• Anatolij T. Fomenko
  • Tosiyasu L. Kinii


We consider Euclidean space ℝn and define in it the standard Euclidean scalar product
$$\langle \xi ,\eta \rangle = {\xi ^1}{\eta ^1} + \cdots + {\xi ^n}{\eta ^n}$$
for any vectors ξ and η. With each vector ξ we associate a real number, called its length and defined as
$$\left| \xi \right| = {\left\langle {\xi ,\xi } \right\rangle ^{\frac{1}{2}}}$$


Jacobian Matrix Smooth Curve Rigid Motion Plane Curf Polar Coordinate System 
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Copyright information

© Springer Japan 1997

Authors and Affiliations

  • Anatolij T. Fomenko
    • 1
  • Tosiyasu L. Kinii
    • 2
    • 3
  1. 1.Department of Differential Geometry and Application, Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia
  2. 2.Laboratory of Digital Art and TechnologyTokyo, 113Japan
  3. 3.Senior Partner of MONOLITH Co. LtdTokyo, 106Japan

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