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Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

A root-finding algorithm based on the iteration formula x_(n+1)=x_n-(f(x_n))/(f^'(x_n)){1+(f(x_n)f^('')(x_n))/(2[f^'(x_n)]^2)}. This method, like Newton's method, has poor ...

An axiom proposed by Huntington (1933) as part of his definition of a Boolean algebra, H(x,y)=!(!x v y) v !(!x v !y)=x, (1) where !x denotes NOT and x v y denotes OR. Taken ...

A technically defined extension of the ordinary determinant to "higher dimensional" hypermatrices. Cayley (1845) originally coined the term, but subsequently used it to refer ...

The hypotenuse of a right triangle is the triangle's longest side, i.e., the side opposite the right angle. The word derives from the Greek hypo- ("under") and teinein ("to ...

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) = ...

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 ...