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Hofstadter points
In triangle geometry, a Hofstadter point is a special point associated with every plane triangle. In fact there are several Hofstadter points associated with a triangle. All of them are triangle centers. Two of them, the Hofstadter zero-point and Hofstadter one-point, are particularly interesting. They are two transcendental triangle centers. Hofstadter zero-point is the center designated as X(360) and the Hofstafter one-point is the center denoted as X(359) in Clark Kimberling's Encyclopedia of Triangle Centers. The Hofstadter zero-point was discovered by Douglas Hofstadter in 1992.〔
==Hofstadter triangles==
Let ''ABC'' be a given triangle. Let ''r'' be a positive real constant.
Rotate the line segment ''BC'' about ''B'' through an angle ''rB'' towards ''A'' and let ''LBC'' be the line containing this line segment. Next rotate the line segment ''BC'' about ''C'' through an angle ''rC'' towards ''A''. Let ''L'BC '' be the line containing this line segment. Let the lines ''LBC'' and ''L'BC '' intersect at ''A''(''r''). In a similar way the points ''B''(''r'') and ''C''(''r'') are constructed. The triangle whose vertices are ''A''(''r''), ''B''(''r''), ''C''(''r'') is the Hofstadter ''r''-triangle (or, the ''r''-Hofstadter triangle) of triangle ''ABC''.〔
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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