FRENCH CURVE (Burmester curve) - (15-Year Anniversary Tag)

Please help me travel and see a lot of great geocachers. Take pictures with objects like hyperbolas; ellipses and parabolas.

French curve

A set of the three most common French curves, also known as a Burmester set. The bottom object is most commonly used for hyperbolas; the smaller one above it is suited for ellipses. The large one is used mostly for parabolas.

A French curve is a template usually made from metal, wood, or plastic composed of many different segments of the Euler spiral (aka the clothoid curve). It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The curve is placed on the drawing material, and a pencil, knife, or other implement is traced around its curves to produce the desired result. They were invented by the German mathematician Ludwig Burmester and are also known as Burmester (curve) set.

Ludwig Ernst Hans Burmester (5 May 1840 – 20 April 1927) was a German kinematician and geometer.

His doctoral thesis Über die Elemente einer Theorie der Isophoten (About the elements of a theory of isophotes) concerned lines on a surface defined by light direction. After a period as a teacher in Łódź he became a professor of synthetic geometry at Dresden where his growing interest in kinematics culminated in his Lehrbuch der Kinematik, Erster Band, Die ebene Bewegung (Textbook of Kinematics, First Volume, Planar Motion) of 1888, developing the approach to the theory of linkages introduced by Franz Reuleaux, whereby a planar mechanism was understood as a collection of Euclidean planes in relative motion with one degree of freedom. Burmester considered both the theory of planar kinematics and practically all actual mechanisms known in his time. In doing so, Burmester developed Burmester's theory which applies projective geometry to the loci of points on planes moving in straight lines and in circles, where any motion may be understood in relation to four Burmester points.

The Burmester linkage of 1888 is a four-bar linkage part of whose coupler curve is an approximately straight line (see also Watt's linkage). Burmester is also known for his focal linkage, which is a highly over-constrained but movable linkage related to Kempe's focal linkage and Hart's straight-line linkages.

Lekaal

Lekaal on kindla või muudetava kujuga joonestusvahend kõverjoonte tegemiseks. Tavaliselt on kasutusel kolmest lekaalist koosnevad komplektid - Burmesteri šabloonid - kus üks element sobib ellipsite joonestamiseks, teine sobib hüperboolide laiade osade joonestamiseks ja kolmas, kõige suurem komplektist, sobib paraboolide joonestamiseks.

Pohatu Nuva 15 Year Anniversary Tag
Use TB9J0EA to reference this item.