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A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a ...

Let R[z]>0, 0<=alpha,beta<=1, and Lambda(alpha,beta,z)=sum_(r=0)^infty[lambda((r+alpha)z-ibeta)+lambda((r+1-alpha)z+ibeta)], (1) where lambda(x) = -ln(1-e^(-2pix)) (2) = ...

The term isocline derives from the Greek words for "same slope." For a first-order ordinary differential equation y^'=f(t,y) is, a curve with equation f(t,y)=C for some ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

Jenny's constant is the name given (Munroe 2012) to the positive real constant defined by J = (7^(e-1/e)-9)pi^2 (1) = 867.53090198... (2) (OEIS A182369), the first few digits ...

x_(n+1) = 2x_n (1) y_(n+1) = alphay_n+cos(4pix_n), (2) where x_n, y_n are computed mod 1 (Kaplan and Yorke 1979). The Kaplan-Yorke map with alpha=0.2 has correlation exponent ...

A curve also known as Gutschoven's curve which was first studied by G. van Gutschoven around 1662 (MacTutor Archive). It was also studied by Newton and, some years later, by ...

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...