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Osculating sphere

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at a point of a curve

The sphere having contact of order with at (see Osculation). The osculating sphere can also be defined as the limit of a variable sphere passing through four points of as these points approach . If the radius of curvature of at is equal to and is the torsion, then the formula for calculating the radius of the osculating sphere has the form

where denotes the differential along an arc of .


Comments

References

[a1] R.S. Millman, G.D. Parker, "Elements of differential geometry" , Prentice-Hall (1979) pp. 39
[a2] D.J. Struik, "Lectures on classical differential geometry" , Dover, reprint (1988) pp. 25
How to Cite This Entry:
Osculating sphere. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Osculating_sphere&oldid=31967
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article