Saturday, November 8, 2008

Introduction

I'm currently tutoring 3 sophomores in Geometry, 1 sophomore in Algebra 1B, 1 8th grader in Algebra 1. My daughter is also an 8th grader in Algebra 1.

My intention for this blog is to discuss things my students are having trouble with and things that seem to help them, as well as connecting math concepts to everyday life.

At this point, I'd like to issue a blanket invitation, especially to my current students, to post comments and questions. I'd also like some suggestions on what I should name my business. After I receive some suggestions, I'll make a poll and let people vote! If you have any success stories to share, as well, I'll make sure they get posted.

Like the intro to the TV show Numb3rs says, "We all use Math everyday! To make change, to predict weather" and many other aspects of our lives.

For today, I'd like to share a website that connects one of my favorite hobbies, knitting, to advanced mathematics: Toroidal Snark

This page is wonderful and includes knitting and crochet explorations of mathematical concepts of Mobius strips and Hyperbolic Geometry.

Have you ever played with a paper Mobius strip?

Start with a long strip of paper, a couple of inches wide. Actually, let's start with 2 strips.

With the first one, tape the ends together. Now you have something resembling a bracelet, right? Take a pen, marker, crayon or whatever, and draw a line on the "inside" of the bracelet, starting and ending where the ends join.

So, now you have a bracelet with a line on the inside of it. This object has a true "inside" and "outside." A two sided circle.

Now, take the other strip, put the ends close together, but before you tape the ends together, twist one end. There's a good picture of the two shapes you should have now here. Now, just like with the bracelet, start drawing a line where the two ends are taped together. Move the paper, not the pen, and keep the pen on the paper, pressing into the table. After a few minutes, when you reach the point where you started, you should realize that your line in on both "sides" of the paper. This is a strip with only ONE side. It does NOT have an inside or an outside.

All over the internet, there are lots of lessons you can read and play with your Mobius strip. Here is one.

So, the fact that there is a way to KNIT one of these crazy things with no seam, is pretty cool. Well, to my twisted mind, anyway. I've got a Mobius poncho that I wear when it is a little chilly outside. What makes it interesting is that the twist helps it lay flat against my body, without bunching up all over the place.

But wait! I promised to connect math stuff to real life. So, what is the PRACTICAL, real-world application of this concept? Besides the shawl I mentioned, there is a way to make a conveyor belt using a Mobius strip. With a conventional conveyor belt, more like our bracelet up above, one side of the belt will be worn out long before the other side is barely used, making the belt useless. But with the Mobius design, the "inside" and "outside" will wear more evenly, and last twice as long!

Again, I invite anyone to post questions, comments, ideas for future posts, ideas for my business name or anything at all!

2 comments:

  1. Jennifer has been working with my daughter for over a Year. During that time she has increased her study and math skills and has become a true advocate for success. She has not only increased her math skills but has successfully gotten her through Algebra 1 and helped her through a summer school class for Algebra 2 which she scored a "B" which made her eligible to take Geometry her Sophmore year. This was a huge task and a big goal for our daughter. Math has always been a weak subject and she couldnt have made it this far without Jennifer's Help-- Thank you Jennifer

    ReplyDelete
  2. Just a note here: Krissy's daughter took Algebra 1A and Algebra 1B, essentially Algebra 1 taught as two courses instead of one. She did not take Algebra 2 before Geometry.

    I will copy this comment into a seperate "guest blog" post at some point in the future, so people will be able to find "success stories" easily.

    Thank you, Krissy!

    ReplyDelete