A Graphic Method for Constructing Spherical Indicatrices
作者:
LeeLawrence L.,
期刊:
The American Mathematical Monthly
(Taylor Available online 1977)
卷期:
Volume 84,
issue 6
页码: 461-463
ISSN:0002-9890
年代: 1977
DOI:10.1080/00029890.1977.11994385
出版商: Taylor&Francis
数据来源: Taylor
摘要:
AbstractA graphic method is presented for constructing the spherical indicatrices of the tangent, principal-normal, and binormal of space curves described by intrinsic equations. Using this method, it will not be necessary to integrate the Serret-Frenet formulas. The indicatrices are obtained directly by mapping plane curves onto a unit sphere. This mapping requires the sphere to roll on the plane such that the locus of the contact point in the plane is the preimage and the corresponding locus on the sphere is the desired indicatrix. Equations for the plane curves are derived and procedures for performing the graphic mapping are outlined.
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