What does the term 'spherical excess' refer to?

The term 'spherical excess' specifically refers to the measure of the amount by which the sum of the angles of a spherical triangle exceeds 180 degrees. In the context of spherical geometry, this occurs due to the curvature of the sphere, which affects how angles are perceived compared to flat geometry.

When dealing with three points on a sphere and the triangle formed by connecting them, the angles in this spherical triangle will sum to more than 180 degrees. The difference between this sum and 180 degrees is what is termed as the 'spherical excess.' This concept is fundamental in various applications, including geodesy and navigation, where spherical triangles are used to calculate distances and angles on the Earth’s surface.

The other choices do not accurately capture the definition of spherical excess. The difference in angles between flat and spherical shapes would pertain to geometric principles but does not specifically encompass the complete definition of spherical excess. Measurement of curvature on a flat surface does not relate to spherical geometry, while the stability angle of material and measurement of area in square units involve different physical and mathematical concepts without direct relation to the angle summation of spherical triangles.