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A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

The Fredholm integral equation of the second kind f(x)=1+1/piint_(-1)^1(f(t))/((x-t)^2+1)dt that arises in electrostatics (Love 1949, Fox and Goodwin 1953, and Abbott 2002).

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n+1)st and successive polygons are ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

A rotor is a convex figure that can be rotated inside a polygon (or polyhedron) while always touching every side (or face). The least area rotor in a square is the Reuleaux ...

The salinon is the figure illustrated above formed from four connected semicircles. The word salinon is Greek for "salt cellar," which the figure resembles. If the radius of ...

Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

The surface of revolution obtained by cutting a conical "wedge" with vertex at the center of a sphere out of the sphere. It is therefore a cone plus a spherical cap, and is a ...

In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...

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 ...