Interactive · 1 question
There are many constructions that can be done with the use of a compass alone. These include, but are not limited to:
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Construct segments multiple times as large as a given segment.
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It is possible to find a point C such that AC is perpendicular to a given segment AB.
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Construct segments multiple times smaller than AB.
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Construct a Regular Pentagon using various angles.
What is one of the only things that a ruler can do that a compass alone cannot do?
This is an explanation as offered by the Cut-The-Knot website. This website also has more details as to how to make some of the other constructions I mentioned above. I take no credit for the following excerpt from the website's explanation:
Swing an arc with the center B of radius AB. With the same radius swing first an arc with the center A until it intersects the first arc at a point C. With C as the center draw and arc to obtained the point D. With D as the center draw and arc to obtained the point E. The segment AE is twice as big as the segment AB. In a similar fashion segment BE can be extended to EF, twice as big a segment as BE. Then AF is three times as long as AB. Etc.
So as you can see, even if you have nothing but a pencil and a compass, you can still do many interesting constructions.