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The Zeckendorf representation of a positive integer n is a representation of n as a sum of nonconsecutive distinct Fibonacci numbers, n=sum_(k=2)^Lepsilon_kF_k, where ...

In this illusion, the vertical lines in the above figure are parallel, but appear to be tilted at an angle. In 1860, F. Zöllner sent his discovery in a letter to physicist ...

Linear Algebra

q-calculus or quantum calculus is a methodology comparable to the usual study of calculus but which is centered on the idea of deriving q-analogous results without the use of ...

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...

The (unilateral) Z-transform of a sequence {a_k}_(k=0)^infty is defined as Z[{a_k}_(k=0)^infty](z)=sum_(k=0)^infty(a_k)/(z^k). (1) This definition is implemented in the ...

The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The divergence of a vector field F, denoted div(F) or del ·F (the notation used in this work), is defined by a limit of the surface integral del ·F=lim_(V->0)(∮_SF·da)/V (1) ...

Dürer's solid, also known as the truncated triangular trapezohedron, is the 8-faced solid depicted in an engraving entitled Melencolia I by Albrecht Dürer (The British ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...