Search results
Results From The WOW.Com Content Network
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
The area of the triangle is times the length of any side times the perpendicular distance from the side to the centroid. [15] A triangle's centroid lies on its Euler line between its orthocenter and its circumcenter, exactly twice as close to the latter as to the former: [16] [17]
A 3-orthoscheme is a tetrahedron where all four faces are right triangles. A 3-orthoscheme is not a disphenoid, because its opposite edges are not of equal length. It is not possible to construct a disphenoid with right triangle or obtuse triangle faces.
A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry , a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane , a tetrahedron for points in three-dimensional space , etc.).
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
[3] [4] The internal angle of an equilateral triangle are equal, 60°. [5] Because of these properties, the equilateral triangles are regular polygons. The cevians of an equilateral triangle are all equal in length, resulting in the median and angle bisector being equal in length, considering those lines as their altitude depending on the base ...
[21] [22] A tetrahedron or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base. Because the faces are regular, it is an example of a Platonic solid and deltahedra, and it has tetrahedral symmetry. [23] [24] A pyramid with the base as circle is known as ...
The Nagel point is the isotomic conjugate of the Gergonne point.The Nagel point, the centroid, and the incenter are collinear on a line called the Nagel line.The incenter is the Nagel point of the medial triangle; [2] [3] equivalently, the Nagel point is the incenter of the anticomplementary triangle.