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Given three circles, each intersecting the other two in two points, the line segments connecting their points of intersection satisfy (ace)/(bdf)=1 (Honsberger 1995).

An a×b rectangle can be packed with 1×n strips iff n|a or n|b.

If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...

Let E and F be paired spaces with S a family of absolutely convex bounded sets of F such that the sets of S generate F and, if B_1,B_2 in S, there exists a B_3 in S such that ...

A necessary and sufficient condition that [alpha^'] should be comparable with [alpha] for all positive values of the a is that one of (alpha^') and (alpha) should be ...

The volume of a prismatoid is equal to the sum of the volumes of a pyramid, a wedge, and a parallelepiped.

There exist numbers y_1<y_2<...<y_(n-1), a<y_(n-1), y_(n-1)<b, such that lambda_nu=alpha(y_nu)-alpha(y_(nu-1)), (1) where nu=1, 2, ..., n, y_0=a and y_n=b. Furthermore, the ...

For a point P inside an equilateral triangle DeltaABC, the sum of the perpendiculars p_i from P to the sides of the triangle is equal to the altitude h. This result is simply ...

Given a quadratic form Q(x,y)=x^2+y^2, (1) then Q(x,y)Q(x^',y^')=Q(xx^'-yy^',x^'y+xy^'), (2) since (x^2+y^2)(x^('2)+y^('2)) = (xx^'-yy^')^2+(xy^'+x^'y)^2 (3) = ...

A metatheorem in mathematical logic also known under the name "conditional proof." It states that if the sentential formula B can be derived from the set of sentential ...