When the Enterprise is advised by a passing Klingon vessel that there is strange debris in orbit around a nearby planet, they investigate only to find a piece of a NASA spacecraft emblazoned with the US flag. The planet below has severe weather and an unbreathable atmosphere except for one small area that appears to be inhabitable by humans. Riker, Data and Worf beam down to the surface only to find a single revolving door leading them to the casino floor in the Hotel Royale. They soon find that they are trapped there and cannot exit. As they explore the hotel, they find the remains of a human, dead for several centuries. They also find his diary and a cheap pulp fiction novel that seems to be the story taking place in the hotel itself. Written by
Did You Know?
This episode, airing in 1988, predicts that Fermat's Last Theorem would have gone unsolved for 800 years as of the mid-24th century. It was actually solved in 1993 by Princeton University Professor Andrew Wiles
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After beaming the ship debris aboard, Riker immediately picks it up. But the metal would still be as cold as space (-270 Celcius [-454 Fahrenheit]) which would freeze the skin off of his bare fingers. See more
[Picard and Riker are discussing Fermat's Theorem
Captain Jean-Luc Picard
I find it stimulating. Also, it puts things in perspective. In our arrogance, we feel we are so advanced. And yet, we cannot unravel a simple knot tied by a part-time French mathematician, working alone without a computer.
References The Questor Tapes