Lemniscata lui bernoulli. In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the locus of points P so that PF1·PF2 = c2. Lemniscata lui Bernoulli În matematică, lemniscata lui Bernoulli este o curbă algebrică plană descrisă de ecuația carteziană: ( x 2 + y 2 ) 2 = 2 a 2 ( x 2 − y 2 ) {\displaystyle (x^ {2}+y^ {2})^ {2}=2a^ {2} (x^ {2}-y^ {2})\,} Curba are forma similară cifrei 8 și simbolului . Lemniscata a fost descrisă prima dată în 1694 de Jakob Bernoulli ca o modificare a unei elipse, care Lemniscata lui Bernoulli [gr. - the lemniscate of Bernoulli is a synodal curve of all the intersecting lines passing by the double point: Lemniscate of Bernoulli is the intersection of a plane tangent to the inner ring of a torus whose inner radius equals to its radius of generating circle. Terms of Use wolfram Move the mouse around the circle starting at = 0 The National Curve Bank project for students of mathematics The lemniscate of Bernoulli, also known simply as a lemniscate, is a curve 'shaped like a figure 8, or a knot, or the bow of a ribbon' in the words of Jacob Bernoulli in an article published in 1694. 4 days ago · The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the product of distances from two fixed points (-a,0) and (a,0) (which can be considered a kind of foci with respect to multiplication instead of addition) is a constant a^2. (See: Cassinian oval). Both the ellipse and the lemniscate (from the Latin " lēmniscātus " meaning "decorated with ribbons") start with two fixed points, the foci (focuses). lemniscos "panglică"] este o curbă plană, loc geometric al punctelor pentru care produsul distanţelor la două puncte fixe este egal cu pătratul jumătăţii distanţei dintre punctele fixe: unde sunt punctele fixe cu Lemniscata este un caz particular al ovalelelor lui Cassini şi are ecuaţia carteziană: 4 days ago · About MathWorld MathWorld Classroom Contribute MathWorld Book 13,278 Entries Last Updated: Wed Sep 24 2025 ©1999–2025 Wolfram Research, Inc. …of the rectification of the lemniscate, a ribbon-shaped curve discovered by Jakob Bernoulli in 1694, Giulio Carlo Fagnano (1682–1766) introduced ingenious analytic transformations that laid the foundation for the theory of elliptic integrals. Lemniscata a fost descrisă prima dată în 1694 de Jakob Bernoulli ca o modificare a unei elipse, care este locul geometric al punctelor pentru care suma distanțelor la două puncte fixe, numite focare, este . Dec 17, 2019 · He described what's now called the Lemniscate of Bernoulli in 1694 as a modification of the Ellipse. Jacob Bernoulli was not aware that the curve he was describing was a special case of a Cassinian Oval which had been described by Cassini in 1680. Lemniscate * The Lemniscate is a figure-eight curve with a simple me-chanical construction attributed to Bernoulli: Choose two ’focal’ points F1, F2 at distance L := 2 dd, then take three rods, one of length L, two of length ∗ ( x 2 + y 2 ) 2 = 2 a 2 ( x 2 − y 2 ) {\displaystyle (x^ {2}+y^ {2})^ {2}=2a^ {2} (x^ {2}-y^ {2})\,} Lemniscata lui Bernoulli Curba are forma similară cifrei 8 și simbolului . The general properties of the lemniscate were discovered by Giovanni Fagnano in 1750. - the asymptotic curves of the Plücker conoid are projected on lemniscates of Bernoulli. 31pf4 sgim d0xgey i3w3r 1cl lmw snyu e66gj3ud gbrr dpud