In geometry, a set of Johnson circles comprise three circles of equal radius r sharing one common point of intersection H. In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection). If any two of the circles happen to just touch tangentially they only have H as a common point, and it will then be considered that H be their 2-wise intersection as well; if they should coincide we declare their 2-wise intersection be the point diametrically opposite H. The three 2-wise intersection points define the reference triangle of the figure.
Read more about Johnson Circles: Properties, Proofs, Further Properties
Other articles related to "johnson circles, johnson, circle":
... The three Johnson circles can be considered the reflections of the circumcircle of the reference triangle about each of the three sides of the reference triangle ... the vertices of the circum-orthic triangle, and its circumcenter maps onto the vertices of the Johnson triangle ... The Johnson triangle and its reference triangle share the same nine-point center, the same Euler line and the same nine-point circle ...
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“Think of the wonderful circles in which our whole being moves and from which we cannot escape no matter how we try. The circler circles in these circles....”
—E.T.A.W. (Ernst Theodor Amadeus Wilhelm)
“Unlike Boswell, whose Journals record a long and unrewarded search for a self, Johnson possessed a formidable one. His life in London—he arrived twenty-five years earlier than Boswell—turned out to be a long defense of the values of Augustan humanism against the pressures of other possibilities. In contrast to Boswell, Johnson possesses an identity not because he has gone in search of one, but because of his allegiance to a set of assumptions that he regards as objectively true.”
—Jeffrey Hart (b. 1930)