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

Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle ...

The pentagonal prism is a prism having two pentagonal bases and five rectangular sides. It is a heptahedron. The regular right pentagonal prism is uniform polyhedron U_(76). ...

A quartic algebraic curve also called the peg-top curve and given by the Cartesian equation a^4y^2=b^2x^3(2a-x) (1) and the parametric curves x = a(1+sint) (2) y = ...

A primitive right triangle is a right triangle having integer sides a, b, and c such that GCD(a,b,c)=1, where GCD(a,b,c) is the greatest common divisor. The set of values ...

The Latin prefix quadri- is used to indicate the number 4, for example, quadrilateral, quadrant, etc. However, it also very commonly used to denote objects involving the ...

The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...

The regular hendecagon is the regular polygon with 11 sides, as illustrated above, and has Schläfli symbol {11}. The regular hendecagon cannot be constructed using the ...

The regular octagon is the regular polygon with eight sides, as illustrated above. The inradius r, circumradius R, and area A of the regular octagon can be computed directly ...

The second Morley triangle is made by rotating line BC toward vertex A about vertex B by angle (B+2pi)/3. It is an equilateral triangle. It has trilinear vertex matrix [1 ...