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The mixtilinear triangle is the triangle connecting the centers of the mixtilinear incircles. It has trilinear vertex matrix (1) In has area (2) where Delta is the area of ...

The second Yff triangle is the Cevian triangle DeltaA^'B^'C^' of the second Yff point. The area of the second Yff triangle is Delta=(u^3)/(2R), where R is the circumradius of ...

If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

The Maltese cross curve is the cubic algebraic curve with Cartesian equation xy(x^2-y^2)=x^2+y^2 (1) and polar equation r=2/(sqrt(sin(4theta))) (2) (Cundy and Rollett 1989, ...

The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Archive). It can be used for angle trisection or, more ...

Bubbles can meet only at angles of 120 degrees (for three bubbles) and cos^(-1)(-1/3) approx 109 degrees28^'16^('') (for four bubbles), where cos^(-1)(-1/3) is the ...

The path traced out by a point P on the edge of a circle of radius b rolling on the outside of a circle of radius a. An epicycloid is therefore an epitrochoid with h=b. ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The (m,q)-Ustimenko graph is the distance-1 or distance-2 graph of the dual polar graph on [C_m(q)] (Brouwer et al. 1989, p. 279). The Ustimenko graph with parameters m and q ...

A statement about theorems. It usually gives a criterion for getting a new theorem from an old one, either by changing its objects according to a rule (duality principle), or ...