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Triangle geometry is the study of the properties of triangles, including associated triangle centers, triangle lines, central circles, triangle cubics, and many others. These ...

The regular dodecahedron, often simply called "the" dodecahedron, is the Platonic solid composed of 20 polyhedron vertices, 30 polyhedron edges, and 12 pentagonal faces, ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

Cantellation, also known as (polyhedron) expansion (Stott 1910, not to be confused with general geometric expansion) is the process of radially displacing the edges or faces ...

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

Gaussian curvature, sometimes also called total curvature (Kreyszig 1991, p. 131), is an intrinsic property of a space independent of the coordinate system used to describe ...

The gnomon was an L-shaped movable sundial used for astronomical studies. It operated by resting on one leg so that the other pointed vertically upward. By measuring the ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...