“Schiffler point”的意思、由来-开放百科全书

词条

Schiffler point

释义

Definition
Coordinates
References
External links

In geometry, the Schiffler point of a triangle is a triangle center, a point defined from the triangle that is equivariant under Euclidean transformations of the triangle. This point was first defined and investigated by Schiffler et al. (1985).

Definition

A triangle ABC with the incenter I has its Schiffler point at the point of concurrence of the Euler lines of the four triangles BCI, CAI, ABI, and ABC. Schiffler's theorem states that these four lines all meet at a single point.

Coordinates

Trilinear coordinates for the Schiffler point are

or, equivalently,

where a, b, and c denote the side lengths of triangle ABC.

References

{{cite journal

|author1=Emelyanov, Lev |author2=Emelyanova, Tatiana | title = A note on the Schiffler point
| journal = Forum Geometricorum
| volume = 3
| year = 2003
| pages = 113–116
| mr=2004116
| url = http://forumgeom.fau.edu/FG2003volume3/FG200312index.html}}

{{cite journal

| author1=Hatzipolakis, Antreas P.
| author2=van Lamoen, Floor
| author3=Wolk, Barry
| author4=Yiu, Paul
| title = Concurrency of four Euler lines
| journal = Forum Geometricorum
| volume = 1
| year = 2001
| pages = 59–68
| mr=1891516
| url = http://forumgeom.fau.edu/FG2001volume1/FG200109index.html}}

{{cite journal

| author = Nguyen, Khoa Lu
| title = On the complement of the Schiffler point
| journal = Forum Geometricorum
| volume = 5
| year = 2005
| pages = 149–164
| mr=2195745
| url = http://forumgeom.fau.edu/FG2005volume5/FG200521index.html}}

{{cite journal

| author = Schiffler, Kurt
| lastauthoramp=yes
| title = Problem 1018
| year = 1985
| journal = Crux Mathematicorum
| volume = 11
| pages = 51
|url = https://cms.math.ca/crux/backfile/Crux_v11n02_Feb.pdf }}

{{cite journal

| author1=Veldkamp, G. R.
| author2=van der Spek, W. A.
| lastauthoramp=yes
| title = Solution to Problem 1018
| year = 1986
| journal = Crux Mathematicorum
| volume = 12
| pages = 150–152
|url = https://cms.math.ca/crux/backfile/Crux_v12n06_Jun.pdf}}

{{cite journal

| author = Thas, Charles
| title = On the Schiffler center
| journal = Forum Geometricorum
| volume = 4
| year = 2004
| pages = 85–95
|mr=2081772
| url = http://forumgeom.fau.edu/FG2004volume4/FG200412index.html}}

External links

{{MathWorld|title=Schiffler Point|urlname=SchifflerPoint}}

1 : Triangle centers

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。