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The cylinder function is defined as C(x,y)={1 for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a. (1) The Bessel functions are sometimes also called cylinder functions. To find the ...

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

In the above figure, the identical squares A, B, C appear different in width and height, because subdividing a space makes it appear larger. A different orientation can also ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...

The regularized beta function is defined by I(z;a,b)=(B(z;a,b))/(B(a,b)), where B(z;a,b) is the incomplete beta function and B(a,b) is the (complete) beta function. The ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

The function defined by T_n(x)=((-1)^(n-1))/(sqrt(n!))Z^((n-1))(x), where Z(x)=1/(sqrt(2pi))e^(-x^2/2) and Z^((k))(x) is the kth derivative of Z(x).

The conversion of a quadratic polynomial of the form ax^2+bx+c to the form a(x+b/(2a))^2+(c-(b^2)/(4a)), which, defining B=b/2a and C=c-b^2/4a, simplifies to a(x+B)^2+C.

The term used by Hunter and Madachy (1975, p. 24) and Madachy (1979, p. 87) to refer to a panmagic square.