Geekin' those Conic Sections

I've always been a geek... a serious math geek, and an unapologetic artist. Many a day at ETSU was spent ditching class for the library where I'd research the connections between math and art. Back in high school, my favorite math teacher ever, Mr. Mast, said to me more than once... "Where the hell have you been for the last week?" My reply: "I had to paint." 

So, when I saw what my brilliant blacksmith friend, John Winer (Laughing Crow Forge) was doing with conic sections and curves, I just had to share.

What are conic sections? Conic sections are the elegant shapes that you get when you slice a cone in a straight line. Going back to the Greeks, mathematicians have gone to great lengths to study these shapes. We graph them, write equations for them (click for details), solve problems with them. For example, the lovely parabola can predict the path of a projectile (click for an example), and find the maximum profit in a business situation by modeling  a cost revenue function (another example) . Keppler noticed that the planetary orbits were ellipses. The scientific applications are nearly endless and so much fun... but back to what brought us to this discussion... 

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So, I'm minding my business painting on the mural, John is forging, focusing on a precise curve in what will become a bed, and then there he is with a french curve and a cone mandrel! Turns out, he is using conic sections to create elegant curves in his work as a blacksmith!

He uses the cone to create an infinite number of precision arcs in which there are no kinks in the flow of the line. These precision arcs are all parabolas, hyperbola sections, circles, or ellipses! 

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The classic twist at left shows another of the properties of steel that can be modeled mathematically. I'll post a picture of the bed when it's finished, but for now, maybe the drawing on the shop floor (right) will help us to visualize what it will become. The layout, I should say, was squared up using an application of the Pythagorean Theorem.

A nice example of John's application of elegant curves

...and one of mine, too.

Here are a couple more ways you can have fun with this math and art connection:

          Curve Stitching

For visual folks, curve stitching is a fun and easy way to apply these ideas visually. You can draw curves or use string in cardstock or fabric (or even on a fence!) to create a nice project in an afternoon. Click here for a a nicely done overview and tutorial. 

         Solar Cooker

For a more functional application, here's a video that shows how to make a solar cooker with some cardboard and aluminum foil. The reflective material around  your car's headlights, the bulb of your flashlight, and your satellite dish, all capitalize on the fact that a light source placed at the focus of a parabola will bounce light directly out, as illustrated in the diagram,.. or in, as in the application of the solar cooker or a liquid mirror telescope (read about that here). We've had some fun with this one. 

I hope you found something here that interested you, and I look forward to hearing about your adventures!