This is a nice collection of some lovely mathematical images and animations:
There are some knot animations, some 3-D fractals, and some cool surfaces. It seems as though these images and animations were generated in Maple.
There are also some nice images generated in some kind of ray-tracing program that may or may not be called vort.
Vort could also be the name of the person who created all these images. I’m not sure; my Dutch isn’t very good.
I have definitely wasted some time playing around with this: a website that uses side-by-side Google Maps to show a locations’s antipodal point on Earth.
Apparently I was never in any danger of digging my way to China as a young boy. To do that, I would have had to start in Argentina.
Another pleasant way to pass the time at the sea: assembling a family of quadrilaterals!
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?
My love of binder clips makes me appreciate this binder clip sphere even more.
This is another excellent installment of Math Monday at Make Magazine by George Hart, curator of the Museum of Mathematics.
You can find the instructions here.