Two dimensional shapes have only surface area such as polygons whereas three dimensional shapes have surface area and volume such as polyhedrons.
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To define the energy or diameter parameters between two different objects, such as two types of atoms
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No, the geometric mean is not the same as the mean of two numbers.
Geometric mean of 2 and 12 is 4.898979485566356. Look at link: "Calculation of the geometric mean of two numbers".
Geometric mean of 175 and 7 is 35. Look at link: "Calculation of the geometric mean of two numbers".