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,
Floyd's triangle of an "n" × "n" magic square . Summing up the row sums in Floyd's triangle reveals the doubly triangular numbers (triangular numbers with an index that is triangular) 1 = 1 = T(T(1)) <br><br><br> 1 = 6 = T(T(2)) <br> 2 + 3 <br><br><br> 1 <br> 2 + 3 = 21 = T(T(3))<br> 4 + 5 + 6 <br> Floyd's triangle Floyd's triangle is a right-angled triangular array of natural numbers, used in computer science education. It is named after Robert Floyd. It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1