Viviani determined the tangent to the cycloid but he was not the first to succeed in this.
He defines evolutes and involutes of curves and, after giving some elementary properties, finds the evolutes of the cycloid and of the parabola.
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.
To estimate the relative surface area of basal lamina and apertures, we used a line intercept technique with cycloids .
Huygens believed that a pendulum swinging in a large are would be more useful at sea and he invented the cycloidal pendulum with this in mind.
Many famous mathematicians, including Descartes, have worked on a class of curves called cycloids .
The ships are fitted with two independent Voith Schneider 18GH cycloidal propellers, which provide propulsion and steering in cruising and minehunting modes, and two twin tube bow thrusters.
He also worked on cycloidal pendulums, the laws of resistance in a fluid and differential geometry.
Desargues proposed cycloidal teeth for gear wheels in the 1630's.
Our arch is a cycloidal arch, inspired by the one in Kahn's Kimbell Museum.