Isotomic lines
Encyclopedia
In geometry
, the isotomic lines of a point
in relation to a triangle
are the cevian
s through the point from each polygon
vertex
which meet the opposite sides. The isotomic conjugate
can be constructed from the iscotomic lines.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the isotomic lines of a point
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
in relation to a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
are the cevian
Cevian
In geometry, a cevian is any line segment in a triangle with one endpoint on a vertex of the triangle and the other endpoint on the opposite side. Medians, altitudes, and angle bisectors are special cases of cevians...
s through the point from each polygon
Polygon
In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...
vertex
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...
which meet the opposite sides. The isotomic conjugate
Isotomic conjugate
In geometry, the isotomic conjugate of a point P not on a sideline of triangle ABC is constructed as follows: Let A, B, C be the points in which the lines AP, BP, CP meet the lines BC, CA, AB, respectively. Reflect ABC in the midpoints of sides BC, CA, AB to obtain points A", B", C", respectively...
can be constructed from the iscotomic lines.