Archive for the ‘Technology’ Category

Fun With Geogebra: Cardioid Tortilla

Somewhere out there a tortilla maker is striving to make a perfect Cardioid Tortilla.

But there is still work to do.

Click here to see more in Appreciation.

Ancient Lego Robotics

June 16, 2012 2 comments

The antikythera machine is commonly referred to as the “world’s oldest computer”.  Dating back to around 150 B.C., the mechanism was discovered in a shipwreck around 1900, and it has amazed scientists and engineers with its precision craftsmanship.  Recent x-ray analyses of the object helped bolster the conclusion that it was designed to predict eclipses, and probably was able to do so with remarkable accuracy.

What could be more amazing than a 2000 year old computer?  Perhaps this working replica of it, made entirely out of legos.

This video shows the functioning lego replica and gives some of the mathematical background relevant to how the machine operates (apparently the ratio 5/19  is extremely important for calculating the cycles of ellipses) .  Throughout the video, the machine is deconsrtucted and you can see the inner-workings of the various parts.  Truly amazing.

Click here to see more in Technology.

Cool Graphs of Implicit Relations

This is a cool collection of graphs of relations using software called GrafEq:

For example, at the right is the graph of

e^{sinx + cosy} = sin(e^{x+y}).

There are several other cool graphs displayed here, and one commenter points out that WolframAlpha can graph these relations, too.  For example, the here’s the W|A rendering of the above equation:

W|A captures the spirit of the graph here, although the image is not as detailed or attractive as the GrafEq version.

Click here to see more in Appreciation.

More Free E-Books

This site has hundreds, if not thousands, of free e-books on a wide range of topics:

In addition to hundreds of math e-books on topics such as Linear Algebra, Geometry, Applied Mathematics, and Probability Theory, there are also selections of free books on many Computer Science topics, Chemistry, Physics, Languages, and much more!

Click here to see more in Resources.

Visualizing Ocean Currents

April 23, 2012 1 comment

This is a beautiful representation of ocean currents around the world:

Put together by the NASA/Goddard Space Flight Center Scientific Visualization Studio, this short video circles the digital globe, showing the relative strengths and directions of ocean movement.

Watching this allows one to see some of the basic mathematics of fluid flow, like tendency toward rotation and how fluid behaves at boundaries.  In addition, global phenomena like the jet stream and trade winds can also be perceived.

This dynamic representation of data is similar to this wind map in how it brings to life the ideas of vector fields and flow lines.

Click here to see more in Representation.

Notes on the Digital Department

Collaboration and sharing with virtual colleagues has become an invaluable part of my professional life.  Like so many others, I turn to social media for teaching ideas, mathematical conversation, and a supportive and constructive space to reflect.

The extent to which this works continues to amaze me.  And every now and then something happens that reminds me just how remarkable it is.

Recently, I received an email from an English teacher in my school whom I’d never met.  Apparently this teacher had been using 12 Ways to Use the New York Times to Develop Math Literacy with her students all year, completely unaware of my connection to it!  Only because we share a student in common were we ever made aware of our indirect collaboration.

Hopefully as tools and practices continue to grow and expand, the gap between the physical and the digital school will continue to close.  Until then, there are sure to be many more amusing moments like this!

Click here to see more in Teaching.

Statistically Solving Crossword Puzzles

I am lover of crossword puzzles.  I do the NYT crossword puzzle regularly, I’ve competed in the American Crossword Puzzle Tournament, and I’ve even dabbled in constructing puzzles myself.

There’s a great deal of crossover between math lovers and crossword puzzle lovers, and one example of this crossover is Matthew Ginsberg.  Ginsberg is a regular puzzle constructor, has a PhD in math from Oxford, and is an expert in artificial intelligence.

Not a huge stretch, then, that he has developed a rather effective crossword puzzle solving robot, Dr. Fill, that is now challenging the top human performers .

Ginsberg runs a company that produces software for the Air Force that helps calculate the most efficient flight path for airplanes.  Here’s the cool part:  “Some of the statistical techniques [used to calculate optimal paths of airplanes] are also handy, it turns out, for solving crossword puzzles.

Yet another example of how statistical reasoning is emerging as primary tool in modern science and society!

Click here to see more in Application.

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