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 RianoCalculus & Analysis
46 articlesMandelbrot Set
A famous fractal generated from a simple equation in the complex plane.
Numerical Integration
Visualizing Riemann sums, Trapezoidal, and Simpson's rules to approximate definite integrals.
Logistic Map & Chaos
Exploring bifurcation and deterministic chaos.
Taylor Series
Approximating functions with polynomials.
Complex Number Visualization
Complex Number Visualization
Euler's Formula
Visualizing e^(iθ) on the complex plane and the world's most beautiful equation.
Linear Algebra
41 articlesBezier Curves
Parametric curves for computer graphics.
Matrix Multiplication
Visualize how 2x2 matrices transform space and combine through multiplication.
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.
Cross Product
Cross Product
Probability & Statistics
41 articlesRandom 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.
Bayes' Theorem
A fundamental theorem for updating probabilities based on new evidence.
Birthday Paradox
Birthday Paradox
Physics
44 articlesHarmonic 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.
Electromagnetic Waves
Electromagnetic Waves
Fluid Dynamics
Interactive fluid dynamics simulation.
Computer Science
39 articlesSorting 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.
Graph Traversal (BFS/DFS)
Visualize how Breadth-First and Depth-First Search algorithms navigate through graph data structures.
Convex Hull
Convex Hull
Machine Learning
43 articlesGradient Descent
Finding the minimum of a cost function.
Perceptron
Visualize the Perceptron algorithm learning a linear decision boundary.
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.
Attention Mechanism
Attention Mechanism
Decision Boundaries
Visualize how model complexity and regularization shape the separation between classes.
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