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"Self-education is, I firmly believe, the only kind of education there is."
- Isaac Asimov

Half-Sphere Force Field  
  A protective force field that can manifest even as a half-sphere.  

Anybody can make a spherical force field, but I enjoyed this brief excursion into solid geometry from Heinlein.

There flickered into being over the bench, hanging in the air unsupported, a silvery ball some two feet across... it made Don think of a Christmas tree ornament.

...Conrad bent over the controls. "Act two," he announced. "We now cancel out half of the locus..." Another shape took being, a perfect half-sphere otherwise like the last.

From Between Planets, by Robert Heinlein.
Published by Charles Scribner's Sons in 1951
Additional resources -

It is invulnerable to harm, and ordinary processes (like a burning cigarette) inside the sphere are uninterrupted. And how does it work?

"...There is no popular way to explain it. If you were willing to spend five hard years with me, working up through the math, I could probably bring you up to the same level of ignorance and confusion that I enjoy. Some of the tensor equations involved are, to put it mildly, unique..."

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Additional resources:
  More Ideas and Technology from Between Planets
  More Ideas and Technology by Robert Heinlein
  Tech news articles related to Between Planets
  Tech news articles related to works by Robert Heinlein

Half-Sphere Force Field-related news articles:
  - Trophy Active Defense System Not Quite A Force Field

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