Viewing the World from Different Angles: Plato's Timaeus 54E-55A

The present article investigates a passage of the Timaeus in which Plato describes the construction of the pyramid. Scholars traditionally inter- preted it as involving that the solid angle at the vertex of the pyramid is equal, or nearly so, to 180°, a value which they took to be that of the most obtuse of plane angles. I argue that this interpretation is not warranted, because it con- flicts with both the geometrical principles which Plato in all probability knew and the context of the Timaeus. As well as recalling the definitions and proper- ties of plane angles and solid angles in Euclid's Elements, I offer an alternative interpretation, which in my opinion improves the comprehension of the pas- sage, and makes it consistent with both the immediate and wider context of the Timaeus. I suggest that the passage marks a transition from plane geometry to solid geometry within Plato's account of the universe.