Illustrating the Multiplication of Quadratic Factors

Each term needs to multiply the other two terms in the opposite parenthesis, so start with the reds, then do the two mixed colors, then the blues, and finally, combine the mixed colors.

I’ve been playing around with ways of showing how to multiply out quadratic factors like the one above. I’m still not perfectly happy with these animations but they’re the best I’ve come up with so far. A smoother, Flash or svg animation might work better though.

In this second version the terms being multiplied are highlighted. I like how the highlighting gives some more stability to the animation, but I’m always leery of putting too much color or bells and whistles because they tend to complicate the picture. In this case at least, I think all the colors have meaning and are useful.

Multiplication of quadratic factors.

Kindness and Community

Just as each species in a biological community contributes something that helps sustain the community, people need to contribute to each other in their communities to to keep them stable, productive, and happy.

We’ve been talking about social action this cycle. Students have been finding and reading articles, and thinking about what they could do — themselves right now — to promote social justice. The articles have come from a number of different places: local stories from the Memphis newspaper, the Commercial Appeal; national articles from the New York Times; and even international things from the from BBC. Now, for Personal World, they’re thinking at the really small scale, about what they do for their classroom community.

The objective is twofold. First, I want them to contribute more to each other, and think about what they’re contributing, to maintain a healthy community. A little self reflection should help them realize if what they think they’re doing for others is actually helping. But, secondly, I also want them to recognize the efforts of their peers for what they are: attempts, even if futile or misguided, to be helpful.

It’s sometimes easier to think about doing charitable things for people far away, because it’s impersonal. There’s little risk of being embarrassed. But even the smallest groups need some altruism to grease the wheels of community.

Social Action: Extracting Potable Water from the Air

Shreerang Chhatre is working on a mesh that captures droplets of fog from the air to provide water in places where drinkable water is hard to get.

Chhatre is working on this at MIT which has some interesting programs for people interested in social action. He’s in the Chemical Engineering program but works with their Legatum Center for Development and Entrepreneurship.

Writing should first focus on the text

I have a great antipathy when my word processor tells me what to do, or, even worse, “corrects” my writing without my permission. So I avoid MS Word like the plague. OpenOffice is little better. Now I’ll admit that my writing is usually in great need of a good editor, but not looking over my shoulder, inserting little, irritating suggestions while I’m caught up in the turbulent rapids of self-expression. Getting into the flow of productive writing is difficult enough; I don’t need the extra distraction.

Instead I much prefer the plain text editors; Smultron has been a favorite of mine since I’ve been using Macs, and I spend a lot of time writing on the class Wiki (MediaWiki) and on this blog (WordPress), which both have very simple text-entry boxes.

WordPress and MediaWiki also process the text and make it presentable. Like most websites these days, this blog has a theme that tells it where to put the text, how to format it, what background to have, where to insert images, what to have in the header and footer, …. The theme I use was created by Karen Blundell and adapted to put in a couple of my own details, like the little citation thing, and the ability to name the reviewer and editors at the bottom of the post. I did spend a lot of time getting these things to work, but I did learn quite a bit about the inner workings of WordPress and CSS in doing them, and once they were done, I could forget about them entirely and just focus on the writing.

Similarly, with LaTeX, although it’s much more of a pain to figure out how to use. On the Muddle I use LaTeX to add mathematical equations, but it really is a fully-fledged typesetting program, designed for professionals.

Two pages from a booklet my class and I put together about a display of fossils. I used LaTeX to typeset.

My class recently created a little display of fossils collected from Coon Creek for a school fundraiser, and we put together a booklet for it. I had the students write their essays and put them up on our Wiki. Then I copied and pasted their text into a LaTeX document, added a couple chapters from some of my blog posts, and it did the rest to create a very nice looking book, complete with title page, table of contents and bibliography.

Setting up the LaTeX file was not trivial, since I’ve not used it in a number of years, and this was the first time I tried to format a book. But it creates beautifully looking documents, without all the mysterious formatting features that inevitably show up if you tried something this complex with Word.

There are, I’m sure, other software for publishing documents like this. However, LaTeX is free and so is the old version of Smultron. Smultron’s new version costs $4.99, but is probably worth it.

Comments are NOT Closed

I discovered yesterday, that for some reason or the other, a number of my posts’ comments sections were closed. I’ve re-opened them all again, but I’m still not sure why they closed themselves.

Also, as I mentioned before, if you try to post a comment and it does not show up it was probably caught up in my spam-filter. I’ve caught a few like that, but it’s impossible to check them all. A direct email should suffice to solve that problem if it occurs (see contact me). I appreciate all the feedback.

Weather versus Climate: The Seasonal Migration of the Sub-Polar Low

The cold front of this mid latitude cyclone spawned several fatal tornados on April 28, 2011. The cold front is the blue line with triangles pointing toward the east. Image via NOAA HPC.

The cold fronts of mid-latitude cyclones bring thunderstorms, rain and spawn tornadoes like the ones we’ve seen over the last few days. In the spring and fall, these cyclones just sweep across the southern U.S. again and again. The line of their passage sort-of marks the northward migration of the sub-polar low in picture of the global atmospheric circulation system.

The circulation cells of the global atmospheric circulation system migrate north and south with the seasons. Image links to larger version (1 Mb).

Each individual front, with its storms, is a feature of the weather. Climate, on the other hand, is the result of the average position over time: the series of fronts which make the southern U.S. wet in the spring and fall.

The sub-polar low is not the only feature that brings lots of seasonal rain. The ITCZ does also, and the rains that the ITCZ’s movement north and south of the equator bring, are what we call the monsoons. The yellow star on the animation, just to the north of the equator, sees monsoonal rains in the summer. Since the ITCZ follows the sun with the seasons, the monsoons always come in the summer; even in the southern hemisphere.