Theory & Explanations

Explore the Theory

Deep dives into mathematical and scientific concepts. Each article pairs with an interactive module on Riano where you can experiment in real time.

Start Exploring on Riano
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Calculus & Analysis

6 articles

Mandelbrot Set

A famous fractal generated from a simple equation in the complex plane.

Logistic Map & Chaos

Exploring bifurcation and deterministic chaos.

Taylor Series

Approximating functions with polynomials.

Euler's Formula

Visualizing e^(iθ) on the complex plane and the world's most beautiful equation.

Fibonacci & Golden Ratio

Exploring the Fibonacci sequence and its connection to the golden ratio.

Fourier Transform

Decompose a complex wave into simple sine waves.
⊞

Linear Algebra

4 articles

Bezier Curves

Parametric curves for computer graphics.

Dot Product & Projection

Visualizing vector projection and orthogonality.

Eigenvalues & Eigenvectors

Discovering the special directions that remain unchanged under linear transformations.

Linear Transformations

Visualizing 2D transformations via matrix operations.
📊

Probability & Statistics

4 articles

Random Walk

Visualize a 1D random walk over time.

Monte Carlo Simulation

Estimating Pi using random points in a circle.

Central Limit Theorem

Sample means converge to a normal distribution regardless of the population shape.

Probability Distributions

Exploring continuous probability density functions and their parameters.
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Physics

4 articles

Harmonic Oscillation

Simulating spring-mass systems and damping.

Projectile Motion

Simulating parabolic trajectories under gravity.

Boyle's Law

Exploring the inverse relationship between pressure and volume in an ideal gas at constant temperature.

Wave Interference

Visualizing constructive and destructive interference from two point sources.
⌨

Computer Science

4 articles

Sorting Algorithms

Visualizing how data is ordered.

A* Pathfinding

Finds the shortest path on a grid using heuristics.

Binary Search

Finding elements in sorted data by halving the search space.

Dijkstra's Algorithm

Finding the shortest path in a weighted graph by greedily exploring the nearest unvisited node.
🧠

Machine Learning

3 articles

Gradient Descent

Finding the minimum of a cost function.

K-Means Clustering

Partitioning data into clusters by iteratively assigning points and updating centroids.

Linear Regression

Fitting a line to data by minimizing the sum of squared residuals.

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