender.de/fractaline/ Mandlebrot: http://www.phy.tulane.edu/mandlebrot.gif Credits butterfly: http://www.planetpals.com/butterfly.gif world map: http://about.reuters.com/media/map/world.jpg sonic boom: http://www.kettering.edu/~drussell/Demos/doppler/mach1.html pizza: http://gifs123.tripod.com/adm/interstitial/remote.html pizza eating: http://web.mit.edu/aglenn/www/mitpics/pizza.jpg Credits