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The Incredible Umbrella (1979)
Marvin Kaye

Contributed by Vijay Fafat

An English professor, one Mr. Phillimore, finds a magical umbrella which can whisk him away to fictional worlds. Deux ex Machina, and thence, a series of adventures follows, ending in Flatland. The professor is convinced Sherlock Holmes' arch enemy, the evil mathematician Moriarty, did not die during his fall over Reichenbach Falls but instead, had a similar magical umbrella and is now using it to go through the lands of literature. Why does he believe this? He explains:

(quoted from The Incredible Umbrella)

“Moriarty himself prefigured the possibility of a dimensional transfer engine in his brilliant paper on The Dynamics of an Asteroid. Not in so many words, you understand, but the concept was buried within if one had the comprehension and the philosophical tools to prize it forth. The Professor certainly foresaw the ramifications of his theory', at least in this interesting—and rather distressing—side-channel of his research.”

As he chases Moriarty into Flatland, Phillimore finds himself surrounded by a hostile army of isosceles triangles:

(quoted from The Incredible Umbrella)

“They stopped quite close to the professor and as they did, Phillimore noted their dimensionality, inferred their shape. They were not lines after all, but rather a great array of narrow triangles, probably isosceles, and they all had their deadly points aimed at him. They only appeared as lines because he was eye-level with their perimeters. If he could rise straight up and hover over them, he would be able to view them as the triangles they must certainly be from above [...] Now Phillimore knew precisely where he was. Flatland. ‘‘Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard and with luminous edges—” He remembered quite well the satirical masterpiece by one Edwin A, Abbott. ”

It turns out that his entry has suddenly disrupted the revolution Moriarty had started fomenting in Flatland. Since the flatlanders are unable to understand his speech, Phillimore gets imprisoned in a 2-dimensional mental institution, alongside the narrator of the original Flatland story, A Square. He is subsequently rescued by Sherlock Holmes, Moriarty dies at the points of an isosceles triangle and all’s well that ends in the epilogue of Fairyland.

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Works Similar to The Incredible Umbrella
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. The Phantom Tollbooth by Norton Juster / Jules Feiffer (Illustrator)
  2. Arcadia by Iain Pears
  3. The Ultimate Crime by Isaac Asimov
  4. The Adventure of the Russian Grave by William Barton / Michael Capobianco
  5. Professor and Colonel by Ruth Berman
  6. Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott
  7. Threshold by Sara Douglass
  8. Operation Chaos / Operation Changeling by Poul Anderson
  9. Three times table by Sara Maitland
  10. Napier's Bones by Derryl Murphy
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MotifEvil mathematicians, Sherlock Holmes,

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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

(Maintained by Alex Kasman, College of Charleston)