Euclid's Heritage: Is Space Three-Dimensional? by Peter Janich (Paperback, 2010)

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We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving­ abouts'), as having three dimensions.