A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius radius of a rolling circle .
Curtate cycloids are used by some violin makers for the back arches of some instruments,
and they resemble those found in some of the great Cremonese instruments of the early
18th century, such as those by Stradivari (Playfair 1999).
A curtate cycloid has parametric equations
The arc length from
(3)
where elliptic integral
of the second kind .
See also Curtate Cycloid Evolute ,
Cycloid ,
Prolate Cycloid ,
Trochoid
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References Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Harris, J. W. and Stocker, H. Handbook
of Mathematics and Computational Science. Lawrence, J. D. A
Catalog of Special Plane Curves. Lockwood, E. H. A
Book of Curves. Mann, S. "CCylcoid 3.1." http://www.cgl.uwaterloo.ca/~smann/ccycloid/ . Playfair,
Q. "Cremona's Forgotten Curve." The Strad 110 , 1194-1197,
1999. Steinhaus, H. Mathematical
Snapshots, 3rd ed. Zwillinger,
D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Referenced on Wolfram|Alpha Curtate Cycloid
Cite this as:
Weisstein, Eric W. "Curtate Cycloid."
From MathWorld https://mathworld.wolfram.com/CurtateCycloid.html
Subject classifications
, where 
is the radius of a rolling circle.
Curtate cycloids are used by some violin makers for the back arches of some instruments,
and they resemble those found in some of the great Cremonese instruments of the early
18th century, such as those by Stradivari (Playfair 1999).
is
is an incomplete elliptic integral
of the second kind.
