Pins-and-string method The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string, and a pencil. In this method, pins are pushed into the paper at two points, which become the ellipse's foci. A string is tied at each end to the two pins; its length after tying is . The tip of the pencil then traces an ellipse if it is moved while keeping the string taut. Using two pegs and a rope, gardeners use this procedure to outline an elliptical flower bed—thus it is called the gardener's ellipse. The Byzantine architect Anthemius of Tralles () described how this method could be used to construct an elliptical reflector,From [Concerning Wondrous Machines]: "If, then, we stretch a string surrounding the points A, B tightly around the first point from which the rays are to be reflected, the line will be drawn which is part of the so-called ellipse, with respect to which the surface of the mirror must be situated." and it was elaborated in a now-lost 9th-century treatise by Al-Ḥasan ibn Mūsā.Al-Ḥasan's work was titled [The Book of the Elongated Circular Figure].
Pins-and-string method The characterization of an ellipse as the locus of points so that sum of the distances to the foci is constant leads to a method of drawing one using two drawing pins, a length of string and a pencil In this method, pins are pushed into the paper at two points, which become the ellipse's foci. A string is tied at each end to the two pins; its length after tying is . The tip of the pencil then traces an ellipse if it is moved while keeping the string taut. Using two pegs and a rope, gardeners use this procedure to outline an elliptical flower bed—thus it is called the gardener's ellipse. The Byzantine architect Anthemius of Tralles () described how this method could be used to construct an elliptical reflector,From [Concerning Wondrous Machines]: "If, then, we stretch a string surrounding the points A, B tightly around the first point from which the rays are to be reflected, the line will be drawn which is part of the so-called ellipse, with respect to which the surface of the mirror must be situated." and it was elaborated in a now-lost 9th-century treatise by Al-Ḥasan ibn Mūsā.Al-Ḥasan's work was titled [The Book of the Elongated Circular Figure].