The FirstPrinciple Blog

STEM, explained from scratch.

First-principles tutorials on math, physics, and computer science — paired with free interactive tools.

Theory of ComputationMar 9, 2026·2 min read

Turing Machine Simulator — Turing Machines Explained Interactively

Learn Turing Machines from first principles with our free interactive Turing Machine Simulator. Visual explanations, real-time simulations, no login required.

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Operating SystemsMar 9, 2026·2 min read

Memory Allocator — Memory Allocation Explained Interactively

Learn Memory Allocation from first principles with our free interactive Memory Allocator. Visual explanations, real-time simulations, no login required.

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Computer ArchitectureMar 9, 2026·2 min read

CPU Pipeline Simulator — CPU Pipelining Explained Interactively

Learn CPU Pipelining from first principles with our free interactive CPU Pipeline Simulator. Visual explanations, real-time simulations, no login required.

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Digital LogicMar 9, 2026·2 min read

Logic Gate Simulator — Logic Gates Explained Interactively

Learn Logic Gates from first principles with our free interactive Logic Gate Simulator. Visual explanations, real-time simulations, no login required.

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Data StructuresMar 9, 2026·2 min read

Hash Table Visualizer — Hash Tables Explained Interactively

Learn Hash Tables from first principles with our free interactive Hash Table Visualizer. Visual explanations, real-time simulations, no login required.

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NetworkingMar 9, 2026·2 min read

Packet Simulator — Network Packets Explained Interactively

Learn Network Packets from first principles with our free interactive Packet Simulator. Visual explanations, real-time simulations, no login required.

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ProgrammingMar 9, 2026·2 min read

Code Visualizer — Code Execution Explained Interactively

Learn Code Execution from first principles with our free interactive Code Visualizer. Visual explanations, real-time simulations, no login required.

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AutomataMar 9, 2026·2 min read

Finite State Machine Builder — Finite Automata Explained Interactively

Learn Finite Automata from first principles with our free interactive Finite State Machine Builder. Visual explanations, real-time simulations, no login require

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ProgrammingMar 9, 2026·2 min read

Regex Tester — Regular Expressions Explained Interactively

Learn Regular Expressions from first principles with our free interactive Regex Tester. Visual explanations, real-time simulations, no login required.

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AlgorithmsMar 9, 2026·2 min read

Big-O Comparator — Big-O Notation Explained Interactively

Learn Big-O Notation from first principles with our free interactive Big-O Comparator. Visual explanations, real-time simulations, no login required.

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Data StructuresMar 9, 2026·2 min read

Linked List Visualizer — Linked Lists Explained Interactively

Learn Linked Lists from first principles with our free interactive Linked List Visualizer. Visual explanations, real-time simulations, no login required.

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Data StructuresMar 9, 2026·2 min read

Stack & Queue Visualizer — Stacks and Queues Explained Interactively

Learn Stacks and Queues from first principles with our free interactive Stack & Queue Visualizer. Visual explanations, real-time simulations, no login required.

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Data StructuresMar 9, 2026·2 min read

Binary Search Tree — Binary Search Trees Explained Interactively

Learn Binary Search Trees from first principles with our free interactive Binary Search Tree. Visual explanations, real-time simulations, no login required.

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AlgorithmsMar 9, 2026·2 min read

Recursion Visualizer — Recursion Explained Interactively

Learn Recursion from first principles with our free interactive Recursion Visualizer. Visual explanations, real-time simulations, no login required.

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Graph AlgorithmsMar 9, 2026·2 min read

Graph Traversal — Graph Traversal Explained Interactively

Learn Graph Traversal from first principles with our free interactive Graph Traversal. Visual explanations, real-time simulations, no login required.

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AlgorithmsMar 9, 2026·2 min read

Sorting Visualizer — Sorting Algorithms Explained Interactively

Learn Sorting Algorithms from first principles with our free interactive Sorting Visualizer. Visual explanations, real-time simulations, no login required.

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DatabasesMar 9, 2026·2 min read

SQL Visualizer — SQL Queries Explained Interactively

Learn SQL Queries from first principles with our free interactive SQL Visualizer. Visual explanations, real-time simulations, no login required.

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Graph AlgorithmsMar 9, 2026·2 min read

Pathfinding Visualizer — Pathfinding Algorithms Explained Interactively

Learn Pathfinding Algorithms from first principles with our free interactive Pathfinding Visualizer. Visual explanations, real-time simulations, no login requir

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OpticsMar 9, 2026·2 min read

Lens & Mirror Calculator — Thin Lens Optics Explained Interactively

Learn Thin Lens Optics from first principles with our free interactive Lens & Mirror Calculator. Visual explanations, real-time simulations, no login required.

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ElectromagnetismMar 9, 2026·2 min read

Electromagnetic Induction — Electromagnetic Induction Explained Interactively

Learn Electromagnetic Induction from first principles with our free interactive Electromagnetic Induction. Visual explanations, real-time simulations, no login

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Quantum MechanicsMar 9, 2026·2 min read

Quantum Wave Function — Quantum Wave Functions Explained Interactively

Learn Quantum Wave Functions from first principles with our free interactive Quantum Wave Function. Visual explanations, real-time simulations, no login require

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ThermodynamicsMar 9, 2026·2 min read

PV Diagram Tool — PV Diagrams Explained Interactively

Learn PV Diagrams from first principles with our free interactive PV Diagram Tool. Visual explanations, real-time simulations, no login required.

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MechanicsMar 9, 2026·2 min read

Free Body Diagram — Force Diagrams Explained Interactively

Learn Force Diagrams from first principles with our free interactive Free Body Diagram. Visual explanations, real-time simulations, no login required.

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WavesMar 9, 2026·2 min read

Wave Superposition — Wave Interference Explained Interactively

Learn Wave Interference from first principles with our free interactive Wave Superposition. Visual explanations, real-time simulations, no login required.

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ElectromagnetismMar 9, 2026·2 min read

Electric Field Visualizer — Electric Fields Explained Interactively

Learn Electric Fields from first principles with our free interactive Electric Field Visualizer. Visual explanations, real-time simulations, no login required.

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MechanicsMar 9, 2026·2 min read

Projectile Motion Lab — Projectile Motion Explained Interactively

Learn Projectile Motion from first principles with our free interactive Projectile Motion Lab. Visual explanations, real-time simulations, no login required.

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MechanicsMar 9, 2026·2 min read

Momentum Conservation Lab — Conservation of Momentum Explained Interactively

Learn Conservation of Momentum from first principles with our free interactive Momentum Conservation Lab. Visual explanations, real-time simulations, no login r

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MechanicsMar 9, 2026·2 min read

Spring-Mass System — Simple Harmonic Motion Explained Interactively

Learn Simple Harmonic Motion from first principles with our free interactive Spring-Mass System. Visual explanations, real-time simulations, no login required.

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Chaos TheoryMar 9, 2026·2 min read

Double Pendulum — Chaos Theory Explained Interactively

Learn Chaos Theory from first principles with our free interactive Double Pendulum. Visual explanations, real-time simulations, no login required.

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OpticsMar 9, 2026·2 min read

Ray Optics Simulator — Ray Optics Explained Interactively

Learn Ray Optics from first principles with our free interactive Ray Optics Simulator. Visual explanations, real-time simulations, no login required.

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MechanicsMar 9, 2026·2 min read

Orbital Gravity Simulator — Orbital Mechanics Explained Interactively

Learn Orbital Mechanics from first principles with our free interactive Orbital Gravity Simulator. Visual explanations, real-time simulations, no login required

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ElectromagnetismMar 9, 2026·2 min read

Circuit Builder — Circuit Analysis Explained Interactively

Learn Circuit Analysis from first principles with our free interactive Circuit Builder. Visual explanations, real-time simulations, no login required.

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Linear AlgebraMar 9, 2026·2 min read

Linear Algebra Visualizer — Linear Transformations Explained Interactively

Learn Linear Transformations from first principles with our free interactive Linear Algebra Visualizer. Visual explanations, real-time simulations, no login req

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Number TheoryMar 9, 2026·2 min read

Number Theory Explorer — Number Theory Explained Interactively

Learn Number Theory from first principles with our free interactive Number Theory Explorer. Visual explanations, real-time simulations, no login required.

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StatisticsMar 9, 2026·2 min read

Statistics Calculator — Descriptive Statistics Explained Interactively

Learn Descriptive Statistics from first principles with our free interactive Statistics Calculator. Visual explanations, real-time simulations, no login require

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StatisticsMar 9, 2026·2 min read

Monte Carlo Simulator — Monte Carlo Methods Explained Interactively

Learn Monte Carlo Methods from first principles with our free interactive Monte Carlo Simulator. Visual explanations, real-time simulations, no login required.

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Multivariable CalculusMar 9, 2026·2 min read

Vector Field Visualizer — Vector Fields Explained Interactively

Learn Vector Fields from first principles with our free interactive Vector Field Visualizer. Visual explanations, real-time simulations, no login required.

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Signals & SystemsMar 9, 2026·2 min read

Laplace Transform Visualizer — The Laplace Transform Explained Interactively

Learn the Laplace Transform from first principles with our free interactive Laplace Transform Visualizer. Visual explanations, real-time simulations, no login r

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SignalsMar 9, 2026·2 min read

Fourier Transform — The Fourier Transform Explained Interactively

Learn the Fourier Transform from first principles with our free interactive Fourier Transform. Visual explanations, real-time simulations, no login required.

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SignalsMar 9, 2026·2 min read

Fourier Series — Fourier Series Explained Interactively

Learn Fourier Series from first principles with our free interactive Fourier Series. Visual explanations, real-time simulations, no login required.

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AlgebraMar 9, 2026·2 min read

Equation Solver — Equation Solving Explained Interactively

Learn Equation Solving from first principles with our free interactive Equation Solver. Visual explanations, real-time simulations, no login required.

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Complex AnalysisMar 9, 2026·2 min read

Complex Number Plotter — Complex Numbers Explained Interactively

Learn Complex Numbers from first principles with our free interactive Complex Number Plotter. Visual explanations, real-time simulations, no login required.

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CalculusMar 9, 2026·2 min read

Taylor Series Explorer — Taylor Series Explained Interactively

Learn Taylor Series from first principles with our free interactive Taylor Series Explorer. Visual explanations, real-time simulations, no login required.

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StatisticsMar 9, 2026·2 min read

Probability Simulator — Probability Simulations Explained Interactively

Learn Probability Simulations from first principles with our free interactive Probability Simulator. Visual explanations, real-time simulations, no login requir

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CalculusMar 9, 2026·2 min read

Integration Visualizer — Riemann Sums Explained Interactively

Learn Riemann Sums from first principles with our free interactive Integration Visualizer. Visual explanations, real-time simulations, no login required.

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Linear AlgebraMar 9, 2026·2 min read

Matrix Calculator — Matrix Operations Explained Interactively

Learn Matrix Operations from first principles with our free interactive Matrix Calculator. Visual explanations, real-time simulations, no login required.

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Differential EquationsMar 9, 2026·2 min read

Differential Equation Solver — Differential Equations Explained Interactively

Learn Differential Equations from first principles with our free interactive Differential Equation Solver. Visual explanations, real-time simulations, no login

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Algebra & CalculusMar 9, 2026·2 min read

Graphing Calculator — Function Graphing Explained Interactively

Learn Function Graphing from first principles with our free interactive Graphing Calculator. Visual explanations, real-time simulations, no login required.

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CalculusMar 9, 2026·2 min read

Differentiation & Integration — Derivatives and Integrals Explained Interactively

Learn Derivatives and Integrals from first principles with our free interactive Differentiation & Integration. Visual explanations, real-time simulations, no lo

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Differential EquationsMar 9, 2026·2 min read

Slope Field Visualizer — Slope Fields Explained Interactively

Learn Slope Fields from first principles with our free interactive Slope Field Visualizer. Visual explanations, real-time simulations, no login required.

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Multivariable CalculusMar 9, 2026·2 min read

3D Surface Plotter — 3D Surface Plotting Explained Interactively

Learn 3D Surface Plotting from first principles with our free interactive 3D Surface Plotter. Visual explanations, real-time simulations, no login required.

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TrigonometryMar 9, 2026·2 min read

Unit Circle Explorer — The Unit Circle Explained Interactively

Learn the Unit Circle from first principles with our free interactive Unit Circle Explorer. Visual explanations, real-time simulations, no login required.

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Computer ScienceMar 8, 2026·2 min read

Binary Trees Explained Visually — The Data Structure Behind Everything

From file systems to databases, binary trees power the digital world. Interactive visualizations that make tree operations intuitive.

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PhysicsMar 8, 2026·2 min read

Understanding Projectile Motion — Why Baseballs Curve and Rockets Arc

A first-principles breakdown of projectile motion with interactive simulations. Learn why 45° gives maximum range.

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Computer ScienceMar 8, 2026·2 min read

Sorting Algorithms Visualized — Which One Is Actually Fastest?

Watch Bubble Sort, Merge Sort, Quick Sort, and more race side by side. Interactive visualizations that make algorithm complexity click.

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MathematicsMar 8, 2026·2 min read

5 Mind-Blowing Math Facts That Will Change How You See the World

From the birthday paradox to Euler's identity, these 5 mathematical facts are so surprising they feel like magic.

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PhysicsMar 8, 2026·2 min read

How to Build & Simulate Circuits Online — A Beginner's Guide

Learn to build real circuits in your browser with our free Circuit Builder. Place resistors, capacitors, LEDs, and batteries — then watch current flow in real time.

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