Thursday, March 7, 2013

French curves revisited

Go to a store that sells school supplies you may notice bags of tools for architecture students. Ah, the 30-60-90 and 45-45-90 triangle. I know these special triangles since high school. (Are you able to tell why they are so special?) Come on, you know the compass and protractor. The triangular architect ruler is not for drawing, but for measuring. In modern times students probably all just go to the computer and not need to bother to draw by hand anyway. I am afraid that store won't sell a lot of these. But one curious tool is the French curve. I never knew where it came from. In real life, circles and lines just don't cut it... curves are needed. They are used to draw curves... but why that shape? I decide to find out.

Sure you can look it up too. Oh my it is based on the Euler Spiral. It is Euler again! Yes the guy who has a constant named after him: e, among many other things. Look, this Euler Spiral is how people build curves for roller coasters and highways. Uh, I admit I am not totally understand everything about the spiral here. (Yikes I feel so uneducated) But you see those integrals? Calculus was here.

To the guy who dare to ask me: "Tell me one use of calculus." On that day I wasn't able to tell right away on top of my head instantly... other than, "it allows you to solve problems not able to solve without". Here you go!

Look at this graphical presentation. I am very impressed.

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