Definition:Compass and Straightedge Construction

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A compass and straightedge construction is a technique of drawing geometric figures using only a straightedge and a compass.

The operations available are:

using the straightedge to draw a straight line determined by two given points
using the compass to draw a circle whose center is at a given point and whose radius is the distance between two given points
finding the points of intersection between straight lines and circles.

Also known as

A compass and straightedge construction has some obvious alternatives:

straightedge and compass construction
compass and straight-edge construction
compass-and-straightedge construction

and so on.

Use whatever you feel comfortable with.

Some sources use the term Euclidean construction.

Some sources use the term Euclidean tools, while others recognize that term but decry it.

Some sources use the word ruler for straightedge, but this can be confused with a device which has markings on it to allow measurement; a true Euclidean straightedge has no such markings.

Also see

  • Results about compass and straightedge constructions can be found here.

Historical Note

Some sources suggest that it was the Greek mathematician Oenopides of Chios who imposed the restriction that compass and straightedge were the only tools that were "philosophically suitable" for geometric constructions.

Others suggest that this restriction originated with Plato's Academy.

The fact that the constructions made in Euclid's The Elements implicitly impose such a restriction suggest that Euclid himself may well have been an Academy student.

However, when necessary, the Greeks were quite ready to use other tools to achieve constructions that cannot be made with just a straightedge and a compass.