Archives

New here? Here’s a few popular articles to get you started:

• Developing Math Intuition
• Imaginary Numbers
• Exponents and the Number e
• The Natural Logarithm
• Euler’s Formula
• The Fourier Transform
• Introduction To Calculus
• Bayes’ Theorem
• Linear Algebra Intro
• Intuitive Trigonometry

I have a list of translated articles, just contact me if you have any to add.

Post Series

• Business
  • The Rule of 72 (January 25, 2007)
  • Understanding Accounting Basics (ALOE and Balance Sheets) (November 20, 2007)
  • Understanding Debt, Risk and Leverage (November 17, 2008)
  • What You Should Know About The Stock Market (November 14, 2007)
  • Understanding the Pareto Principle (The 80/20 Rule) (March 8, 2007)
  • Combining Simplicity and Complexity (March 2, 2007)
• Calculus
  • A Gentle Introduction To Learning Calculus (May 2, 2008)
  • Understanding Calculus With A Bank Account Metaphor (March 16, 2011)
  • Prehistoric Calculus: Discovering Pi (May 29, 2008)
  • A Calculus Analogy: Integrals as Multiplication (July 15, 2009)
  • Calculus: Building Intuition for the Derivative (March 29, 2012)
  • How To Understand Derivatives: The Product, Power & Chain Rules (May 11, 2012)
  • How To Understand Derivatives: The Quotient Rule, Exponents, and Logarithms (June 12, 2012)
  • An Intuitive Introduction To Limits (April 15, 2013)
  • Intuition for Taylor Series (DNA Analogy) (January 23, 2019)
  • Why Do We Need Limits and Infinitesimals? (November 12, 2009)
  • Learning Calculus: Overcoming Our Artificial Need for Precision (August 21, 2008)
  • A Friendly Chat About Whether 0.999... = 1 (November 18, 2009)
  • Analogy: The Calculus Camera (May 17, 2016)
  • Abstraction Practice: Calculus Graphs (June 22, 2016)
  • Quick Insight: Easier Arithmetic With Calculus (July 28, 2016)
  • How to Add 1 through 100 using Calculus (February 17, 2017)
  • Integral of Sin(x): Geometric Intuition (November 19, 2019)
• Computer Science
  • Number Systems and Bases (December 29, 2006)
  • The Quick Guide to GUIDs (April 18, 2007)
  • Understanding Quake's Fast Inverse Square Root (February 5, 2007)
  • A Simple Introduction To Computer Networking (March 16, 2009)
  • Swap two variables using XOR (January 16, 2007)
  • Understanding Big and Little Endian Byte Order (September 19, 2006)
  • Unicode and You (December 28, 2006)
  • A little diddy about binary file formats (December 28, 2006)
  • Sorting Algorithms (December 28, 2006)
• Developer Tools
  • A Visual Guide to Version Control (September 27, 2007)
  • Intro to Distributed Version Control (Illustrated) (October 15, 2007)
  • Aha! Moments When Learning Git (March 10, 2010)
• Essays
  • Developing Your Intuition For Math (January 8, 2009)
  • Why Do We Learn Math? (September 14, 2012)
  • How to Develop a Mindset for Math (November 26, 2007)
  • Learning math? Think like a cartoonist. (July 24, 2014)
  • Math As Language: Understanding the Equals Sign (September 24, 2012)
  • Avoiding The Adjective Fallacy (September 27, 2015)
  • Finding Unity in the Math Wars (August 21, 2012)
  • Brevity Is Beautiful (April 22, 2010)
  • Learn Difficult Concepts with the ADEPT Method (October 10, 2014)
  • Intuition, Details and the Bow/Arrow Metaphor (November 16, 2011)
  • Learning To Learn: Intuition Isn't Optional (June 4, 2015)
  • Learning To Learn: Embrace Analogies (April 24, 2012)
  • Learning To Learn: Pencil, Then Ink (January 13, 2010)
  • Learning to Learn: Math Abstraction (May 28, 2016)
  • Learning Tip: Fix the Limiting Factor (May 4, 2016)
  • Honest and Realistic Guides for Learning (April 9, 2016)
  • Empathy-Driven Mathematics (July 8, 2016)
  • Studying a Course (Machine Learning) with the ADEPT Method (August 29, 2016)
  • Math and Analogies (May 3, 2018)
  • Colorized Math Equations (December 12, 2017)
  • Analogy: Math and Cooking (February 28, 2019)
  • Learning Math (Mega Man vs. Tetris) (November 21, 2016)
• Interviews & Discussions
  • Life Lessons After 10 Years of BetterExplained.com (January 11, 2017)
  • BetterExplained Podcast Interview with Developer Tea (April 6, 2016)
  • Interview with MetaLearn (How to Get Better at Math) (April 11, 2017)
  • Interview with Developer Tea (February 1, 2017)
  • Newton's Law of Gravity (Metalearn Podcast) (February 14, 2018)
  • Einstein's Theory of Special Relativity (MetaLearn Podcast) (March 30, 2018)
  • Zen and the Art of Learning Math (Book Discussion) (June 30, 2017)
  • Surely You're Joking Mr. Feynman (Book Discussion) (September 13, 2017)
• Math - Advanced Topics
  • A Visual, Intuitive Guide to Imaginary Numbers (December 21, 2007)
  • Intuitive Arithmetic With Complex Numbers (January 2, 2008)
  • Understanding Why Complex Multiplication Works (August 3, 2011)
  • Intuitive Guide to Angles, Degrees and Radians (July 9, 2008)
  • Intuitive Understanding Of Euler's Formula (July 19, 2010)
  • An Interactive Guide To The Fourier Transform (December 19, 2012)
  • Intuitive Guide to Convolution (November 23, 2020)
  • Intuitive Understanding of Sine Waves (April 17, 2011)
  • An Intuitive Guide to Linear Algebra (October 9, 2012)
  • A Programmer's Intuition for Matrix Multiplication (September 14, 2016)
  • Imaginary Multiplication vs. Imaginary Exponents (August 31, 2018)
  • Intuitive Guide to Hyperbolic Functions (April 26, 2021)
• Math - Algebra
  • Understanding Algebra: Why do we factor equations? (August 30, 2012)
  • A Quick Intuition For Parametric Equations (January 15, 2014)
  • Intuition for the Quadratic Formula (May 1, 2019)
  • Intuition for Slope-Intercept Form (July 13, 2018)
  • Intuition For Graphed Functions (November 1, 2018)
  • Intuition For Polynomials (March 26, 2019)
• Math - Combinations
  • Easy Permutations and Combinations (February 11, 2007)
  • Navigate a Grid Using Combinations And Permutations (October 20, 2009)
  • How To Understand Combinations Using Multiplication (February 25, 2008)
  • Why do we multiply combinations? (August 15, 2017)
• Math - Essentials
  • Mental Math Shortcuts (January 22, 2007)
  • Understand Ratios with "Oomph" and "Often" (April 14, 2014)
  • How to Develop a Sense of Scale (January 30, 2008)
• Math - Exponents & Logs
  • An Intuitive Guide To Exponential Functions & e (May 1, 2007)
  • Demystifying the Natural Logarithm (ln) (May 20, 2007)
  • A Visual Guide to Simple, Compound and Continuous Interest Rates (January 13, 2008)
  • Common Definitions of e (Colorized) (January 29, 2018)
  • Understanding Exponents (Why does 0^0 = 1?) (February 17, 2009)
  • Using Logarithms in the Real World (January 30, 2012)
  • How To Think With Exponents And Logarithms (June 16, 2014)
  • Understanding Discrete vs. Continuous Growth (March 9, 2017)
  • What does an exponent really mean? (December 6, 2018)
  • Q: Why is e special? (2.718..., not 2, 3.7 or another number?) (August 3, 2018)
• Math - Geometry
  • How To Measure Any Distance With The Pythagorean Theorem (November 5, 2007)
  • Surprising Uses of the Pythagorean Theorem (October 24, 2007)
  • Pythagorean Theorem As Sweeping Area (June 19, 2019)
  • Rescaling the Pythagorean Theorem (February 16, 2008)
  • Understanding Why Similarity Works (February 1, 2011)
• Math - Numbers
  • Techniques for Adding the Numbers 1 to 100 (February 13, 2007)
  • Rethinking Arithmetic: A Visual Guide (December 13, 2007)
  • Quick Insight: Intuitive Meaning of Division (February 28, 2018)
  • Quick Insight: Subtracting Negative Numbers (July 13, 2017)
  • Surprising Patterns in the Square Numbers (1, 4, 9, 16…) (October 15, 2010)
  • Fun With Modular Arithmetic (February 1, 2010)
  • Learning How to Count (Avoiding The Fencepost Problem) (April 28, 2009)
  • A Quirky Introduction To Number Systems (December 7, 2007)
  • Another Look at Prime Numbers (September 9, 2007)
  • Intuition For The Golden Ratio (April 3, 2017)
  • Different Interpretations for the Number Zero (April 21, 2016)
• Math - Trigonometry
  • How To Learn Trigonometry Intuitively (February 24, 2014)
  • Easy Trig Identities With Euler's Formula (November 4, 2015)
  • Intuition For The Law Of Cosines (November 13, 2014)
  • Intuition For The Law Of Sines (October 21, 2014)
  • How to Learn Trig Derivatives (August 3, 2022)
• Statistics
  • A Brief Introduction to Probability & Statistics (September 5, 2012)
  • An Intuitive (and Short) Explanation of Bayes' Theorem (May 6, 2007)
  • Understanding Bayes Theorem With Ratios (March 1, 2013)
  • Understanding the Monty Hall Problem (September 4, 2009)
  • How To Analyze Data Using the Average (March 14, 2008)
  • Understanding the Birthday Paradox (April 26, 2007)
• Vector Calculus
  • Vector Calculus: Understanding the Dot Product (February 22, 2012)
  • Vector Calculus: Understanding the Cross Product (April 15, 2015)
  • Vector Calculus: Understanding Flux (September 16, 2006)
  • Vector Calculus: Understanding Divergence (September 20, 2006)
  • Vector Calculus: Understanding Circulation and Curl (February 19, 2007)
  • Vector Calculus: Understanding the Gradient (February 17, 2007)
  • Understanding Pythagorean Distance and the Gradient (November 4, 2011)
• Web Development
  • Starting Ruby on Rails: What I Wish I Knew (June 16, 2007)
  • Intermediate Rails: Understanding Models, Views and Controllers (August 11, 2007)
  • A Simple, Comprehensive Overview of Javascript (February 23, 2007)
  • Using JSON to Exchange Data (January 11, 2007)
  • How To Make a Bookmarklet For Your Web Application (April 16, 2008)
• Website Optimization
  • How To Optimize Your Site With HTTP Caching (April 7, 2007)
  • How To Optimize Your Site With GZIP Compression (April 4, 2007)
  • How To Debug Web Applications With Firefox (March 19, 2007)
  • Speed Up Your Javascript Load Time (February 21, 2007)
  • Speed Up Your Javascript, Part 2: Downloadable Examples! (February 25, 2007)

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