Powers are an accumulation of their shells (or their nexus numbers.)

= 4^{^3}

S₃ = 3x^2 - 3x + 1

First cube plus three more shells of the power of 3. 

= 4^{^2}

S₂ = 2x - 1

First square plus three more shells in the power of 2. 

See also Math World on squares.

Shells in the powers of 1, 2, and 3 are easily imaginable and sketch-able.  In drawings of cubes and squares, the first 4 shells will always resemble the above pictures but might have many additional shells beyond these.

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Last modified: 12/16/05