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  2. Normal (geometry) - Wikipedia

    en.wikipedia.org/wiki/Normal_(geometry)

    In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point. A normal vector of length one is called a unit normal vector.

  3. Osculating circle - Wikipedia

    en.wikipedia.org/wiki/Osculating_circle

    The circle with center at Q and with radius R is called the osculating circle to the curve γ at the point P. If C is a regular space curve then the osculating circle is defined in a similar way, using the principal normal vector N. It lies in the osculating plane, the plane spanned by the tangent and principal normal vectors T and N at the ...

  4. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...

  5. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    The concept of unit circle (the set of all vectors of norm 1) is different in different norms: for the 1-norm, the unit circle is a square oriented as a diamond; for the 2-norm (Euclidean norm), it is the well-known unit circle; while for the infinity norm, it is an axis-aligned square.

  6. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    Differential geometry of curves is the branch of geometry that ... The tangent and the normal vector at point t define the ... A circle with radius r ...

  7. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.

  8. Analytic geometry - Wikipedia

    en.wikipedia.org/wiki/Analytic_geometry

    In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.

  9. Frenet–Serret formulas - Wikipedia

    en.wikipedia.org/wiki/Frenet–Serret_formulas

    A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.