cissoid

American  

[sis-oid] / ˈsɪs ɔɪd /

noun

Geometry.

1. a curve having a cusp at the origin and a point of inflection at infinity. Equation: r = 2 a sin(θ)tan(θ).

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cissoid British  

/ ˈsɪsɔɪd /

noun

1. a geometric curve whose two branches meet in a cusp at the origin and are asymptotic to a line parallel to the y -axis. Its equation is y ²(2a – x ) =x ³ where 2a is the distance between the y -axis and this line

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adjective

1. contained between the concave sides of two intersecting curves Compare sistroid

Other Word Forms

• cissoidal adjective

Etymology

Origin of cissoid

1650–60; < Greek kissoeidḗs, equivalent to kiss ( ós ) ivy + -oeidēs -oid

Example Sentences

Apollonius was followed by Nicomedes, the inventor of the conchoid; Diocles, the inventor of the cissoid; Zenodorus, the founder of the study of isoperimetrical figures; Hipparchus, the founder of trigonometry; and Heron the elder, who wrote after the manner of the Egyptians, and primarily directed attention to problems of practical surveying.

From Project Gutenberg

The Greeks could not solve this equation, which also arose in the problems of duplicating a cube and trisecting an angle, by the ruler and compasses, but only by mechanical curves such as the cissoid, conchoid and quadratrix.

From Project Gutenberg

Take a rod LMN bent at right angles at M, such that MN = AB; let the leg LM always pass through a fixed point O on AB produced such that OA = CA, where C is the middle point of AB, and cause N to travel along the line perpendicular to AB at C; then the midpoint of MN traces the cissoid.

From Project Gutenberg

Let APB be a semicircle, BT the tangent at B, and APT a line cutting the circle in P and BT at T; take a point Q on AT so that AQ always equals PT; then the locus of Q is the cissoid.

From Project Gutenberg

The cissoid is the first positive pedal of the parabola y� + 8ax = 0 for the vertex, and the inverse of the parabola y� = 8ax, the vertex being the centre of inversion, and the semi-latus rectum the constant of inversion.

From Project Gutenberg