See Curve of constant width.
I do not understand and cannot visualize the complicated contraption described at the end of Poul Anderson's "The Three-Cornered Wheel": a wheelless wagon using constant-width polygons (V, p. 245), moving on eight revolving rollers (VII, p. 259) - although I thought that rollers were round and forbidden? No:
"Each roller had three curved sides." (p. 259)
- but:
"They revolved between planks..." (p. 259)
Does one plank slide along the ground under the rollers? No, there is further explanation which I do not follow. The narrator is still directly addressing the reader with instructions about drawing arcs on the sides of an equilateral triangle on the last page of the story.
A visual adaptation of this story would have to show the vehicle. A screen adaptation would have to show it moving. Would it have to be built to be filmed? How can seventeen year old Davy Falkayn think of something that no one else does?
Martin Schuster initiates two conceptual revolutions:
Kepler's laws and Newtonian gravitation presented as mathematical fictions to astronomers who still believe in circular orbits with their sun at the center of the universe;
the Kabbalah presented to beings who are already monotheists.
Falkayn conceives of a third: the argument that circles are not perfect but imperfect because they are degenerations from higher-order forms.
I found Shuster's Kabbalah exposition completely unconvincing but the idea is that it might intrigue the dogmatic Consecrates.
1 comment:
Kaor, Paul!
As one of the other characters said in the story, Falkayn was able to think of the complex device he described because he was closer to textbook geometry and maths and the examples such works would show than the older men. Such things would naturally fade away as years passed.
Yes, such a device as the kind described by Falkayn would need to be actually built and used in any filmed version of "The Three-Cornered Wheel" for it to make sense.
Yes, things like the Kabbalah are unconvincing to me as well, but the Consecrates of a long stagnant Larsum, on Ivanhoe, unused to new and strange ideas, could well find it intriguing! Some of them, anyway.
Ad astra! Sean
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