Intereting Posts

Is it possible to solve the Zebra Puzzle/Einstein's Riddle using pure math?
Recast the scalar SPDE $du_t(Φ_t(x))=f_t(Φ_t(x))dt+∇ u_t(Φ_t(x))⋅ξ_t(Φ_t(x))dW_t$ into a SDE in an infinite dimensional function space.
How many positive integers $ n$ with $1 \le n \le 2500$ are prime relative to $3$ and $5$?
Compute the Galois group of $p(x)=x^4+ax^3+bx^2+cx+d$
Is the sequence $a_{n}=\prod\limits_{i=1}^{n}\left(1+\frac{i}{n^2}\right)$ decreasing?
Length of a Parabolic Curve
$\zeta(2)=\frac{\pi^2}{6}$ proof improvement.
Strict cyclic order
Formula relating Euler characteristics $\chi(A)$, $\chi(X)$, $\chi(Y)$, $\chi(Y \cup_f X)$ when $X$ and $Y$ are finite.
proof of that a continuous function has a fixed point
Proving that $x$ is an integer, if the differences between any two of $x^{1919}$, $x^{1960}$, and $x^{2100}$ are integers
central limit theorem for a product
How to logically analyze the statement: “Nobody in the calculus class is smarter than everybody in the discrete math class.”
Topology: Proof that a finitely generated cone is closed
What is wrong in my proof that 90 = 95? Or is it correct?

I would like to calculate the exponential map in the n-sphere, however, i don’t know how to get started. Someone could give me a tip or bibliographic reference?

- Shape operator and principal curvature
- A determinant coming out from the computation of a volume form
- Prerequisite for Petersen's Riemannian Geometry
- Manifolds with geodesics which minimize length globally
- Need help finding a good book on Riemann Geometry
- Exponential map on the the n-sphere
- Is length adimensional when space is not flat?
- horizontal vector in tangent bundle
- the Levi-Civita connection on a product of Riemannian manifolds
- Mean curvature in terms of Christoffel symbols

$\newcommand{\Vec}[1]{\mathbf{#1}}$If $\Vec{v}$ is a non-zero tangent vector to the $n$-sphere at a point $\Vec{p}$, the geodesic starting at $\Vec{p}$ with initial velocity $\Vec{v}$ is a circle of speed $\|\Vec{v}\|$ lying in the plane spanned by $\Vec{p}$ and $\Vec{v}$:

$$

\gamma(t) = \cos(\|\Vec{v}\|t) \Vec{p} + \sin(\|\Vec{v}\|t) \frac{\Vec{v}}{\|\Vec{v}\|}.

$$

- How to derive inverse hyperbolic trigonometric functions
- Proving Crapo's Lemma
- Left and right ideals of $R=\left\{\bigl(\begin{smallmatrix}a&b\\0&c \end{smallmatrix}\bigr) : a\in\mathbb Z, \ b,c\in\mathbb Q\right\}$
- How does $\cos x=\frac12(e^{ix}+e^{-ix})$?
- Is the image of a tensor product equal to the tensor product of the images?
- Bound variance proxy of a subGaussian random variable by its variance
- proof of l'Hôpital's rule
- Suprema proof: prove $\sup(f+g) \le \sup f + \sup g$
- What are the angle brackets in Linear Algebra?
- On functions with Fourier transform having compact support
- Counting some special derangements
- Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?
- Proving all primes are 1 or -1 modulo 6
- Are the real product rule and quotient rule for integration already known?
- Bounded variation, difference of two increasing functions