Natural Blogarithms

I had a lot of fun a few years back preparing a module and a talk for a regional Mathematics and Science teachers conference at WTAMU.  In fact, this year was the first in several years that I did not prepare a talk for this particular conference.  I am already preparing one for next year on utilizing specific web 2.0 tools in the mathematics classroom.  The talk I mentioned above was on Graph Theory, which basically models the pairwise connectedness between objects from a certain set.  Of course it included as a launching point, one of the earliest results from graph theory, the Seven Bridges of Königsberg, which demonstrated that it was impossible to traverse a path that crossed all seven bridges without crossing any bridge twice.

I thought the applet below was a fairly neat application of graph theory, converting a website into a color coded graph.  Once you type in a website it will create the graph showing the aspects of the websites such as forms, tables, links, and other sorts of html tags.  They are presented as dots (vertices) with pairwise connections, thus creating a graph.  The specifics of the generation are unclear but it does have a nifty result.  I’ve played with it longer than a should have creating graphs for all of my websites.  This blog’s “graph” is pictured.

Websites As Graphs (you can enter the url of any website)

Graphify my blog

written by SplineGuy

1. JediWPMConcentrate (Windows)
   If any of you read Lifehacker you saw this come up last week.  There was apparently a little “toy” application (WPM Tray) that would track your typing speed down in the system tray. It would display your current typing rate in words per minute. I’m not exactly sure what time span it averaged the rate over but I was surprised to learn that when I am typing these blogs I am in the 70-90 wpm range. That was quite a surprise. I remember in high school competing in the typing contest but I thought my skills as a typist had waned greatly over the years but apparently I have been playing around with this blog stuff that my typing rate is back up. Anyways, the application here is combined with an other app JediConcentrate (an application focus app). So what does this get you?
   
   

   Something really cool. Basically, once your typing speed passes a certain threshold (the default is 40wpm, but you can change it), every window but the one you’re typing in fades to black - the point being that once you hit a certain typing speed, JediWPMConcentrate acts as a sort of “bloodlust” mode for your typing and focus. Once you drop below the typing threshold, the background fades back to normal.
   – Lifehacker

2. Juice, the cross-platform podcast receiver
   Within the last week, I started looking closer at using my IPAQ to download and listen to podcasts (or netcasts, as I prefer to call them, thanks to Leo Laporte). There are several out there that I have been wanting to listen to and had not really found an efficient way to put them both on my laptop and my Pocket PC. This is definitely the software I recommend for subscribing to podcasts on a desktop or laptop. However, since I also want this on my IPAQ, the feature I like most was the automatic playlist creation. I could open Windows Media Player after downloading the podcasts of my choice and there would be playlist that I could then sync to my IPAQ. Now, I know all you Apple people out there know that this is a streamlined process when using iTunes and an iPod, but I always do things the hard way, uh, I mean, the Microsoft way. Pure habit.
3. FeederReader, podcatching software for the PocketPC
   I am very pleased with this utility that allows me to import my OPML file from Juice and while connected either through a sync cable, or via wireless, I can download my favorite podcasts directly to the IPAQ. Since this is almost exclusively where I want to listen to my podcasts I prefer to skip the middle man (Juice) and download straight to my IPAQ. This software, once I understood how to use it, worked perfectly for this. I can tell it exactly with podcasts to download, meaning that it doesn’t have to automatically download every single one that I am subscribed to every time I connect. I am addicted to tool tips in the windows interface so there was a learning curve with this software. Several of the buttons didn’t make sense to me as to what they did. I actually had to read the user’s manual, but once I did, it functioned perfectly.

written by SplineGuy

I didn’t think I fit into the typical category of an absent minded professor. Perhaps those that know me will disagree. However, today, I proved myself wrong. I realized just a few minutes ago that I taught my entire Intermediate Algebra class with my sweater vest on inside out.

I blame it on Christopher Columbus! (Emily is out from school today, so I didn’t have to get up as early, so I overslept and rushed out the door this morning)

written by SplineGuy

I thought I’d throw out a simple little problem that intrigued me and led me off on a wild goose chase. In the end, I got almost none of my intended work done before class, while I was exploring all sorts of problems of perimeters of overlapping figures.

PROBLEM:

Pairs of identical rectanglular strips, each measuring 3 by 1, are overlapped in a number of different ways to form three different shapes, shown in the diagram below.

Which shape has the greatest perimeter?

I accept that this is really not that difficult of a problem but the question that got me distracted was the last of the following: What if the dimensions of the rectangles were 5 by 2? 9 by 7? a by b?
What if the rectangles do not overlap at right angles?

HT: mathschallenge.net

written by SplineGuy