Let me ask a question. I see two different definitions of smooth curve. One is that smooth curve is $C^1$ (tangent continuous); The other is $C^{\infty}$ (infinitely differentiable). What is the motivation for this different definition?
2026-03-27 07:18:46.1774595926
What is the motivation for these different definitions of smooth curve?
39 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in DEFINITION
- How are these definitions of continuous relations equivalent?
- If a set is open, does it mean that every point is an interior point?
- What does $a^b$ mean in the definition of a cartesian closed category?
- $\lim_{n\to \infty}\sum_{j=0}^{[n/2]} \frac{1}{n} f\left( \frac{j}{n}\right)$
- Definition of "Normal topological space"
- How to verify $(a,b) = (c,d) \implies a = c \wedge b = d$ naively
- Why wolfram alpha assumed $ x>0$ as a domain of definition for $x^x $?
- Showing $x = x' \implies f(x) = f(x')$
- Inferior limit when t decreases to 0
- Is Hilbert space a Normed Space or a Inner Product Space? Or it have to be both at the same time?
Related Questions in SMOOTH-MANIFOLDS
- Smooth Principal Bundle from continuous transition functions?
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- "Defining a smooth structure on a topological manifold with boundary"
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- A finite group G acts freely on a simply connected manifold M
- An elementary proof that low rank maps cannot be open
- What does it mean by standard coordinates on $R^n$
- Partial Differential Equation using theory of manifolds
- Showing that a diffeomorphism preserves the boundary
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 SMOOTH-FUNCTIONS
- Connecting smooth functions in a smooth way
- Is the restriction (to lower dimensions) of a smooth function still smooth?
- Understanding the proof of the Concentration-Compactness principle
- Does an integral inequality imply a pointwise inequality?
- A weird definition of regular function
- Are charts for smooth manifolds homeomorphisms or diffeomorphisms?
- Find a sequence $(\phi_n)_n \subset C^{\infty}_c(\mathbb{R}^N)$ which converges in both $L^p(\nu)$ and $L^q(\mu)$ to $1_E$
- Straight Lines are Strict Minimizers of Arclength in Euclidean Space
- Several Questions on Smooth Urysohn's Lemma
- For what functions is $\lim_{n\to \infty}|f^{(n)}(x)|=0$? (Where $f^{(n)}(x)$ is the $n$th derivative of $f$)
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?