There are three ways a line and a circle can be associated, ie the line cuts the circle at two distinct points, the line is a tangent to the circle or the line misses the circle. To work out which ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

Abstract We calculate the intersection ring of 3-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold’s underlying graph is a ...