Thursday, March 14, 2013

Turn Me Right Round

What makes for these mathematical mini-obsessions?

Whenever I put something up on, I make sure that I pose questions on
at least 10 posts from other people. (I also never skip. [So will I ever have questioned everything? #anyqs] Though for some it can be hard to find mathematical questions. [Orange.]) On a recent trip I saw Alex Shum's cool revolving door picture.

It reminded me of the problems where you're trying to take a sofa around a corner. (Which reminded me of my very first favorite screensaver, inspired by Douglas Adams, of trying to fit a sofa down a staircase.) Whatever the reason, I immediately wanted to make a GeoGebra sketch.

I made a first pass. That got me wondering how big are those openings? In particular, would a revolving door ever have and opening straight through like the one in the diagram to the left? (Seems to defeat the purpose of a revolving door.)

What are the standards for revolving doors? Thanks to Google and the International Revolving Door Company, I now know more than I ever knew I wanted to know.

In particular:

So much to wonder about these. I love the idea of describing circles as circumscribing a rectangle and it makes perfect sense for construction. But now I want to know about this data. What kind of function is it? Does it make it so the opening is always more narrow the one sector of the door? Is the angle of the opening from the center constant? How do you choose between a 3 wing and 4 wing?

First pass on the data was pretty curious.
Good for making the sketch, but weird. Why would the three wing doors have narrower openings?

GeoGebra sketch for
download or mobile applet
I made a weird little function to give the door openings, 2*radius (0.475 + 0.21 (doors - 3)), so that the ratio is .475 for 3 wings, .685 for four wings.

I liked the opportunity for modeling that this turned into, and it's also a good problem to show where modeling either supports calculation or is more efficient than calculations. Constructing the model in GeoGebra required data fitting, and some algebra to find the appropriate boundaries for the geometric objects.

And it helped me understand why 3 wing doors have narrower opening than 4 wing doors.

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