isodynamic การใช้

• A map of intensity contours is called an " isodynamic chart ".
• The isogonal conjugates of the Fermat points are the isodynamic points and vice versa.
• The two isodynamic points are inverses of each other relative to the circumcircle of the triangle.
• The second isodynamic point may be constructed similarly but with the equilateral triangles erected outwards rather than inwards.
• That is, the isodynamic point is the point for which the harmonic measure of the three arcs is equal.
• This line is perpendicular to the radical axis defined by the isodynamic points S and S ^ { \ prime }.
• All three circles pass through two points, denoted as the isodynamic points S and S ^ { \ prime } of the triangle.
• Among all the equilateral triangles inscribed in triangle ABC, the pedal triangle of the first isodynamic point is the one with minimum area.
• This usage could also be justified on the ground that the isodynamic points are related to the three Apollonian circles associated with a triangle.
• In the literature, the term " " Apollonius points " " has also been used to refer to the isodynamic points of a triangle.
• The line A'A " crosses the similarly constructed lines B'B " and C'C " at the first isodynamic point.
• The 2nd Brocard cubic passes through the centroid, symmedian point, both Fermat points, both isodynamic points, the Parry point, other triangle centers, and the vertices of the 2nd and 4th Brocard triangles.
• The angles formed by the first isodynamic point with the triangle vertices satisfy the equations ASB = ACB + \ pi / 3, ASC = ABC + \ pi / 3, and BSC = BAC + \ pi / 3.
• The pedal triangle of an isodynamic point, the triangle formed by dropping perpendiculars from S to each of the three sides of triangle ABC, is equilateral, as is the triangle formed by reflecting S across each side of the triangle.
• If a circle is partitioned into three arcs, the first isodynamic point of the arc endpoints is the unique point inside the circle with the property that each of the three arcs is equally likely to be the first arc reached by a Brownian motion starting at that point.
• An "'isodynamic tetrahedron "'is one in which the cevians that join the vertices to the concurrent, and an "'isogonic tetrahedron "'has concurrent cevians that join the vertices to the points of contact of the opposite faces with the inscribed sphere of the tetrahedron.
• The Neuberg cubic passes through the following points : incenter, circumcenter, orthocenter, both Fermat points, both isodynamic points, the Euler infinity point, other triangle centers, the excenters, the reflections of " A ", " B ", " C " in the sidelines of " ABC ", and the vertices of the six equilateral triangles erected on the sides of " ABC ".
• In this approach the symmetry groups are known as " Schr鰀inger supergroups " and consist of two types of operations ( and their combinations ) : ( 1 ) the geometric symmetry operations ( rotations, reflections, inversions ) of rigid molecules, and ( 2 ) " isodynamic operations ", which take a nonrigid molecule into an energetically equivalent form by a physically reasonable process such as rotation about a single bond ( as in ethane ) or a molecular inversion ( as in ammonia ).