Why construct?
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Description
Euclid spends a lot of time in the Elements constructing figures with his ubiquitous ruler and compass. Why did he think this was important? Why did he think this was better than a geometry that has only theorems and no constructions? In fact, constructions protect geometry from foundational problems to which it would otherwise be susceptible, such as inconsistencies, hidden assumptions, verbal logic fallacies, and diagrammatic fallacies.
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Copernicus’s planetary models contain elements also found in the works of late medieval Islamic astronomers associated with the Maragha School, including the Tusi couple and Ibn al-Shatir’s models for the Moon and Mercury. On this basis many historians have concluded that Copernicus must have...
Published 11/29/23
Einstein’s theory of special relativity defines time and space operationally, that is to say, in terms of the actions performed to measure them. This is analogous to the constructivist spirit of classical geometry.
Published 07/23/23