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!

bubble sort dance

And just to be thorough, the troupe does dance-representations of Insert-Sort,  Shell-Sort, and Select-Sort algorithms as well!

By patrick honner, ago

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).

circle of appolonius

This story is nice reminder that sometimes the best thing to do as a teacher is get out of the student’s way!

By patrick honner, ago

Math Quiz: NYT Learning Network

federal budgetThrough 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?

By patrick honner, ago

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.

CDs -- Right

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”

CDs -- Wavy 1

has the same volume as  the original cylinder.  Now, this object should also have the same volume

CDs -- Wavy 2

however some center-of-mass issues may foil our elegant mathematical demonstration.

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By patrick honner, ago

Math Photo: Solid Family

My niece and I were playing around with Magnaformers and we had just enough to create this family of geometric solids.

Solid Family -- 1

My niece argued that the figures should be ordered from smallest to biggest.  Unimpressed by my argument that they were ordered smallest to biggest, if you considered the number of sides of each figure, she insisted on reordering them and we took another photo.

Solid Family -- 2

For someone who claims not to like math, my niece sure does enjoy playing around with mathematical ideas!

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By patrick honner, ago
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