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,
Alan (given name) century, where it was about even with "Simon", and more numerous than "Henry". Early occurrences of the name in British records include: "Alanus" in 1066 (in the "Domesday Book"); and "Alain" in 1183. The name became popular in Scotland in part through the Stewarts. This family descends from Alan fitz Flaad, an Anglo-Breton knight, who possessed lands in what is modern day Shropshire, England. Alan (given name) Alan is a masculine given name in the English language. There are numerous differing etymologies attributed to the name. The name was first introduced into England by Bretons who took part in the