| 词条 | Splitter (geometry) |
| 释义 |
In plane geometry, a splitter is a line segment through one of the vertices of a triangle (that is, a cevian) that bisects the perimeter of the triangle.[1][2] PropertiesThe opposite endpoint of a splitter to the chosen triangle vertex lies at the point on the triangle's side where one of the excircles of the triangle is tangent to that side.[1][2] This point is also called a splitting point of the triangle.[2] It is additionally a vertex of the extouch triangle and one of the points where the Mandart inellipse is tangent to the triangle side.[3] The three splitters concur at the Nagel point of the triangle,[1] which is also called its splitting center.[2] GeneralizationSome authors have used the term "splitter" in a more general sense, for any line segment that bisects the perimeter of the triangle. Other line segments of this type include the cleavers, which are perimeter-bisecting segments that pass through the midpoint of a triangle side, and the equalizers, segments that bisect both the area and perimeter of a triangle.[4] References1. ^1 2 {{citation | last = Honsberger | first = Ross | author-link = Ross Honsberger | contribution = Chapter 1: Cleavers and Splitters | pages = 1–14 | publisher = Mathematical Association of America | title = Episodes in Nineteenth and Twentieth Century Euclidean Geometry | year = 1995}}. 2. ^1 2 3 {{citation | last = Avishalom | first = Dov | issue = 1 | journal = Mathematics Magazine | jstor = 2688140 | mr = 1571272 | pages = 60–62 | title = The perimetric bisection of triangles | volume = 36 | year = 1963}}. 3. ^{{citation | last = Juhász | first = Imre | journal = Annales Mathematicae et Informaticae | mr = 3005114 | pages = 37–46 | title = Control point based representation of inellipses of triangles | url = http://ami.ektf.hu/uploads/papers/finalpdf/AMI_40_from37to46.pdf | volume = 40 | year = 2012}}. 4. ^{{citation | last = Kodokostas | first = Dimitrios | doi = 10.4169/002557010X482916 | issue = 2 | journal = Mathematics Magazine | pages = 141–146 | title = Triangle equalizers | volume = 83 | year = 2010}}. External links
1 : Triangle geometry |
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