2026-07 on Andrey's Notes on Everything

Interactive Mathematical Pendulum Simulation

Fri, 03 Jul 2026 00:00:00 +0000

Mathematical pendulums are among the most fundamental oscillating systems studied in physics. This interactive simulation allows you to explore how pendulum motion depends on length, gravity, and initial displacement. The model uses the full nonlinear pendulum equation and integrates the motion using a fourth-order Runge–Kutta method for improved numerical accuracy.

Interactive Pendulum Wave Simulation

Fri, 03 Jul 2026 00:00:00 +0000

A pendulum wave is a mesmerizing physical phenomenon created by multiple pendulums of different lengths oscillating from the same support. Although all pendulums start in phase, their slightly different natural periods gradually cause them to drift apart, forming beautiful wave-like patterns. After a certain amount of time, the system partially or fully synchronizes again, creating repeating visual structures.

This interactive simulation lets you experiment with pendulum lengths, initial angle, gravity, and time scale while observing how differences in oscillation period influence phase relationships between multiple pendulums.

Lemniscate of Bernoulli

Fri, 03 Jul 2026 00:00:00 +0000

The Lemniscate of Bernoulli is a fascinating plane curve discovered by the Swiss mathematician Jakob Bernoulli in 1694. Its characteristic figure-eight shape makes it one of the most recognizable curves in mathematics. The curve can be defined as the set of points for which the product of the distances to two fixed points (foci) remains constant.

Visualizing Sorting Algorithms in Real Time

Fri, 03 Jul 2026 00:00:00 +0000

Sorting algorithms are one of the fundamental building blocks of computer science. While their source code is often only a few lines long, understanding how elements move through a collection can be much easier when the process is visualized.