Category: College Algebra

Famous Curves Index

I found this nice website while looking around the website of a community college in Maine. The Famous Curves Index (published by a school of mathematics in Scotland) has 63 famous curves complete with equations, graphs (like this nice one of Fermat’s Spiral below), a short history of the curve, and a link to interactive Java code for manipulating the curve. This one is the interactive Java code for a Hypocycloid (given by a parametric equation)… very nice! What a great resource for Precalculus and Calculus classes. I will have to pull up some of these curves next week when we talk about implicit differentiation. If you’re teaching parametric equations or polar equations, this site would be great! I didn’t have any trouble getting the Java applets to work. Kudos to the School of Mathematics and Statistics, University of St. Andrews, Scotland for a great collection of curves! Possibly Related Posts: Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College Algebra Group Exploration in Math Learning at Scale Slides from ICTCM Abandoning Ship on Wolfram...

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Progress in Technology is EXPONENTIAL

Today I am forwarding you on to Ray Kurzweil’s Ted Talk “How technology’s accelerating power will transform us” This whole talk is about exponential trends. There are several beautiful log-plots of modern examples of exponential growth and decay. DNA Sequencing, World-wide-web, size of computers, Moore’s Law, evolution of technology, etc. He also talks about their research creating mathematical models to predict trends in technology. There is also an interesting segment in here on proposed nanobot red blood cells (tiny spheres that act as red blood cells, only more efficiently)… fascinating. Kurzweil predicts we will have succeded at reverse-engineering the human brain by the year 2020. By 2029… we won’t even see computers anymore. Computers will be integrated into our brains, clothing, and bodies. The merging of our brains with technology will provide us with the intelligence to evolve to the ability to understand our own intelligence. Just for the record, I will still be YEARS away from retirement in 2029… so while this might not concern you… I have to consider it a real possibility during my teaching career. How will we train a brain that integrates nanobots? Will that be considered “cheating” or no different than the use of a graphing calculator to assist in drawing a function? Yikes! I became curious about Ray Kurzweil after watching his talk, and spent some time poking around his websites KurzweilAI.net...

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LineRider

Line Rider, in its infancy, had only one tool, the pen. With this tool, you drew your masterpiece curve (or piecewise curves), on which, the little hatted dude rides his sled. There were rules about the curves, when drawn left to right, the were riding curves, when drawn right to left, decoration… or something like that. However, the new version of LineRider has multicolored pens, an eraser tool (woo hoo) and now with the addition of the magical Jing program… I can easily record and share my masterpiece with you. If you watch my masterpiece, keep in mind that I have just nicely demonstrated two types of discontinuities in my work… removable discontinuities (the little dude just glides over the hole) and jump discontinuities (the little dude leaps from one part of the curve to another). LineRider can be an interesting and fun study in slopes for algebra students, asymptotes for pre-calculus students, and limits for calculus students. However, the true works of art are the ones created and set to music like these classic LineRiders all available on YouTube: (turn on your sound) Jagged Peak Adventure Urban Run Electronic Adventures LineRider SuperMario (okay… that one is really clever!) These are good for a 5-minute break in class… you know… for those students that refuse to get out of their seats and stretch… they might as well be entertained!...

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The power of a good video (Mobius Transformations)

I remember never really “getting” mobius transformations when I took complex analysis. I could perform the mathematics, but what, really, was I doing? This elegant video (thanks to Karen for the link) reveals the Mobius transformations in a way that is so simple and elegant, it is truly remarkable. I will show it to my intermediate algebra class when we get to complex numbers simply because it is an application of complex numbers that they can at least see visually. You’ll probably want to make the video full screen, and there is nice music to accompany the text and transformations, so turn up your volume! Follow the link to the Science Friday file and scroll down to the Mobius Transformations Revealed. If you visit the website where Arnold and Rogness host this video, they have a downloadable version, in case your classroom does not have Internet. Possibly Related Posts: Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College Algebra Group Exploration in Math Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in...

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Can you say ‘Asymptotic’?

Go on, tell me these aren’t some of the most beautiful real-world exponential graphs you’ve seen lately… I was minding my own business, watching Chris Anderson (of WIRED magazine) discuss Technology’s Long Tail in one of the TedTalks (this is one of the things I do while I do mundane tasks like building PDF files and letting Camtasia build .avi video files) … when I saw some of the most beautiful examples of exponential growth and decay in graph after graph after graph. If you’re teaching pre-calculus or calculus this semester, you’ve got to see this and use it in your classes. Personally, I’m sick of population problems and radioactive decay problems… and I bet our students are too! Apparently, Chris Anderson has written an entire book about the “long tail,” that is, the asymptotic behavior at the end-life of a certain kind of technology, when it begins to approach “FREE.” The book is called “The Long Tail” and is available in bookstores everywhere. If you want to read more of Anderson’s musings about technology and the future, his blog can be found here. Possibly Related Posts: Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College Algebra Group Exploration in Math Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in...

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