Grow your own spiral galaxy
$m\approx\dfrac{\kappa^2R}{2\pi G\Sigma X},\quad X\approx2$
A live N-body disc in your browser: light discs, massive discs, bars, tidal encounters and the winding problem
Welcome to my blog.
I’m Igor, an applied mathematician. I write here about geometry, optimal control, formal proofs, machine learning and software engineering, mostly as research series with their equations, figures and code.
Exploring prime spirals through sunflower geometry
$z_p=\sqrt p\,e^{2\pi i\beta p},\quad \beta=1/\varphi^2$
Golden angles, quadratic tracks, and the divisibility behind the patterns
Proof Atlas: Compiled Proof Graphs and Article Coverage
739 + 1,359 declarations · 1,277,896 shared nodes
Complete compiled proof graphs from two Lean corpora, their shared structure, and the limits of correspondence with a mathematical article.
Hidden Protostars: Survey Evidence and Its Limits
14/27 vs 15/27 positives at 18 reviews
Reproducible catalogue associations, a non-identifiability result, and failed ranking and uncertainty gates define what the present surveys establish.
The Shortest Path When You Cannot Move Sideways
$\dot q=u_1X_1+u_2X_2,\quad X_1=\cos\theta\,\partial_x+\sin\theta\,\partial_y$
An interactive guide to the geometry of motion in the plane: from a simple constraint to the pendulum, competing routes, and the complete shortest-path solution.
Beyond the Shortest Path: Geodesics on SE(2)
$\operatorname{sn}^2(\psi+p)=r(p)$
One research program, three questions: when a path loses local optimality, where nearby paths focus, and how many paths reach the same position and heading. Follow the pendulum, explore the conjugate locus, and count the inverse images.
Forbidden Directions: Exact Magnetic Laws and Estimator Limits
$\delta(\varepsilon)=1-\tfrac{2}{\pi}K(2\varepsilon),\quad \varepsilon<\tfrac12$
A holonomy growth law and exact magnetic identities hold under stated assumptions. Matched estimator comparisons favour standard fits, and a purported magnetospheric null census fails its domain audit.