Beautiful Numbers vs Electrolyte Equilibria

Ever stared at a number line and wondered what numbers really are? That’s what happened when I tried to explain real numbers to my daughter. They weren’t just “points on a line” - they were invisible ideas that didn’t feel real at all. So I built a way to make them visible. With sliders, colors, and movement, she could see numbers stretch, merge, and grow. Suddenly, math wasn’t about memorising - it was about discovering. That small project grew into Beautiful Numbers - an interactive world where numbers come alive. See math like never before: - Add, subtract, multiply, divide — and watch numbers dance in real time. - Play with intervals: drag their ends, see them merge, overlap, and split. - Explore powers and roots: what happens when you flip or combine them? - Understand absolute value: visualise distance and tackle equations like |x−4| = 6. - Master percents and growth: from simple increases to compound interest that grows like magic. Whether you’re a student, teacher, or curious explorer, Beautiful Numbers helps you see what math really means - and maybe even fall in love with it. Download Beautiful Numbers and explore the world of real numbers - beautifully.

The Electrolyte Equilibria application is designed to calculate the equilibrium composition of multicomponent aqueous electrolyte solutions based on known thermodynamic equilibrium constants and the analytical concentrations of the solution components. The application uses a universal approach that describes the system of equilibria in matrix form, enabling a unified calculation scheme regardless of the type of equilibrium process or the problem's complexity. The program is based on real-world algorithms for precise chemical calculations used in professional environments. Equilibria calculations are possible for both simple systems—single-component solutions with a single equilibrium process—and for multicomponent solutions with virtually no limit to the number of equilibrium reactions. The calculations account for ion-ion interactions through the solution's ionic strength and activity coefficients, implemented iteratively. The results of equilibrium composition calculations for multicomponent solutions are presented in a table that includes the equilibrium concentrations of all particles, the ionic strength of the solutions, and the activity coefficients of ions with different charge types. The equilibrium composition calculation procedure is implemented by solving a system of nonlinear equations. When studying a series of solutions, a graphical illustration of the dependence of the equilibrium particle concentrations on the concentration of any selected component is provided. Electrolyte Equilibria is an application for modeling and analyzing chemical equilibria in complex multicomponent systems. It is a powerful analytical tool designed for chemists, researchers, teachers, and students studying the diverse physicochemical properties of solutions that depend on their equilibrium composition. The mobile version of the program provides accurate, reliable solutions whether you are in the lab or the classroom. This application provides accurate real-time calculations, beautifully visualizes equilibrium-composition diagrams, offers a straightforward interface, and enables data collection and analysis for any study. The application supports data import and export, including graphs, and supports dark and light theme options. The application can be helpful for teachers and students. It is ideal for modeling equilibria in complex systems in the research practice of students and chemical researchers for both educational and scientific purposes.