What does "Umbilical Points" mean?

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Umbilical points are specific locations on a surface where the shape behaves uniformly in all directions. Imagine a smooth, rounded surface where every direction looks the same at a certain point. At these points, the surface does not curve more in one direction than another.

These points can be important in understanding the characteristics of the surface. In some cases, the behavior of a surface around those points can tell us much about its overall shape.

Umbilical points appear in various fields, including geometry and physics. They help scientists and mathematicians study surfaces and their properties more effectively.