Fractals and Kindles

I just can’t help myself. Whenever I get a new gadget, I have to customize it. When my wife and daughters gave me a Kindle four years ago, I was thrilled. It’s a Kindle 3, and it opened to me the amazing world of ebooks. My library now includes collections of G. K. Chesterton, Charles Dickens, Fyodor Dostoyevsky, and Shakespeare. I like the fact that the screen isn’t backlit, so there is no eye strain. It’s a wonderful device that has completely changed the way I purchase and read books.

However, I thought the screensavers that Amazon preloaded on the Kindle were really unattractive, so I tried to replace them with images more to my liking. Easier said than done! I assumed that all I had to do was locate the folder containing the screensaver files and dump my own in there. It turns out Amazon does not want you poking around in there, so that folder is hidden.

Fortunately, after a little research online, I was able to hack into my Kindle and change the screensavers. There are thousands of great images online to choose from (just Google “Kindle screensavers”), and I had a blast exploring them. Then it occurred to me that I could create my own fractal screensavers – all that is necessary is to make sure they are gray-scale images that are 600 by 800 in size.

I decided to use Chaoscope to create my screensavers. (I posted a tutorial on how to use Chaoscope here.) Make sure you render them in either Gas or Liquid mode. My first batch is posted below. They are already correctly sized – just click on a thumbnail to access the full-size image, and then save it to your computer. Enjoy!

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Keeping Parents In The Loop

I’ve been a math teacher for 30 years now, and I’ve also been a parent of a math student. I know from experience that high school students don’t rush home every afternoon to share with their parents what they’ve learned that day! So, in order to foster parent/teacher communication and parent/child communication this year, I’ve been emailing newsletters to the parents of my students.

They aren’t long or complicated, but they always have three components:

  1. A quick summary of what we’ve covered since the last newsletter;
  2. A topic or concept parents can discuss with their child;
  3. An interesting website, article, or blog that is math-related.

The response from parents has been very positive, and it’s well worth the time it takes to put together. I use GeoGebra to create the illustrations, and if I want to link to an interactive applet, http://tube.geogebra.org/ has thousands to choose from. One word of advice: make sure you put your recipients’ email addresses in the bcc address box to protect their privacy.

Here’s the latest one I just sent to the parents of my geometry students:

Greetings, Parents of my Geometry Students,

It’s hard to believe we have finished our first quarter. One down, three to go!
We are wrapping up Chapter 3, which is all about parallel lines and angles. When you have two parallel lines intersected by a transversal, all kinds of congruent and supplementary angles are formed. Ask your daughter to point out to you which angles are congruent in the figure below, and which ones are supplementary (adding up to 180 degrees):

Parallel

We also learned why all the interior angles of a triangle always add up to 180 degrees. The figure below is a visual proof of this (if you don’t get it, ask your daughter for help!):

Interior angles

One of the most amazing facts in Euclidean geometry is that the sum of a polygon’s exterior angles is 360 degrees, regardless of how many sides the polygon has. It seems counter-intuitive, but to see why, click here, and drag the slider in the applet (created by Aeolus Ophion).
In our next chapter, we will be exploring triangles and all the ways we can prove that they are congruent.
For the cool math site of this edition of the HH Geometer, click here.
Have a restful Fall Break!

Winning and Losing

An excellent reflection by the Director of our Upper School on winning and losing, and the lessons to be gained.

Bears Repeating

Part of growing up is learning how to play the game. When teaching a young child how to play a card or board game, we usually begin with games of luck. With no real skill involved in these games, a child is able to discover, in a non-threatening environment, that she sometimes wins and sometimes loses. The goal is not as much about memorizing the rules of the game as it is about learning how to behave when we win or lose.

We have seen children, young adults, and older adults win and lose well and not so well.   Winning gracefully is always the easiest, but even that can become challenging when it happens too often in a short period of time. Coaches never want to be the undefeated team going into the finals in a tournament. Feelings of overconfidence can quickly and quietly soften our drive and resolve.   Let’s…

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Sequences Leading Up to Series

You get a two-fer in this post: my regular precalculus class is getting ready to tackle sequences and series. Even though both topics are covered in one section of the text, I decided to split them into two separate screencasts. Sequences are fascinating things – they pop up in nature all the time (try Googling “Fibonacci Sequence”). Series are just sums of sequences, and for centuries mathematicians much smarter than I have found ways to determine those sums without actually adding together infinite terms!