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The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...

The contrapedal curve, also called a normal pedal curve, is defined analogously to a usual pedal curve with "tangent" replaced by "normal." In particular, the contrapedal ...

An infinite sequence of circles such that every four consecutive circles are mutually tangent, and the circles' radii ..., R_(-n), ..., R_(-1), R_0, R_1, R_2, R_3, R_4, ..., ...

An equation of the form y=ax^3+bx^2+cx+d, (1) where the three roots of the equation coincide (and are therefore real), i.e., y=a(x-r)^3=a(x^3-3rx^2-3r^2x-r^3). (2) Loomis ...

The polar curve r=1+2cos(2theta) (1) that can be used for angle trisection. It was devised by Ceva in 1699, who termed it the cycloidum anomalarum (Loomis 1968, p. 29). It ...

Amazingly, the catacaustic of the deltoid when the rays are parallel in any direction is an astroid. In particular, for a deltoid with parametric equations x = 2cost+cos(2t) ...

The diagonal triangle of a complete quadrangle is the triangle formed by its three diagonal points. If the quadrangle is a cyclic quadrilateral, then the circle is the polar ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...

One of the beautiful arrangements of circles found at the Temple of Osiris at Abydos, Egypt (Rawles 1997). The pattern also appears in Phoenician art from the 9th century BC ...