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If the square is instead erected internally, their centers form a triangle DeltaI_AI_BI_C that has (exact) trilinear vertex matrix given by (1) (E. Weisstein, Apr. 25, 2004). ...

The points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_(175) (Kimberling 1994) and has equivalent ...

The inner Soddy circle is the circle tangent to each of the three mutually tangent circles centered at the vertices of a reference triangle. It has circle function ...

The dot product can be defined for two vectors X and Y by X·Y=|X||Y|costheta, (1) where theta is the angle between the vectors and |X| is the norm. It follows immediately ...

A particular type of automorphism group which exists only for groups. For a group G, the inner automorphism group is defined by Inn(G)={sigma_a:a in G} subset Aut(G) where ...

The inner Napoleon circle, a term coined here for the first time, is the circumcircle of the inner Napoleon triangle. It has center at the triangle centroid G (and is thus ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

The interior product is a dual notion of the wedge product in an exterior algebra LambdaV, where V is a vector space. Given an orthonormal basis {e_i} of V, the forms ...

The inner Napoleon triangle is the triangle DeltaN_AN_BN_C formed by the centers of internally erected equilateral triangles DeltaABE_C, DeltaACE_B, and DeltaBCE_A on the ...