The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
Fermat's spiral is a special kind of spiral shape having the polar equation: r = aΘ½. Pierre de Fermat, a French lawyer who studied mathematics in his spare time, developed this shape in 1636. The equation for Fermat's spiral shows that for any given value of Θ there are two corresponding values of r. One value is negative and the other corresponding value is positive. Because of this the resulting spiral is symmetric about the line y = -x as well as the origin. Fermat's spiral is sometimes also referred to as the parabolic spiral.
The general form of a spiral is given by the polar equation r = aΘ1/n, where r is the radial distance, Θ is the angle in polar coordinates, and n is a constant determining how tightly the spiral is wound. There are special names given to spirals having n = -2, -1, 1, and 2. As can be seen in the equation given in the paragraph above for n = 2, the spiral is called Fermat's spiral. If n = -2 the spiral is called the lituus and is equal to the inverse curve of Fermat's spiral with the origin as the inversion center. "Lituus" is translated as "crook" in the sense of a bishop's crosier. The lituus curve originated with Cotes in 1722, well after Fermat developed the spiral that bears his name. The curvature of Fermat's spiral is given by k where: k(Θ) = (((3a2)/(4Θ)) + a2Θ)/(((a2/4Θ) + a2Θ)3/2).