Editing Poncelet–Steiner theorem (section)

=== Steiner constructions ===
The term '''Steiner construction''' typically refers to any geometric construction that utilizes the straightedge tool only, and is sometimes simply called a ''straightedge-only construction'', named for Jakob Steiner who studied the subject. As a restricted construction [[paradigm]], no stipulations are made about what geometric objects already exist in the plane or their relative placement; any such conditions are postulated ahead of time. Also, no implications are made about what is or is not possible to construct. Constructions carried out in adherence with the Poncelet-Steiner theorem - relying solely on the use of a straightedge tool without the aid of a compass - are therefore a particular subset of ''Steiner constructions''.

Whereas Steiner constructions study the straightedge tool, the Poncelet-Steiner theorem stipulates the existence of a circle with its center, and affirms that a single circle is equivalent to a compass. Broadly, Steiner constructions may involve any number of circles, including none, already drawn in the plane, with or without their centers. They may also involve all manner of unique shapes and curves preexisting in the plane, provided that the straightedge tool is the only physical tool at the geometer's disposal.

Therefore, all constructions adhering to the Poncelet-Steiner theorem are Steiner constructions, though not all Steiner constructions abide by the strict condition of there being only one circle with its center provided in the plane. The Poncelet-Steiner theorem does not require an actual compass - it is presumed that the circle preexists in the plane - therefore all constructions herein demonstrating the Poncelet-Steiner theorem are Steiner constructions. The single arbitrary circle (with its center), which is postulated in the Poncelet-Steiner theorem, is therefore the minimal amount of information required to allow Steiner constructions to recover the constructive power and versatility of the traditional compass-straightedge paradigm.