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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 ...

A Trott constant is a real number whose decimal digits are equal to the terms of its continued fraction. The first Trott constant (OEIS A039662) was discovered by M. Trott in ...

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square (Wolfram 2002, p. 875). Truchet's ...

The Tucker circles are a generalization of the cosine circle and first Lemoine circle which can be viewed as a family of circles obtained by parallel displacing sides of the ...

An apodization function A(x)=1, (1) having instrument function I(k)=2asinc(2pika). (2) The peak of I(k) is 2a. The full width at half maximum of I(k) can found by setting ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G). The König-Egeváry theorem states that the ...

A curve named after James Watt (1736-1819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a linkage of rods connecting two ...