Animated Video on the Sum of an Arithmetic Series

It's no secret that mathematicians like to play with numbers.  The most basic sequences of numbers is 1, 2, 3, 4, ... , which is called an arithmetic sequence of the counting numbers.  One might wonder if you can add these numbers 1 + 2 + 3 + ... up to say, 100, without having to actually add 100 numbers together.  In fact, you can multiply instead of add, and in this video, "Staircases, Handshakes, and the Sum of an Arithmetic Series" I show a few different ways of thinking about this problem using drawings (visual represenations), real world contexts, and symbolic arithmetic equations to justify my reasoning.  Accordingly, this is also a lesson in using multiple representations for a single mathematical concept.  This video is illustrated an animated with Doceri software.   Please feel free to use it in your math classes.

Tags: arithmetic series gauss trick area rectangle diagonal polygon multiple representations elementary high school doceri hand writing software finite series

Animated Video Tutorial on How To Weave Super RAW

I uploaded my first beading video on how to weave super right angle weave (SRAW) with beads.

This is my very first beading video, including photos and animated illustrations, and a bit of rambling at the beginning while I show you a few photos.  If you want to just see the how-to part, zoom ahead to 3:08. I created this video with Doceri software on my iPad.  

This bracelet is bead woven with SRAW. In the video, I mention how the 3mm by 4mm roundels are woven into the weave just like the other "connector" beads (in matte blue, size 8/0), but with three beads (11/0, roundel, 11/0) instead of a single matte blue bead.

Compared to un-embellished RAW, SRAW is tighter and less thread shows.  It also sews up relatively quickly because you pick up five beads on most stitches.  I made this entire bracelet in about three hours.  The weave is still nicely flexible like RAW, but a bit more sturdy.

This bracelet is sold.  Thanks for looking.

New Doceri Videos Including an Introduction to the Mathematics of Symmetry

Doceri now has a Doceri Facebook Fan Page where you can find links to videos showing both how to use the software, and sample lessons using the software.  Here are direct links to the two videos I have made so far.

The Mathematics of Symmetry Using Doceri Software

How to Make a Drawing Using Doceri Software

Stay tuned, because I'm currently working on another video that shows how to weave Super Right Angle Weave with beads.   This software is much easier and faster to present visual, handwritten information than what I had been using before!  So much easier.

Doceri iPad software

I drew these origami instructions on my iPad, and I can now play them back, watching them draw themselves.

My boyfriend has been working for a solid year developing the most amazing software for the iPad, for teachers and presenters.  The Doceri system turns your iPad into a remote control for your computer AND lets you handwrite or draw over any desktop image or background.  Now you can write your board work ahead of time, and then play back your writing for your class.  Everything you write is fully editable at any time.  If you teach, you'll want this software.  

If you get the Doceri software, be sure to watch the demonstration samples.  Writing the demos was my contribution... and the color palette.   They let me pick the colors :)

Journal of Mathematics and the Arts

JMA recently posted images of the covers of the journal.  You can see my beaded beads on the second issue, published in 2007.  This cover shows three views of an Octahedral Cluster and another three views of a beaded Sierpinski Tetrahedron, one of which is shown below.  If you would like to read the paper that goes with the cover, download a free copy of my paper on the symmetry of beaded beads (pdf).