cartesian oval
Wenn man einen Faden von einem Stift an einem Fokus streckt, um einen Stift an einem zweiten Fokus zu umwickeln, und das freie Ende des Fadens an einen Stift bindet, bildet der Weg, den der Stift nimmt, wenn der Faden fest gespannt ist, einen kartesischen oval mit einem Verhältnis von 2: 1 zwischen den Abständen von den beiden Brennpunkten.
The set of points (x,y) satisfying the quartic polynomial equation, where c is the distance d(P,Q){\displaystyle {\text{d}}(P,Q)}between the two fixed foci P = (0, 0) and Q = (c, 0), forms two ovals, the sets of points satisfying the two of the four equations. Linguee. However, Newton rejected such constructions as insufficiently rigorous. A Dynamical Theory of the Electromagnetic Field. The caustic formed by spherical aberration in this case may therefore be described as the evolute of a Cartesian oval. The ovals of Descartes were first studied by René Descartes in 1637, in connection with their applications in optics. Eine Methode zum Zeichnen bestimmter kartesischer Ovale, die bereits von Descartes verwendet wurde, ist analog zu einer Standardkonstruktion einer Ellipse durch gestreckten Faden. Then the Cartesian oval is the locus of points S satisfying d(P,S) + m d(Q,S) = a. These curves were also studied by Newton beginning in 1664. The freeform is created by a set of primitive surface elements, which are generalized Cartesian ovals adapted to the given optical system. d Look up words and phrases in comprehensive, reliable bilingual dictionaries and search through billions of online translations. James Clerk Maxwell rediscovered these curves, generalized them to curves defined by keeping constant the weighted sum of distances from three or more foci, and wrote a paper titled Observations on Circumscribed Figures Having a Plurality of Foci, and Radii of Various Proportions. , The two ovals are generally disjoint, except in the case that P or Q belongs to them. Benjamin Williamson, An Elementary Treatise on the Differential Calculus, Containing the Theory of Plane Curves (1884), https://en.wikipedia.org/w/index.php?title=Cartesian_oval&oldid=931280199. Linear combination. Ein Bericht über seine Ergebnisse mit dem Titel Über die Beschreibung von ovalen Kurven und solchen mit mehreren Schwerpunkten wurde von JD Forbes verfasst und 1846 der Royal Society of Edinburgh vorgelegt , als Maxwell 14 Jahre alt war (fast 15 Jahre) ). The caustic formed by spherical aberration in this case may therefore be described as the evolute of a Cartesian oval. )
Beispiel kartesischer Ovalen. Open menu. Wie Descartes entdeckt, kann cartesianischen Ovalen in verwendet werden , Linsendesign. < Für eine andere Parametrisierung und das daraus resultierende Quartic siehe Lawrence. As Descartes discovered, Cartesian ovals may be used in lens design. Wenn es ein Limaçon von Pascal ist. Kartovals - Cartesian oval. < An account of his results, titled On the description of oval curves, and those having a plurality of foci, was written by J.D. Translator. Sei m und a beliebige reelle Zahlen . Definition. Let P and Q be fixed points in the plane, and let d(P,S) and d(Q,S) denote the Euclidean distances from these points to a third variable point S. Let m and a be arbitrary real numbers. Cassini Ovals. Forbes and presented to the Royal Society of Edinburgh in 1846, when Maxwell was at the young age of 14 (almost 15).
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