made with Mathematica technology MathWorld
Algebra
Applied Mathematics
Calculus and Analysis
Discrete Mathematics
Foundations of Mathematics
Geometry
History and Terminology
Number Theory
Probability and Statistics
Recreational Mathematics
Topology
Alphabetical Index
Interactive Entries
Random Entry
New in MathWorld
MathWorld Classroom
About MathWorld
Contribute to MathWorld
Send a Message to the Team
MathWorld Book
12,905 entries
Last updated: Mon Jan 5 2009

Created, developed, and nurtured by Eric Weisstein
at Wolfram Research
Geometry > Curves > Plane Curves > Algebraic Curves >

Dumbbell Curve
DOWNLOAD Mathematica Notebook
DumbbellCurve

The dumbbell curve is the sextic curve

y^2=a^2(x^4-x^6).
(1)

It has area

A=1/4pia^2
(2)

and approximate arc length

s approx 5.541.
(3)

For the parametrization

x=t
(4)
y=t^2sqrt(1-t^2),
(5)

the curvature is

kappa=(2-9t^2+6t^4)/((1+3t^2-12t^4+9t^6)^(3/2)).
(6)

SEE ALSO: Barbell Graph, Butterfly Curve, Devil's Curve, Eight Curve, Lemniscate, Piriform, Teardrop Curve

REFERENCES:

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.




CITE THIS AS:

Weisstein, Eric W. "Dumbbell Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DumbbellCurve.html

SendContact the MathWorld Team
© 1999-2009 Wolfram Research, Inc. | Terms of Use

The Wolfram Demonstrations Project Browse Topics View Latest
JUST RELEASED: Wolfram Mathematica 7
 Other Wolfram Web Resources »
Wolfram Research
Mathematica Home Page
Mathematica Documentation Center
Wolfram Demonstrations Project
Online Integrator
Functions Site
Wolfram Tones
Wolfram Science
Wolfram Blog
more…