These are the normal curvature, geodesic curvature and geodesic torsion.

A circular helix, ( i. e. one with constant radius ) has constant band curvature and constant torsion.

A curve is a general helix if and only if the ratio of curvature to torsion is constant.

This property is used to check, for example, that even though the Lie derivative and covariant derivative are not tensors, the torsion and curvature tensors built from them are.

Connections also lead to convenient formulations of geometric invariants, such as the curvature ( see also curvature tensor and curvature form ), and torsion tensor.

Also the curvature, torsion, and geodesics may be defined only in terms of the covariant derivative or other related variation on the idea of a linear connection.

The Frenet-Serret formulas show that there is a pair of functions defined on the curve, the torsion and curvature, which are obtained by differentiating the frame, and which describe completely how the frame evolves in time along the curve.

The affine connection may be used to define curvature and torsion, as is usual in Riemannian geometry.

Quantitatively, this is measured by the differential-geometric invariants called the curvature and the torsion of a curve.

It is the main tool in the differential geometric treatment of curves as it is far easier and more natural to describe local properties ( e. g. curvature, torsion ) in terms of a local reference system than using a global one like the Euclidean coordinates.

The second generalized curvature χ < sub > 2 </ sub >( t ) is called torsion and measures the deviance of γ from being a plane curve.

# a six-dimensional directional-measuring device that measures the flow of information with respect to curvature and torsion of spacetime ;

The 6-phase clock described in Fredkin's " Digital Mechanics " might be a counting mechanism for the 6-dimensional directional-measuring device that measures the curvature and torsion of information flow.

Whereas the Riemann curvature applies a tidal acceleration, the torsion causes the geodesics to twist around each other.

the Einstein action in the teleparallel form, where torsion is just an equivalent alternative to curvature.

The main invariants of an affine connection are its torsion and its curvature.

where d / ds is the derivative with respect to arclength, κ is the curvature and τ is the torsion of the curve.

The two scalars κ and τ effectively define the curvature and torsion of a space curve.

where is the curvature and is the torsion.

This is easily visualized in the case when the curvature is a positive constant and the torsion vanishes.

#< li value = 2 > On the example of a torus knot, the tangent vector T, the normal vector N, and the binormal vector B, along with the curvature κ ( s ), and the torsion τ ( s ) are displayed.

Bridges may be classified by how the forces of tension, compression, bending, torsion and shear are distributed through their structure.

The transition to the torsion catapults, which are not considered crossbows and came to dominate Greek and Roman artillery design is first evident in inventories of the Athenian arsenal from between 338 and 326 BC.

The later entry is particularly noteworthy as it constitutes the first clear evidence for the switch to torsion catapults which are more powerful than the flexible crossbows and came to dominate Greek and Roman artillery design thereafter.

Dilated cardiomyopathy and bone cancer are the leading cause of death and like all deep-chested dogs, gastric torsion ( bloat ) is common ; the breed is affected by hereditary intrahepatic portosystemic shunt.

The latter are just the abelian torsion groups.

the two platforms are connected by heavy metal torsion bar that enables the board to twist in the centre.

Based on the same principle as the gold-leaf electroscope, repulsion electrometers are more sensitive indicating devices using a form of torsion balance.

When a moderate number of sheets are inserted between the two " tongues " of the clip, the tongues will be forced apart and cause torsion in the bend of the wire to grip the sheets together.

In addition, moment of inertia should not be confused with polar moment of inertia ( more specifically, polar moment of inertia of area ), which is a measure of an object's ability to resist torsion ( twisting ) only, although, mathematically, they are similar: if the solid for which the moment of inertia is being calculated has uniform thickness in the direction of the rotating axis, and also has uniform mass density, the difference between the two types of moments of inertia is a factor of mass per unit area.

Spring-based shock absorbers commonly use coil springs or leaf springs, though torsion bars are used in torsional shocks as well.

In this model, fixed length polymer segments are linearly connected, and all bond and torsion angles are equiprobable.

Under this fixed angle the segments are still free to rotate and all torsion angles are equally likely.

In the rotational isomeric state model the allowed torsion angles are determined by the positions of the minima in the rotational potential energy.

Snails are distinguished by an anatomical process known as torsion, where the visceral mass of the animal rotates 180 ° to one side during development, such that the anus is situated more or less above the head.

The effects of torsion are primarily physiological-the organism develops an asymmetrical nature with the majority of growth occurring on the left side.

Though less pressing, such individuals are at significant risk of complete torsion and possible subsequent orchiectomy and the recommended treatment is elective bilateral orchiopexy.

* Coil spring or helical spring – a spring ( made by winding a wire around a cylinder ) and the conical spring – these are types of torsion spring, because the wire itself is twisted when the spring is compressed or stretched.

In mathematics, specifically module theory, annihilators are a concept that generalizes torsion and orthogonal complement.

The ( rational ) Betti numbers b < sub > k </ sub >( X ) do not take into account any torsion in the homology groups, but they are very useful basic topological invariants.

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 perform a corkscrew in space.

** The closely related concepts of Reidemeister torsion ( also called R-torsion, Franz torsion, de Rham torsion ) and analytic torsion ( also called Ray-Singer torsion )

Some front-wheel drive automobiles use a related type of torsion beam suspension, usually called a twist beam rear suspension, in which the rear wheels are carried on trailing arms connected by a laterally mounted torsion beam.

** Polar moment of inertia, a property of an object related to its resistance to torsion

He carried out a number of magnetic investigations which resulted in the discovery of many interesting phenomena, some of which have been rediscovered by others ; they related among other things to the effect of mechanical strain on the magnetic properties of the magnetic metals, to the relation between the chemical composition of compound bodies and their magnetic properties, and to a curious parallelism between the laws of torsion and of magnetism ( see Wiedemann effect ).

# In the continuum limit, the translational holonomy becomes affine torsion, the distribution of rotating black holes generates spin density, and the torsion and spin density are related exactly as in Einstein – Cartan theory.

In order to understand why torsion should be related to spin, we can consider how the presence of torsion may affect observers living in contorted spacetime.

For example, it has been suggested that the torsion ( antisymmetric part of the affine connection ) might be related to isospin rather than electromagnetism ; this is related to a discrete ( or " internal ") symmetry known to Einstein as " displacement field duality ".