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cissoid

[ sis-oid ]

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).


cissoid

/ 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
“Collins English Dictionary — Complete & Unabridged” 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

adjective

  1. contained between the concave sides of two intersecting curves Compare sistroid
“Collins English Dictionary — Complete & Unabridged” 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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Other Words From

  • cis·soidal adjective
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Word History and Origins

Origin of cissoid1

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

Origin of cissoid1

C17: from Greek kissoeidēs, literally: ivy-shaped, from kissos ivy
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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.

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.

A cissoid angle is the angle included between the concave sides of two intersecting curves; the convex sides include the sistroid angle.

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.

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.

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