Maximum/minimum distance

Given a geometric object (like a solid or a region), the maximum distance is the greatest possible distance between two points in or on the object, and the minimum distance is the smallest possible distance between two points or between a point and a surface. These problems often require using the distance formula and logical reasoning to identify which points achieve these distances.

Important properties

• Maximum distance in a convex solid is usually between two 'extreme' points (like opposite vertices).

• Minimum distance between a point and a surface is along the perpendicular from the point to the surface.

• Symmetry can help identify candidates for maximum or minimum distances.

• Sometimes, calculus or optimization techniques are needed to find exact values.