Suppose we have a space curve $r(t)=\left(x(t), y(t), z(t)\right)$ and we consider the locus of all centres of curvature of $r$. First, would this be the correct formula? $$r(t) + {1 \over \kappa(t)} N(t)$$ (where $N$ is the normal vector in the TNB-frame and $\kappa$ is curvature). And is there a name for this curve?
2026-03-30 15:57:30.1774886250
Centres of Curvature
86 Views Asked by user142299 https://math.techqa.club/user/user142299/detail At
1
There are 1 best solutions below
Related Questions in DIFFERENTIAL-GEOMETRY
- Smooth Principal Bundle from continuous transition functions?
- Compute Thom and Euler class
- Holonomy bundle is a covering space
- Alternative definition for characteristic foliation of a surface
- Studying regular space curves when restricted to two differentiable functions
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- Regular surfaces with boundary and $C^1$ domains
- Show that two isometries induce the same linear mapping
- geodesic of infinite length without self-intersections
Related Questions in CURVES
- Studying regular space curves when restricted to two differentiable functions
- The problem in my proof that if $\beta(s)=\alpha(-s)$ then the torsions of the curves satisfies $\tau_{\beta}(s)=-\tau_{\alpha}(-s)$
- Given a circle, can i assume that the point where all the normals went thought and the point where all the tangents are equidistants are the same?
- Function determining temperature of points along a curve (find local maxima temp & local minima temp)
- Reference for $L$-functions of curves
- About the Green's Theorem
- inhomogeneous coordinates to homogeneous coordinates
- Can the relocation of one control point of a NURBS curve be compensated by an adjustment of some weights?
- $\| \gamma'(t) \|$ = constant for all $t$, if and only if $\gamma''(t)$ is normal to the tangent vector space for all $t$.
- proving that a curve with constant curvature contained in a sphere its a circle
Related Questions in CURVATURE
- Sign of a curve
- What kind of curvature does a cylinder have?
- A new type of curvature multivector for surfaces?
- A closed manifold of negative Ricci curvature has no conformal vector fields
- CAT(0) references request
- Why is $\kappa$ for a vertical line in 2-space not undefined?
- Discrete points curvature analysis
- Local computation of the curvature form of a line bundle
- Closed surface embedded in $\mathbb R^3$ with nonnegative Gaussian curvature at countable number of points
- What properties of a curve fail to hold when it is not regular?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
For planar curves, it is called the evolute of the curve.
For a discussion of the spatial case, see