As it turned it into a shadow, I think the sun did a pretty good job preserving the rectangularity of this sign.
Appreciation Representation
Dancing Bubble Sort
This is a fun and whimsical demonstration of bubble sorting through dance!
http://www.youtube.com/watch?v=lyZQPjUT5B4
The dancers arrange themselves in numerical order in the same manner one would bubble sort an unordered list. One by one, each number “compares” himself with the number on his left; if they are out of order, they switch places. Make you’re way down the list, and start again at the front. Repeat until no one switches places and voila! everyone’s in order!
And just to be thorough, the troupe does dance-representations of Insert-Sort, Shell-Sort, and Select-Sort algorithms as well!
Geometry Teaching
A New Solution to an Old Problem
This story makes me feel bad for every time I discouraged a student from a math research project because the topic was too well-known.
http://novinite.com/view_news.php?id=122377
A 19-year old Bulgarian student has solved the 2000-year old Problem of Appollonius in a new and unique way. It is the first new solution in 200 years, and only the fifth known solution overall.
The Problem of Appolonius, essentially, is to construct (with straightedge and compass, only) a circle that is tangent to three given objects. Here is an example of an Appolonius Circle (in red) that has been constructed to be tangent to the three given circles (in black).
This story is nice reminder that sometimes the best thing to do as a teacher is get out of the student’s way!
NYT
Math Quiz: NYT Learning Network
Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
http://learning.blogs.nytimes.com/2011/04/18/test-yourself-math-april-18-2011/
This question is based on the recent budget agreement that avoided a government shutdown. A total of $38 billion was cut from a multi-trilion dollar budget: just how much did we reduce spending?
Appreciation Geometry
CDs and Cavalieri’s Principle: Part 2
After demonstrating Cavalieri’s Principle with empty CD cases, I thought I’d do the same with the actual CDs.
Here we see a bunch of discs stacked up to make a right cylinder.
To compute the volume of this cylinder, it would be sufficient to know (a) the volume of one CD, and (b) the number of CDs in the stack. We would simply multiply the two together to get the volume.
The argument is less obvious, but essentially the same, regardless of how the CDs are stacked! So this “prism”
has the same volume as the original cylinder. Now, this object should also have the same volume
however some center-of-mass issues may foil our elegant mathematical demonstration.
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