Definitions
Century Dictionary and Cyclopedia
- In mathematics, related to the lemniscate of Bernoulli.
- In ichthyology, having a hyaline or transparent appearance and ribbonlike form; of or relating to the Lemniscati: as, a lemniscate fish.
- n. In mathematics:
- n. The locus of the point at which the tangent to an equilateral hyperbola meets the perpendicular let fall upon it from the center: a curve invented by James Bernoulli. It may also be defined as the locus of the point the product of whose distances from two fixed points is a quarter of the square of the distance of those points from each other. It is a kind of Cassinian, and is also a lemniscate in sense, below.
- n. Any crunodal curve of the fourth order having only one real branch, and this finite and symmetrical with respect to two axes. [This definition is an attempt to interpret that of certain writers formerly in repute, who say that the lemniscate has the shape of an 8, but who give as the typical form a curve which, having a tacnodal acnode at infinity, is not a bicircular quartic. Curves satisfying this definition are of the 10th, 8th, and 6th classes. See figures and Cassinian.]
- n. The locus of the point at which the tangent to a fixed conic is cut by a perpendicular let fall upon it from the center. Its equation is (x +
y )= ax +by . It is a unicursal bicircular quartic. (Seebicircular .) It has two real and two imaginary bitangents represented by the equationIt is called an elliptic or hyperbolic lemniscate, according as the fixed conic is an ellipse or a hyperbola; in the former case the central node is an acnode, in the latter a crunode. See the figure. - n. A Cassinian: a misapplication of the word originating in Germany.
- n. The locus of the point in which the straight through the center and the projection of a point of a circle on a fixed tangent are cut by the perpendicular from this point to the diameter from the contact point. This is the lemniscate of Gerono, a curve of the form of an 8, whose equation in simplest form is y = y–x.
Wiktionary
Examples
“lemniscate', a particular modification of the so-called Cassinian curves. 2 1”
“Her gaze was caught on the glowing wand and lemniscate, and she thought of radiation.”
“A lemniscate, an infinity symbol, glowed above his head.”
“You mentioned lemniscate periodic systems in one of your chemistry blogs.”
“The one Ariel did recognize shone bright white in the center of the robot's upper torso, a lemniscate crossed by an arrow at an upward angle: the sign of the Managins.”
Mirage
“Some projective-geometrical considerations concerning the lemniscate are to be found in the previously mentioned writings of G. Adams and L. L.cher-Ernst.”
“You have read, too, in _The Secret Doctrine, _ P.ofessor Crooke's theory, endorsed by H.P. Blavatsky, as to how the chemical elements were deposited by a spiral evolutive force, a creative impulse working outward in the form of a caduceus or lemniscate, or figure '8.”
“About the epoch of maximum of sun-spots they are large and nearly circular, having the same character as the curves for the summer months; whilst about the time of sun-spot minimum they are small and lemniscate-shaped, with a striking resemblance to the curves for the winter months.”
Autobiography
“According to the lemniscate arrangement, we should commence with hydrogen as the head of the first negative group, but as it differs wholly from those placed with it, it is better to take it by itself.”
Occult Chemistry Clairvoyant Observations on the Chemical Elements
“We follow here the grouping according to external forms, and the student should compare it with the groups marked in the lemniscate arrangement shown in Article II (p. 377, properly p. 437, February), reading the group by the disks that fall below each other; thus the first group is H, Cl, Br,”
Occult Chemistry Clairvoyant Observations on the Chemical Elements
Lists
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artoparts See: limaçon (Heart-like shape for Valentines Day) Jan 28, 2009
johnmperry nor with Lissajou's figures. Aug 26, 2008
sionnach Not to be confused with a loxodrome Nov 28, 2007
sarra Describes a certain kind of figure-of-eight mathematical curve, an example of which is the infinity sign ∞.
The Latin root is lēmniscus, from the Greek λημνίσκος, lêmniskos, both referring to ribbons. Nov 28, 2007