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Examples of compass-only constructions include Napoleon's problem. It is impossible to take a square root with just a ruler, so some things that cannot be constructed with a ruler can be constructed with a compass; but (by the Poncelet–Steiner theorem) given a single circle and its center, they can be constructed.
When doing constructions in hyperbolic geometry, as long as you are using the proper ruler for the construction, the three compasses (meaning the horocompass, hypercompass, and the standard compass) can all perform the same constructions. [3] A parallel ruler can be used to draw a line through a given point A and parallel to a given ray a [3].
A neusis construction might be performed by means of a marked ruler that is rotatable around the point P (this may be done by putting a pin into the point P and then pressing the ruler against the pin). In the figure one end of the ruler is marked with a yellow eye with crosshairs: this is the origin of the scale division on the ruler.
The concept of constructibility as discussed in this article applies specifically to compass and straightedge constructions. More constructions become possible if other tools are allowed. The so-called neusis constructions, for example, make use of a marked ruler. The constructions are a mathematical idealization and are assumed to be done exactly.
The compass equivalency theorem shows that in all the constructions mentioned above, the familiar modern compass with its fixable aperture, which can be used to transfer distances, may be replaced with a "collapsible compass", a compass that collapses whenever it is lifted from a page, so that it may not be directly used to transfer distances ...
Ruler and compass. The process of geometric drawing is based on constructions with a ruler and compass, which in turn are based on the first three postulates of Euclid's Elements . The historical importance of rulers and compasses as instruments in solving geometric problems leads many authors to limit Geometric Drawing to the representation ...
Pages in category "Compass and straightedge constructions" The following 10 pages are in this category, out of 10 total. This list may not reflect recent changes .
There is a simple neusis construction using a marked ruler for a length which is the cube root of 2 times another length. [14] Mark a ruler with the given length; this will eventually be GH. Construct an equilateral triangle ABC with the given length as side. Extend AB an equal amount again to D. Extend the line BC forming the line CE.