Another construction chooses half of the curve of constant width, meeting certain requirements, and forms from it a body of constant width having the given curve as part of its boundary. The construction begins with a convex curved arc, whose endpoints are the intended width formula_2 apart. The two endpoints must touch parallel supporting lines at distance formula_2 from each other. Additionally, each supporting line that touches another point of the arc must be tangent at that point to a circle of radius formula_2 containing the entire arc; this requirement prevents the curvature of the arc from being less than that of the circle. The completed body of constant width is then the intersection of the interiors of an infinite family of circles, of two types: the ones tangent to the supporting lines, and more circles of the same radius centered at each point of the given arc. This construction is universal: all curves of constant width may be constructed in this way. Victor Puiseux, a 19th-century French mathematician, found curves of constant width containing elliptical arcs that can be constructed in this way from a semi-ellipse. To meet the curvature condition, the semi-ellipse should be bounded by the semi-major axis of its ellipse, and the ellipse should have eccentricity at most formula_5. Equivalently, the semi-major axis should be at most twice the semi-minor axis.