Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
- Additional Readings
A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay off distance a along the secant OQ, in both directions from Q. The locus of the two points thus obtained is a cardioid (see illustration). If a rectangular coordinate system is chosen with O for origin initially and y axis tangent to C at O, the cardioid has the equation (x2 + y2 − ax)2 = a2(x2 + y2). The equation expressed in polar coordinates is ρ = a(1 + cos θ). The cardioid's area is , or six times the area of C, and its length is 8a. See also: Analytic geometry
The content above is only an excerpt.
for your institution. Subscribe
To learn more about subscribing to AccessScience, or to request a no-risk trial of this award-winning scientific reference for your institution, fill in your information and a member of our Sales Team will contact you as soon as possible.
to your librarian. Recommend
Let your librarian know about the award-winning gateway to the most trustworthy and accurate scientific information.
AccessScience provides the most accurate and trustworthy scientific information available.
Recognized as an award-winning gateway to scientific knowledge, AccessScience is an amazing online resource that contains high-quality reference material written specifically for students. Its dedicated editorial team is led by Sagan Award winner John Rennie. Contributors include more than 9000 highly qualified scientists and 39 Nobel Prize winners.
MORE THAN 8500 articles and Research Reviews covering all major scientific disciplines and encompassing the McGraw-Hill Encyclopedia of Science & Technology and McGraw-Hill Yearbook of Science & Technology
115,000-PLUS definitions from the McGraw-Hill Dictionary of Scientific and Technical Terms
3000 biographies of notable scientific figures
MORE THAN 17,000 downloadable images and animations illustrating key topics
ENGAGING VIDEOS highlighting the life and work of award-winning scientists
SUGGESTIONS FOR FURTHER STUDY and additional readings to guide students to deeper understanding and research
LINKS TO CITABLE LITERATURE help students expand their knowledge using primary sources of information