Distance Ratios
The isodynamic points were originally defined from certain equalities of ratios (or equivalently of products) of distances between pairs of points. If and are the isodynamic points of a triangle, then the three products of distances are equal. The analogous equalities also hold for . Equivalently to the product formula, the distances, and are inversely proportional to the corresponding triangle side lengths, and .
and are the common intersection points of the three circles of Apollonius associated with triangle of a triangle, the three circles that pass through one vertex of the triangle and maintain a constant ratio of distances to the other two vertices. Hence, line is the common radical axis for each of the three pairs of circles of Apollonius. The perpendicular bisector of line segment is the Lemoine line, which contains the three centers of the circles of Apollonius.
Read more about this topic: Isodynamic Point
Famous quotes containing the words distance and/or ratios:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)
“Typography is not only a technology but is in itself a natural resource or staple, like cotton or timber or radio; and, like any staple, it shapes not only private sense ratios but also patterns of communal interdependence.”
—Marshall McLuhan (1911–1980)