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Half a circle. The area of a semicircle of radius r is given by A = int_0^rint_(-sqrt(r^2-x^2))^(sqrt(r^2-x^2))dxdy (1) = 2int_0^rsqrt(r^2-x^2)dx (2) = 1/2pir^2. (3) The ...

A small circle is a spheric section that does not contain a diameter of the sphere (Kern and Bland 1948, p. 87; Tietze 1965, p. 25).

Given a triangle DeltaABC with inner and outer Soddy centers S and S^', respectively, the inner Soddy triangle DeltaPQR (respectively, outer Soddy triangle DeltaP^'Q^'R^') is ...

The study of figures on the surface of a sphere (such as the spherical triangle and spherical polygon), as opposed to the type of geometry studied in plane geometry or solid ...

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off ...

The Stammler hyperbola of a triangle is the Feuerbach hyperbola of its tangential triangle, and its center is the focus of the Kiepert parabola, which is Kimberling center ...

The Steiner circle is the central circle with center at the nine-point center X_5 and radius R_S=3/2R, where R is the circumradius of the reference triangle. It is the ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

A toric section is a curve obtained by slicing a torus (generally a horn torus) with a plane. A spiric section is a special case of a toric section in which the slicing plane ...

A Tucker hexagon is a hexagon inscribed in a reference triangle that has sides which are alternately parallel and antiparallel to the corresponding sides of the triangle. ...