Projection of Center of Osculating Sphere on Space Curve
Masayuki Ikeuti
Abstract
Open-access reader
Masayuki Ikeuti
Abstract
Open-access reader
The purpose of this note is to find an adequate conception of properties of space curve by straightedge and compass methods. The horizontal trace of the osculating plane coincides with the tangent line of the locus which is drawn by the horizontal trace of the tangent line moving along the space curve. The radius of curvature, torsion, and the osculating sphere can be found using the projection of the osculating plane. The projection of the center of the osculating sphere can also be drawn using the projection of the osculating plane.
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The purpose of this note is to find an adequate conception of properties of space curve by straightedge and compass methods. The horizontal trace of the osculating plane coincides with the tangent line of the locus which is drawn by the horizontal trace of the tangent line moving along the space curve. The radius of curvature, torsion, and the osculating sphere can be found using the projection of the osculating plane. The projection of the center of the osculating sphere can also be drawn using the projection of the osculating plane.
Key concepts: Osculating circle, Mathematics, Tangent, Center of curvature, Geometry, Projection (relational algebra), Curvature, Mathematical analysis