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A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

A convolution is an integral that expresses the amount of overlap of one function g as it is shifted over another function f. It therefore "blends" one function with another. ...

An algebraic integer of the form a+bsqrt(D) where D is squarefree forms a quadratic field and is denoted Q(sqrt(D)). If D>0, the field is called a real quadratic field, and ...

The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian ...

The quartic surface obtained by replacing the constant b in the equation of the Cassini ovals with b=z, obtaining [(x-a)^2+y^2][(x+a)^2+y^2]=z^4. (1) As can be seen by ...

The hyperbolic cylinder is a quadratic surface given by the equation (x^2)/(a^2)-(y^2)/(b^2)=-1. (1) It is a ruled surface. It can be given parametrically by x = asinhu (2) y ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

The third prime number, which is also the second Fermat prime, the third Sophie Germain prime, and Fibonacci number F_4. It is an Eisenstein prime, but not a Gaussian prime, ...