In geometry, the Petersen–Morley theorem states that, if , ,
are three general skew lines in space, if , , are the lines of shortest distance respectively for the pairs , and , and if , and are the lines of shortest distance respectively for the pairs , and , then there is a single line meeting at right angles all of , , and .
The theorem is named after Johannes Hjelmslev (who published his work on this result under his original name Johannes Trolle Petersen) and Frank Morley.
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