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A topological space decomposes into its connected components. The connectedness relation between two pairs of points satisfies transitivity, i.e., if a∼b and b∼c then a∼c. ...

Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...

In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...

There are at least two Siegel's theorems. The first states that an elliptic curve can have only a finite number of points with integer coordinates. The second states that if ...

The equation of motion for a membrane shaped as a right isosceles triangle of length c on a side and with the sides oriented along the positive x and y axes is given by where ...

Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

A straight angle is an angle equal to 180 degrees=pi radians. Two right angles make a straight angle, and two straight angles make a full angle.

A transformation characterized by an invariant line and a scale factor (one-way stretch) or two invariant lines and corresponding scale factors (two-way stretch).