The standard surgical ellipse, with 30° apical angles and a length-to-width ratio of 2 or 3 to 1, works optimally on a flat surface. The same pattern, when used for excisions on strongly convex or concave surfaces, leads to distortions which may require significant revisions. The reason for these discrepancies is explainable by the mathematical differences between flat Euclidian geometry and curved non-Euclidian geometry. Understanding these basic mathematical principles as applied to cutaneous surgery should lead to better preoperative planning, fewer intraoperative surprises, and more pleasing results.