Another pleasant way to pass the time at the sea: assembling a family of quadrilaterals!
Appreciation Resources
Origami Buckyball
This is a cool video showing the assembly of an origami Buckyball.
http://www.youtube.com/watch?v=Zb2lHNqPm7w
The Buckyball is a geometric form named after the architect, designer, and futurist Buckminster Fuller, who used the shape in his designs. It was later discovered that certain carbon molecules take the shape of buckyballs, and it was even recently confirmed that these molecules existed in deep space.
Related Posts
Application
Kepler’s Planet Search
This is a great poster-style infographic in the New York Times about the how the Kepler telescope looks for planets in space.
http://www.nytimes.com/interactive/2011/01/31/science/space/planet.html
The infographic explains in basic terms how Kepler looks at stars in a small square of space and keeps watch for “flickers” of light as potential planets pass in front of them. Larger objects cause a greater “flicker”, naturally, but the actually decrease in brightness is still small. There are also some nice presentations on confirming the existence of planets and the distribution, by mass, size, and orbit size, of the known exoplanets.
And it’s working: six new planets, and counting!
Challenge Geometry
Geomagic Squares
The magic square is an ancient and well-known mathematical object. In the figure at the right, the sum of every row, column, and diagonal is the same, namely, 30. This is a basic magic square.
Magic squares have been around for thousands of years, and there many variations have been explored. Which makes the invention of a new kind of magic square all the more amazing: the geomagic square.
http://www.newscientist.com/gallery/magical-mathematics/2
These geomagic squares turn the algebraic magic square into something geometrical: instead of numbers summing up to the magic constant in every direction, polygonal tiles can be put together to form the same shape in every direction! Here’s an example.
With some flipping and rotating, every sequence of tiles in this “square” can be arranged to make the same figure, namely, a 4 x 4 square with one small square missing. The example at the right shows the middle row being assembled to form the “magic constant”: the white square in the middle is the missing square.
The natural questions: how do you construct geomagic squares? Can you make a geomagic square for any given “magic constant”? For a given “magic constant”, how many geomagic squares can you create? What others can you think of?
Challenge 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/2011/02/2/test-yourself-math-feb-2-2011/
This problem involves estimating the per-person health care expenditures in the United States.