Euler line the Euler line is parallel to an acute triangle's side "BC" if and only if formula_43 The locus of the centroids of equilateral triangles inscribed in a given triangle is formed by two lines perpendicular to the given triangle's Euler line. In a right triangle, the Euler line coincides with the median to the hypotenuse—that is, it goes through both the right-angled vertex and the midpoint of the side opposite that vertex. This is because the right triangle's orthocenter, the intersection of its altitudes, falls on the right-angled vertex while its circumcenter, the intersection of its perpendicular bisectors of sides,
Shana (given name) Shana (given name) Shana is a feminine given name of multiple origins. The pronunciation of the name varies depending upon the context and source. According to Bruce Lansky, Shana occurs as a familiar diminutive or form of Shannon, a Gaelic name, meaning "small and wise." It relates to the longest river in Ireland, the Shannon, which earned its namesake from Celtic goddess Sionna, who sought the enchanted hazelnuts of wisdom. Legends vary about the creation of the river, but they all recount the drowning of the Sionna, granddaughter of the great sea god Lir, usually at an undersea well. Some