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Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

A reduction system is said to posses the Church-Rosser property if, for all x and y such that x<->_*y, there exists a z such that x->_*z and y->_*z. A reduction system is ...

The Church-Rosser theorem states that lambda calculus as a reduction system with lambda conversion rules satisfies the Church-Rosser property.

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

An (infinite) line determined by two points (x_1,y_1) and (x_2,y_2) may intersect a circle of radius r and center (0, 0) in two imaginary points (left figure), a degenerate ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

The evolute of a circle is a degenerate point at the origin.

A central circle is a circle with trilinear equation (lalpha+mbeta+ngamma)(aalpha+bbeta+cgamma)+k(abetagamma+bgammaalpha+calphabeta)=0 such that l:m:n is a triangle center ...

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

The involute of the circle was first studied by Huygens when he was considering clocks without pendula for use on ships at sea. He used the circle involute in his first ...