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Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

Let a>|b|, and write h(theta)=(acostheta+b)/(2sintheta). (1) Then define P_n(x;a,b) by the generating function f(x,w)=f(costheta,w)=sum_(n=0)^inftyP_n(x;a,b)w^n ...

The Stevanovic circle is a central circle with center X_(650), which has center function alpha_(650)=cosB-cosC, (1) It has radius (2) It has circle function ...

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...

The Laguerre polynomials are solutions L_n(x) to the Laguerre differential equation with nu=0. They are illustrated above for x in [0,1] and n=1, 2, ..., 5, and implemented ...

A notation for large numbers due to Steinhaus (1999). In circle notation, is defined as n in n squares, where numbers written inside squares (and triangles) are interpreted ...

A cylinder can be dissected into unequal squares, with nine squares required at a minimum. Trivial squarings can be constructed by taking rectangle dissections and matching ...

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

The illusion in view by staring at the small black dot for a half minute or so, then switching to the white dot. The black squares appear stationary when staring at the white ...

A large number defined as where the circle notation denotes "n in n squares," and triangles and squares are expanded in terms of Steinhaus-Moser notation (Steinhaus 1999, pp. ...