不固定圆规和直尺的构造

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In Ancient Greece, the compasses designed for geometric constructions collapsed after they were used. This meant that one could not simply open one's compass to the length of a segment, move the compass somewhere else, and then copy the length of that segment onto a new line. Technically, pure straightedge and compass constructions are meant to be performed with a collapsing compass like the ones in Ancient Greece.

As we all know, today's modern compasses can now be fixed at a nonzero length to copy a segment to a new location. This begs the question: has modern technology expanded our repertoire of geometric constructions? The answer is actually no; all constructions attainable with a modern compass were still available to the ancient Greeks with a collapsing compass. The next section will prove this equivalence.

However, it is still worth mentioning that constructions with collapsing compasses are much slower, due to the need of multiple steps for copying a segment. Since we can now carry out this process with only one step, it is a small comfort that actually performing and explaining such constructions will be faster with our modern technology.

Type a concept, like “slope” or “photosynthesis”.

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