Nanotubes and DNA behave like a one dimensional solid when one considers their electronic properties. They are one dimensional because electrons (or positive holes) traveling through them can only follow one path, thus they are analogous to a one way street. Strange as it may sound, quantum dots are an example of a zero dimensional solid. These objects can function as a kind of binary switch, motivating many researchers to try to use them to build quantum computers.

If it seems like we've run out of numbers (3, 2, 1, 0) to put in front of the "D" do not worry. Objects with fractional dimensions (e.g. 2.5-D objects) known as fractals, have an important role in modeling nanoscale systems. These mathematical constructs, that have brought many mathematicians into fields such as chaos theory and complex analysis, are between dimensions. This means that unlike a normal two dimensional object (e.g. a square or circle), a 2.5-D fractal would have an infinite 2-D surface area while being confined within a finite 3-D space. Dendrimers are polymers that branch out at various intervals. Nanoscale examples from nature are starch and glycogen. Such polymers effectively optimize their surface area to mass ratio. Although in dendrimers the surface area is not infinite, nor is the mass zero, the structure of the molecule can be accurately modeled by fractal mathematics and an actual fractal dimension can be calculated for a particular dendrimer.

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Keywords: nanotech mathematics dimensional analysis nanotubes dna one dimensional 1d quantum dots zero 0d binary switch computers fractal nanoscale chaos complex surface area to mass ratio dendrimers starch glycogen molecule