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Found 4 results

1. Geometry of Pasta

How might one manage to find the surface area and volume of the following constructs? Rotini: A geometric figure I've found to be similar is the helicoid. However, the helicoid (having been formed from a 2D plane) has an edge width equal to epsilon, whereas the edges of a fully 3D rotini-like construct would be roughly catenarian in shape. Fusillibucati/Cavatappi: The only difference between the two is length. Cavalieri's principle could possibly be at play here, but the topography could potentially suggest otherwise. Campanelle: No hints for this one, good luck. Casarec
2. Smooth Earth

If all the matter on earth were reassembled uniformly so as to possess a (virtually) perfectly smooth surface (with densities changing as is necessary for the planet's stability, but otherwise also uniform), how would the size and volume change? Furthermore, how apparent would the curve of the planet's surface be from an average human's perspective? Additional thought experiment: What is the farthest distance two points on the surface of the sphere could be from each other, before two average humans holding two ends of a long cellulose fiber rope located on these points would not be ab
3. Seemingly Unnamed Toroid(?) Structure

Is there a specific name for this 3D shape, which appears to be an elliptical torus twisted into a sort of spiral? Additionally, how would one go about graphing a structure like this?
4. Seemingly Unnamed Apeirohedron

What is the specific name of this particular apeirohedron? I've had no luck with reverse image searches, all the results simply list it as "apeirohedron" or "infinite skew polygon" (another name for apeirohedron). Does it not have a specific name? Additionally, how would one go about graphing this shape?
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