Abstract
If a cube is to be separated into smaller ones, in such a way, that each edge is cut into two equal pieces (cf. Fig. 1), three cuts through the cube need to be made. Each cut generates a surface area equal to the surfaces of the original cube parallel to the cut. All together, the overall surface is duplicated while the volume remains to be the same. If each edge is cut into n pieces, the surface is increased by a factor n. Thus, the ratio of surface to volume is changing by the inverse of the factor sf by which the dimensions of a cube (and in general any object) is scaled up or down.
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© 2011 Springer-Verlag Berlin Heidelberg
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Schomburg, W.K. (2011). Scaling Laws. In: Introduction to Microsystem Design. RWTHedition, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19489-4_2
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DOI: https://doi.org/10.1007/978-3-642-19489-4_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19488-7
Online ISBN: 978-3-642-19489-4
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