Where is the Center of the Earth?

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The Earth is not a perfect sphere, so the distance from the center of mass of the Earth to a point on its surface is not the same for all points. So, what point on the Earth's surface has the shortest distance to the center of mass--what point is "directly above" the center? All sorts of civilizations have historically claimed to be located at the center of the Earth, but now that we know the real shape of the Earth, shouldn't we know the real center?
 
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The Earth is an oblate (flattened) sphereoid, therefore the points nearest the center are the poles. Also, any points on the ocean at the same latitude as each other are equadistant from the center of the earth.
what point is "directly above" the center?
Since the center is the center, every point on Earth's surface is directly above it.
All sorts of civilizations have historically claimed to be located at the center of the Earth...
No they didn't. Many did claim to be at the center of the universe, though.