I like the apparent nesting of concentric circles that appears when looking down a long cylindrical pipe. I wonder if it’s possible to find the angle between my sight-line and the central axis of the cylinder by comparing the centers of the various circles?
This is the floor of the butterfly house rotunda at the Detroit Zoo. When we entered the building, a zookeeper began chatting with us, and when he found out I was a math teacher he got very excited: “You are going to like this!” The zookeeper then told me that the pattern was based on the Fibonacci numbers.
I didn’t think much about the substance of his claim, and I generally don’t think much about claims involving the golden ratio that aren’t related to diagonal lengths of pentagons or rhombuses. But after posting this under the original title Fibonacci Flooring, John Sharp’s comments made me realize that I may be unwittingly perpetuating the mythology of the golden ratio.
Following John’s lead, I checked to see if the above spiral was really a golden spiral by loading it into Desmos and seeing if I could fit a golden spiral to it.
Doesn’t look like it! Thus, I have officially changed the title of this photograph to Non-Fibonacci Flooring, and I apologize if I in any way contributed to the cult of the golden ratio. As penance, I will link readers to George Hart’s excellent video debunking of the myth of the Nautilus shell as a golden spiral.
I like the way these ellipses are climbing up their circumscribing cylinder.
And this sculpture puts me in mind of how planes and cylinders intersect: if the plane is perpendicular to the central axis of the cylinder, the intersection is a circle. But if you start to tilt the plane, the circle grows into an ellipse.
While playing around building trains, it occurred to me that one link of curved track was a nice, everyday representation of 
On a recent snowy day, I took a stroll through the park at lunchtime. This lovely round stone caught my eye.
The snow here has accumulated as a spherical cap. I also like how the area under the stone, untouched by snow, is some kind of projection of the sphere. I wonder what we can say about the direction of the snowfall, based on this snowless projection?
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