What is the term for the measure of compression of a circle to form an ellipse?

The measure of compression of a circle to form an ellipse is referred to as "flattening." Flattening is a parameter that describes how much a shape deviates from being a perfect sphere. In the case of the ellipse, flattening is calculated based on the difference between the major and minor axes. Specifically, flattening can be defined mathematically as the ratio of the difference between the semi-major axis and semi-minor axis to the semi-major axis.

This concept is significant in geodesy and geophysics, where understanding the shape of the Earth is crucial. The Earth is approximately an oblate spheroid, meaning its equatorial diameter is greater than its polar diameter. Flattening captures this difference, providing a clear measure of the Earth's shape, which is essential for accurate geodetic calculations.

In contrast, other terms like first eccentricity, second eccentricity, and angular eccentricity deal with a different context or dimensions of ellipses and do not specifically express this measure of compression. First and second eccentricity are specific mathematical constructs related to the shape's geometry rather than a direct measure of its flattening.