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"I share the view of Pythagoras that the world is number. The ultimate substrate of the universe is math. There's no way to test that - it's pure metaphysical speculation."
- Bart Kosko

Orbital Mirror  
  A huge reflective surface in orbit around a planet or moon, the purpose of which is to focus sunlight onto the surface.  

This is the earliest use of this idea in science fiction that I know of, but it was not originated by sf authors.

That ship was quite something. There may be a few of them left - bulky old KH-type ore carriers. The series has been discontinued now, but it seems to me I saw one or two of them on the inter-asteroid runs a few years ago. Her capacity was something like two hundred thousand tons net and she was loaded to the ceil-plates with granular magnesium and sodium for the Sun mirrors of Titan. I don't have to tell you about the seven two-mile-diameter orbital mirrors that circulate around the satellite, making it habitable. You may not know, though, that the girders are all solid mag, because great rigidity isn't needed out there, and mag is cheap. The mirrors are silvered with sodium, which is bright and easy to handle. They have a patrol for each of the mirrors, which patches up meteorite punctures when they occur, squirting liquid sodium around the holes until they fill, then shaving them down with N rays. Well, we were bringing them their stock in trade, and it was interesting cargo to handle.
Technovelgy from Completely Automatic, by Theodore Sturgeon.
Published by Astounding Science-Fiction in 1941
Additional resources -

In 1923, German physicist Hermann Oberth described space mirrors with a diameter of 100 to 300 km in his book Die Rakete zu den Planetenräumen, consisting of a grid network of individually adjustable mirrors. Space mirrors in orbit around the Earth are intended to focus sunlight on individual regions of the earth's surface.

Here's another use of this term, from Star Wars: Revenge of the Sith by Mathew Stover (2005):

The skies of Coruscant blaze with war.

The artificial daylight spread by the capital's orbital mirrors is sliced by intersecting flames of ion drives and punctuated by starburst explosions...

Compare to the electrono-mirror from The Day We Celebrate, by Nelson S. Bond (1941).

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Additional resources:
  More Ideas and Technology from Completely Automatic
  More Ideas and Technology by Theodore Sturgeon
  Tech news articles related to Completely Automatic
  Tech news articles related to works by Theodore Sturgeon

Orbital Mirror-related news articles:
  - NYC Heliostats And Star Wars Orbital Mirrors
  - Crowdfunded Russian Beacon Satellite Is An Orbital Mirror

Articles related to Space Tech
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Solar-Powered Space Trains On The Moon
JWST Finds Bucking Centaur 29P/Schwassmann-Wachmann 1
First Trips To Mars Announced By Elon Musk

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