Alternate dimensions aren't outside our everyday experience. In fact, we can use exotic dimensions, like fractional dimensions, to measure things as common as coastlines. Find out about the Hausdorff Dimension before your next trip to the sea.
A point has zero dimensions. A line has only one dimension to its name. A plane has two, and a voluminous shape has three. But what about a line that shoots back and forth over a page in such a complicated pattern that can't really be defined as a one-dimensional object? We could say that it only takes three points (provided they're not all on one line) to define a plane. So the scribbly line lies within a plane, but does that really define the line? Mathematician Felix Hausdorff said no. The line still technically has no width. It only carves out width. According to Hausdorff, to describe the line, one needs fractional dimensions. These dimensions define many fractal shapes, such as the Menger Sponge, a fractal that is all surface area and no volume and has a dimensional value of 2.73.