The most recent video from Vi Hart. Impressive, as usual.
The story of wind and mr.ug
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Author Archives: Mr. Chase
Geogebra has new skills
A new version of Geogebra has been released, in beta. It’s called Geogebra 5.0, and you can see the news about it here. Or, here’s a direct link to launch it right away. Thanks to The Cheap Researcher for the lead on this. As readers of this blog may already know, I love Geogebra!
One of the main highlights is that Geogebra now supports 3D manipulations. Awesome! However, don’t get too excited–it doesn’t let you graph anything except planes. No surfaces. It will do geometric constructions, like spheres and prisms. Using parametric equations and the locus feature, you can coax it into rendering spirals or other space curves. [edit: I figured this was possible, but it actually wasn’t. Not sure why.]
Another highlight, which I find even more exciting, is that Geogebra now has a built in CAS. Here’s a screen shot of me playing around with a few of its features. It also has a ways to go, especially for those who are used to more robust systems like Mathematica/Maple/Derive/TI-89. But this is a great step in the right direction, and 10 points for the open-source camp!
Notice that it can work with polynomials in ways you would expect, it can symbolically integrate and derive (simple things), perform partial fraction decomposition, evaluate limits, and find roots. Here are a few more things it can do. Strangely, it had problems finding the complex roots of a quadratic (easy), but not a cubic (hard). Just take a look at my screen shot. Seeing that it did okay finding the complex roots, I wondered if it could also plot them for me. I started by entering (copying and pasting) the complex zeros as points in Geogebra, which worked. But then I discovered the new ComplexRoot[] function which approximates the roots and plots them on the coordinate plane all at once. Cool! Here’s the screenshot:
The seven complex roots of f(z)=z^7+5z^4-z^2+z-15
As you can see, I asked for the roots of a 7th degree polynomial. Since the polynomial had real coefficients, notice that every zero’s conjugate is also a zero, as we’d expect. And we also expect that at least one solution of an odd-degreed polynomial will be real (notice this one has only one real root, approximately 1.22).
That’s all I’ve discovered so far. I’ll let you know if I come across anything else exciting. Keep in mind that this is beta, so the final release will likely have all the bugs worked out and more features.
Pi*z^2*a
A pizza with depth a and radius z has a volume of pi z z a.
Not sure what the original source of this witty little expression is, but my hat tip goes to my friend Patrick Schneider. Thanks, Patrick, for sharing!
Vi Hart’s Blog
It’s high time I gave a bit of press to Vi Hart’s Blog. If you haven’t checked it out, do so right away. It’s brilliant. A number of people have pointed me to her blog, including one of my Calc students. Her little math videos are fresh, funny, and insightful. Denise, at Let’s Play Math, gave her some press too, which is what reminded me to finally make this post. Here’s the video Denise highlighted (the most recent of Vi’s creations):
This is particularly appropriate because there were a couple of us in our math department discussing this very question: In total, how many gifts are given during the 12 Days of Christmas song? It’s a nice problem, perfect for a Precalculus student. Or any student. Here’s a super nice explanation of how to calculate this total, posted at squareCircleZ. But before you go clicking that link, take out a piece of scrap paper and a pencil and figure it out yourself!
Here’s another nice video from Vi Hart:
You could spend a lot of time on her site. Here’s another awesome video. I’ll have to have my Precalculus class watch this one when we do our unit on sequences and series.
And you’ve got to love the regular polyhedra made with Smarties , right?
Plus, Vi Hart plays StarCraft, which is awesome too. Back in the day, I really loved playing. I haven’t played in a while, and I certainly haven’t tried SC 2 yet, because then I’d never grade my students’ papers.
Bottom line is, you need to check out all the playful stuff Vi Hart is doing at her blog. Happy Wednesday everyone!
Learning from Mistakes
Watch this inspiring TED talk:
As a teacher, I know I’m succeeding when students feel free to take risks in the classroom. But letting students take risks is risky for a teacher. I’m a bit OC, and that’s the thing that keeps me from letting students take on more creative tasks. There’s also a good argument for teaching with a more systematic approach in such a way that all necessary topics get covered with a reasonable amount of depth in a reasonable amount of time. This reminds me of the discussion surrounding Paul Lockhart’s essay (my response here).
What if we Graded Toddlers?
From techdirt.com
What If We Gave Toddlers An ‘F’ In Walking?
from the rethinking-education dept
theodp writes “To improve math and science education, Physics prof Dr. Yung Tae Kim thinks professors and teachers should take a page from skateboarding. ‘The persistence and the dedication needed in skateboarding — that’s what we need to be teaching,’ explains Kim. ‘No one says to a toddler, ‘You have ten weeks to walk, and if you can’t, you get an F and you’re not allowed to try to walk anymore.’ It’s absurd, right? But the same thing is true with math and science education. If you want to learn trig or calculus, it’s set at such a pace in schools that it guarantees that only the absolutely best students will learn it.’ Kim says it’s possible to ‘polish the turd’ of high school and college education, and lays out his plan for doing so in Building A New Culture Of Teaching And Learning (YouTube: parts 1–2–3), a video drawn from a farewell talk he gave to his Northwestern students. There’s more on The Way of Dr. Tae at DrTae.org and PhysicsOfSkateboarding.com.”
I was just discussing the same point with my father in law this past week. Our education system needs to change in fundamental ways if we want students to truly learn at their own pace. We do a bit of a disservice to students who need to take the material a little slower. There’s nothing wrong with taking things slowly. Likewise, we do disservice to students who could complete the coursework in half the time.
[Hat tip: Tim Chase, as usual :-)]
Log Fail
This was posted recently on FAIL blog. I try to be a bit nicer when I’m grading. It’s still funny though.
[Hat tip: Tim Chase]
Pythagorean Theorem
Just when I said the other day that we care less about the ancient Greek mathematicians than we did 200 years ago, I turn the attention of my readership to the Pythagorean Theorem. It’s a simple repost: I liked the following video that Denise @ Let’s Play Math posted yesterday and wanted to share it. It also connects nicely to the post my dad made the other day about beautiful proofs.
Fractals
Just read two nice posts about fractals today. One from wired.com about electricsheep.com, which produces these amazing fractal videos like the one below by using crowd computing power
And also, I just saw this post from Walking Randomly that talks about the extensive abilities of wolframalpha to generate fractals on command.
Give the Babylonian’s some credit
So says this CNN article from Friday.
Over 1,000 years before Pythagoras was calculating the length of a hypotenuse, sophisticated scribes in Mesopotamia were working with the same theory to calculate the area of their farmland.
Working on clay tablets, students would “write” out their math problems in cuneiform script, a method that involved making wedge-shaped impressions in the clay with a blunt reed.
These tablets bear evidence of practical as well as more advanced theoretical math and show just how sophisticated the ancient Babylonians were with numbers — more than a millennium before Pythagoras and Euclid were doing the same in ancient Greece.
“They are the most sophisticated mathematics from anywhere in the world at that time,” said Alexander Jones, a Professor of the History of the Exact Sciences in Antiquity at New York University.
He is co-curator of “Before Pythagoras: The Culture of Old Babylonian Mathematics,” an exhibition at the Institute for the Study of the Ancient World in New York.
Random Walks 
