These cacti caught my. I can see both a dodecagon and a star in the 12-fold symmetry of the cactus in front. And to my surprise, the cactus behind it has thirteen sections!
I wonder about the range, and deviation, of the number of sections of these cacti. And what are the biological principles that govern these mathematical characteristics?
I put the recent snow day, and a snowball maker, to good use!
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What catches my attention in this photo, after the blue and white squares, is how the beams slowly bend away from center. I suppose knowing the size of those beams, and some trigonometry, would allow you estimate the location of the camera.
On a visit to the Lowline, I noticed an interesting application of mathematics above us.
The ceiling is a tiling of hexagons and equilateral triangles. But unlike a typical tiling of a flat bathroom floor, this tiling seems to create a curved surface! Here’s a closer look:
The underlying pattern is hexagonal, but when a hexagon is replaced with six small, hinged equilateral triangles, the surface gains the potential to curve.
It’s interesting to follow the “straight” line paths as they curve over the surface. And since this tiling is suspended from above, it’s interesting to think about what the surface would look like if it were lying on the ground. How “flat” would it be? Or a better question might be “How far from flat is it?”
I love the geometry of this tower crane as it swings around, creating obtuse projections of its perpendicularity. I wonder how accurately I could estimate my altitude from this picture?