“Petersen–Morley theorem”的意思、由来-开放百科全书

词条

Petersen–Morley theorem

释义

References

In geometry, the Petersen–Morley theorem states that, if

{{math|a}},{{math|b}},{{math|c}}

are three general skew lines in space, if

{{math|a′}},{{math|b′}},{{math|c′}} are the lines of shortest distance

respectively for the pairs {{math|(b,c)}}, {{math|(c,a)}} and {{math|(a,b)}},

and if {{math|p}}, {{math|q}} and {{math|r}}

are the lines of shortest distance respectively

for the pairs {{math|(a,a′)}}, {{math|(b,b′)}} and {{math|(c,c′)}}, then there

is a single line meeting at right angles all of

{{math|p}},{{math|q}},

and

{{math|r}}.

The theorem is named after Julius Petersen and Frank Morley.

References

{{cite news | first1=F. | last1=Morley | authorlink = Frank Morley

|year=1897 | journal=Proc. London Math. Soc. | volume = 29 | number=1 | pages=670–673 |title=On a regular rectangular configuration of ten lines | doi=10.1112/plms/s1-29.1.670}}

{{cite news | first1=R. J. | last1=Lyons | first2=R. |last2=Frith

|title= The Petersen–Morley Theorem I|year=1934 | doi=10.1017/S0305004100016601
|pages=192–196 | volume=30 | number=2 | journal=Math. Proc. Camb. Philos. Soc.}}

{{cite news | first1=H. F. |last1=Baker| authorlink=H. F. Baker|title= Verification of the Petersen–Morley Theorem

|year=1935|pages=24–26 | volume=11 | number=1 | journal=Proc. London Math. Soc.
|doi=10.1112/jlms/s1-11.1.24}}{{DEFAULTSORT:Petersen-Morley theorem}}

2 : Mathematical theorems|Theorems in geometry

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