Math at the Boundary

While in Maine, I took some nice photos of the boundary between the beach and the sea:

Shoreline

It made me think of something I saw a long time ago (maybe on 60 Minutes?) about a scientist who thought deeply about coffee spills on his countertop. The power of the internet helped me locate Sidney Nagel, a physicist who studies the physics of drops, why things get “jammed”, and why a coffee spill leaves a dark ring after it dries.

Is there any way to predict the kind of edge this water will make as it crawls up the beach? Is there any order in this chaos? If this inspires you to great scientific accomplishment, please remember where you got your start.

By patrick honner, ago

The Levytator

LevytatorFrom the “Why Didn’t I Think of This?” files comes the Levytator,

http://www.youtube.com/watch?v=iC_se2zrmLM

The Levytator is a more efficient and flexible take on the escalator.  It runs in a circuit, instead of conveyor-belt style, so you don’t lose half your steps to the useless, upside-down underground path, like in a traditional escalator.  Thus, you get more transportation per square foot of step.

In addition, the interlocking steps are curved and not rectangular, meaning that not only can the Levytator turn around corners, but essentially it can be designed to follow any kind of path a planner might need.

Be sure to check out the video for some cool demonstrations (which remind me a lot of closed-loop integrals).

By patrick honner, ago

The Art of the Ellipse

ellipse -- conicThis article, the first in a series about drawing, is about how important the ellipse is to the artist.

http://opinionator.blogs.nytimes.com/2010/09/23/the-frisbee-of-art/

The author gives a nice, if long, explanation about the significance of the ellipse, but it basically boils down to this:  circles are everywhere. And often, when we are looking at circles, we’re looking at them atilt.  We see projections of the circle, and projections of circles are ellipses.

Think of it this way:  suppose you have a hula hoop and you hold it parallel to the ground.  The shadow you see is circular, but if you tilt the hula hoop, the shadow will change–into an ellipse.

I don’t have a hula hoop, so I made do with a key ring:

Ellipses

As the circular key ring is rotated, it becomes less parallel to the ground; the shadow becomes less circular and more elliptical.  And at the end, the ellipse vanishes–an ellipse eclipse!

By patrick honner, ago

The Self-Replicating Printer

reprapAfter reading a post about 3-D printers, I found out about this assemble-it-yourself 3-D Printer!

http://reprap.org/wiki/Main_Page

Not only is the RepRap cheap to build (people claim it can be done for around $400), but all the software and hardware designs are open-source and free.

But it doesn’t stop there.  If you already have a RepRap, you can use it to build some of the parts you to build another RepRap! In other words, this is a self-replicating machine!  Well, partially at least.

I’m sure there are plenty of people out there with the skills to build one of these themselves.  I’m not sure I’m one of them–after all, building a table that was almost level was a huge success for me.  But this is such a cool idea it might just be worth a shot!

By patrick honner, ago
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