- Show that principal normal to a curve is normal to the locus of center of curvature at points where curvature is stationary.
or
Show that principal normal to a curve is normal to the locus of center of osculating circle at points where curvature is stationary.
or
Show that principal normal to a curve is normal to the locus of center of circle of curvature at points where curvature is stationary.
center of curvature =center of osculating circle=center of circle of curvature
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Show that radius of osculating circle of a circular helix is equal to radius of osculating sphere.
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Show that tangent to the locus of center of osculating sphere is parallel to the binormal of the curve at corresponding points.
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Show that for a curve of constant curvature center of osculating sphere coincides with center of osculating circle.
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Show that tangent to the locus of center of osculating sphere passes through the center of osculating circle.
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If a curve lies on a sphere, show that \( \rho \) and \( \sigma \) are connected by the relation \( \rho \tau + \frac{d}{ds}(\sigma \rho')=0 \)
or
Show that necessary and sufficient condition for a curve to lie on a surface of sphere is \( \rho \tau + \frac{d}{ds}(\sigma \rho')=0 \)
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