This was a surprising exhibit at the Liberty Science Center in Jersey City, New Jersey: a fairly simple pulley-system makes this large spherical net expand and collapse.
It definitely caught me off guard the first time! Here’s a lovely video of the sphere in action.
While travelling in Europe, I became fascinated with the variety of toilet-flushing mechanisms I encountered. The typical toilet had a low-flow / high-flow option (which I imagine saves a great deal of water in the long run) , and a lot of creativity emerged in the way this two-flush system was implemented.
While documenting the many ways to flush, I found this rectangular model oddly familiar and appealing.
And then it hit me: this looks like the golden rectangle!
The golden ratio has long been used by artists and architects to create aesthetically pleasing work. It is, after all, the divine proportion. Could it be that these toilet-makers took their cues from the masters of art and math? I had to find out.
I dropped my image into Geogebra and took some measurements.
The total length of the rectangle divided by its height is around 1.71. So, it’s not quite the golden ratio, but it’s pretty close. This flush-design is about 90% divine, I suppose.
Maybe their next design will be closer to the perfect proportion.
This pointilist images puts me in mind of some fundamental ideas of information theory.
Even though you are seeing a limited set of data here, 140 dots, each of uniform color, it is fairly clear what this image represents. (Hint: standing a bit farther back might help!)
A fundamental concept in information theory is the compression of information. Suppose you want to communicate something, like a painting: a mathematical way to do this would be to describe the color of each pixel, in some order. That would require the transmission, reception, and translation of millions, or even billions, of numbers.
Here we see a very complicated and intricate image being communicated with a very small set of data. Finding more efficient ways to pass along (and store) information is more important than ever before, and is a focus of much modern mathematics.
Of course, recognition of this image relies on the experience of the viewer, who must bring the appropriate context to this information in order to decode it. But that is required in all successful communication.
Here is a fully formed Real Analysis course freely offered online:
http://www.webskate101.com/webnotes/home.htmld/home.html
The course includes a sequence of 60 classes with notes, a fully hyper-linked Analysis textbook, and a set of homework assignments.
This resource comes from John Lindsay Orr, a mathematician at the University of Nebraska.
It seems as though this WebNotes platform might be available for other teachers to create their own online courses.
This is a great resource: thousands of free video lectures on a variety of topics from CosmoLearning.
There are over a thousand videos on mathematics, including full courses in Single-Variable Calculus, Vector Calculus, Differential Equations, Trigonometry, Statistics, and the History of Mathematics.
There are also standalone videos on a wide variety of topics like Topology, Probability, and Algebra.
In addition to Mathematics, there are thousands of other videos ranging from Anthropology to Veterinary Medicine!