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The radian is a unit of angular measure defined such that an angle of one radian subtended from the center of a unit circle produces an arc with arc length 1. A full angle is ...

The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

The trace of a second-tensor rank tensor T is a scalar given by the contracted mixed tensor equal to T_i^i. The trace satisfies ...

By the definition of the functions of trigonometry, the sine of pi is equal to the y-coordinate of the point with polar coordinates (r,theta)=(1,pi), giving sinpi=0. ...

By the definition of the functions of trigonometry, the sine of pi/2 is equal to the y-coordinate of the point with polar coordinates (r,theta)=(1,pi/2), giving sin(pi/2)=1. ...

Construction of the angle pi/4=45 degrees produces an isosceles right triangle. Since the sides are equal, sin^2theta+cos^2theta=2sin^2theta=1, (1) so solving for ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

The point on a line segment dividing it into two segments of equal length. The midpoint of a line segment is easy to locate by first constructing a lens using circular arcs, ...

The first theorem of Pappus states that the surface area S of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of ...