Geometry on graph paper

Geometry on graph paper involves studying geometric figures whose vertices are at lattice points (points with integer coordinates) on a regular grid. Problems often involve counting, measuring, or analyzing properties of these figures using combinatorial and coordinate methods.

Important properties

• Lattice points have integer coordinates (x, y).

• Distances between points can be calculated using the Pythagorean theorem.

• Areas of polygons with lattice point vertices can be found using formulas like Pick's Theorem.

• Counting problems may ask for the number of lattice points inside or on the boundary of a figure.