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Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

A Tychonoff plank is a topological space that is an example of a normal space which has a non-normal subset, thus showing that normality is not a hereditary property. Let ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

Several differing definitions of almost planar (as well as nearly planar) have been used in the literature (cf. Lipton et al. 2016). For example, Gubser (1996) defines an ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

The area moment of inertia is a property of a two-dimensional plane shape which characterizes its deflection under loading. It is also known as the second moment of area or ...