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Discussion of Problem 1285. Thread in a Hyperspace

Vladimir Yakovlev (USU) Problem 1285 "Thread in a Hyperspace" has been rejudged [2] // Problem 1285. Thread in a Hyperspace 30 Apr 2018 01:04
New tests have been added to the problem which exploit a common mistake when using acos function. Hint: try to calculate acos(sqrt(3.0) * sqrt(3.0) - 4.0) in your programming language. 269 authors (58%) with accepted solutions have been challenged.
Why is this a mistake?

How to modify the solution to avoid the mistake? Who knows?
OK, just need to add a clamp for acos' arg.