Definition of cycloid in US English:



  • A curve (resembling a series of arches) traced by a point on a circle being rolled along a straight line.

    • ‘Neile's parabola was the first algebraic curve to have its arc length calculated; only the arc lengths of transcendental curves such as the cycloid and the logarithmic spiral had been calculated before this.’
    • ‘Viviani determined the tangent to the cycloid but he was not the first to succeed in this.’
    • ‘To estimate the relative surface area of basal lamina and apertures, we used a line intercept technique with cycloids.’
    • ‘He defines evolutes and involutes of curves and, after giving some elementary properties, finds the evolutes of the cycloid and of the parabola.’
    • ‘Many famous mathematicians, including Descartes, have worked on a class of curves called cycloids.’


Mid 17th century: from Greek kukloeidēs ‘circular’, from kuklos ‘circle’.