The geometric center is the spot that is the same distance from the circumference of a circle. If we want the center of some strange shape it won’t be the same distance from every part of the edge. If we want to balance something we usually pivot it on its center. For a teeter totter that is the middle, which is the same distance from each end. It works best when the weight of the people on each end are close to the same
The gravitational center has to do with weight distribution. In the teeter totter example, a heavy dude on one end with a little guy on the other makes it really hard to make the thing work. If we move the heavy dude closer to the pivot point, it can work again, because the gravitational center is re-established at that pivot point. Physics stuff. Center stage is equal distance left to right but not necessarily front to back
To be the center of attention is neither a gravitational nor a geometric kind of center. It means to have everyone looking at, or listening to, you. Politicians and actors seek this center, except when the step into some cow pukky. The center of the Universe is not exactly a certain location because the Universe is changing, expanding, morphing all the time. Some people believe that they themselves are the center of the Universe
When we speak of the Center, capital C, we mean a place where a certain kind of activity members meet, like say, the Recreation Center. This place may not be at the geographic center of anything but is a place we can go to and find many people or things that are similar. The Center for Business Development or for the Arts or a Health Center are examples. These are places where expertise and common interest meet
The center is the accumulating place, where it all comes together and that center feels safe. You could center me, bring me back to a feeling of safety and Acceptance and encouragement, confidence. Some people are natural centers. They seem so OK in their own skin, so comforting as they personify ‘yes we can’. I want to be near to those I feel are centers. I want to be a center for others. How about you?
