The Mid-Point Squares

Geometry Level 4

The perimeter of a square is \(2016\text{ cm}\). The midpoints of its sides are joined to form a new square. Again,the midpoints of the sides of this new square are joined to form another square. This process is continued till infinity.

Let \(\mathbf{S}\) denote the perimeter of all such squares formed(including the original square). Evaluate \(\lfloor\mathbf{S}\rfloor \).

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