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The Frenet–Serret frame moving along a helix in space. The Frenet–Serret frame consisting of the tangent T, normal N, and binormal B collectively forms an orthonormal basis of 3-space. At each point of the curve, this attaches a frame of reference or rectilinear coordinate system (see image). The Frenet–Serret formulas admit a kinematic ...
In case all three Frenet–Serret curvatures are constant, the corresponding worldlines are identical to those that follow from the Killing motions in flat spacetime. They are of particular interest since the corresponding proper frames and congruences satisfy the condition of Born rigidity , that is, the spacetime distance of two neighbouring ...
An illustration of the Frenet frame for a point on a space curve. T is the unit tangent, P the unit normal, and B the unit binormal. A Frenet frame is a moving reference frame of n orthonormal vectors e i (t) which are used to describe a curve locally at each point γ(t). It is the main tool in the differential geometric treatment of curves ...
In three dimensions, the third-order behavior of a curve is described by a related notion of torsion, which measures the extent to which a curve tends to move as a helical path in space. The torsion and curvature are related by the Frenet–Serret formulas (in three dimensions) and their generalization (in higher dimensions).
[1] [2] [3] The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures. If the surface is saddle shaped the maxima of both sides are the principal curvatures.
The torsion tensor thus is related to, although distinct from, the torsion of a curve, as it appears in the Frenet–Serret formulas: the torsion of a connection measures a dislocation of a developed curve out of its plane, while the torsion of a curve is also a dislocation out of its osculating plane.
Jean Frédéric Frenet (French:; 7 February 1816 – 12 June 1900) was a French mathematician, astronomer, and meteorologist. He was born and died in Périgueux , France. He is best known for being an independent co-discoverer of the Frenet–Serret formulas .
The "35" in the calculator's name came from the number of keys. The original HP-35 was available from 1972 to 1975. In 2007 HP announced the release of the "retro"-look HP 35s to commemorate the 35th anniversary of the launch of the original HP-35. It was priced at US$59.99. [3] The HP-35 was named an IEEE Milestone in 2009. [4]