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Latest Articles

Why Is Better Explained Different?

Most lessons offer low-level details in a linear, seemingly logical sequence. Better Explained focuses on the big picture — the Aha! moment — and then the specifics. Here’s the difference:
I know which approach keeps my curiosity and enthusiasm. The learning strategy is the ADEPT Method:

Learning isn’t about memorizing facts to pass a test. It’s about unlocking the joy of discovery when an idea finally makes sense. If this approach resonates with you, welcome aboard.

About Kalid Azad

I enjoyed math until a poorly-taught class nearly destroyed that passion. A last-minute Aha! moment showed me math could make sense, even be enjoyable, when presented with:

  • A friendly, curious attitude
  • A mix of intuitive and technical understanding
  • A focus on lasting insight

I share explanations that helped, hoping they help you too. I’m thrilled that Better Explained now reaches millions every year, and has appeared in blogs for the New York Times and Scientific American. Swan Neck Hollower Carbide Tipped Wood Turning Tools Bended Lath

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ADEPT method

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Vocabulary for thinking

Math Intuition

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Pencil, Then Ink

Don't hide the process


Useful, even if "wrong"


Simplify ideas to a caricature

Intuition Isn't Optional

The recipe for knowledge that lasts.

Arithmetic & Numbers

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Sum 1 to 100

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Visual Arithmetic

Every operation is a transformation

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Number Systems

When the odometer ticks over

Everyday Logarithms

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Modular Arithmetic

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Algebra & Counting


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Atoms within numbers

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Surround that critter

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The Number e

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Natural Log

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Imaginary Numbers

Numbers can rotate

Complex Numbers

Arithmetic goes 2d

Complex Multiplication

Scale & rotate


Grow numbers in the expand-o-tron

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Law of Sines

Every angle has an equal perspective.

Law of Cosines

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Trig Identities

Draw the circles yourself.

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See footprints, guess the animal


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Birthday Paradox

23 people, many possibilities

Bayes Theorem

Extra info? Adjust the odds.

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Monty Hall

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Learn the basics, fast.

Lesson 1

1-Minute Summary

Lesson 2

X-Ray Vision

Lesson 3

3D intuition

Lesson 4

Integrals, Derivatives

Lesson 5

Computer Notation

Lesson 6

Improved Algebra

Lesson 7

Linear Changes

Lesson 8

Squared Changes

Lesson 9


Lesson 10


Lesson 11

Fundamental Theorem of Calculus

Lesson 12

Rules: Add, Multiply, Invert

Lesson 13

Patterns In the Rules

Lesson 14

Rules: Powers, Division

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Archimedes' Formulas

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The big insights. All together now.

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Derivatives II

Imagine linked machines

Derivatives III

Quotient, exponents, logs

Calculus Bank Account

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Integral of sin

Whoa: the horizontal change

Taylor Series

DNA of a function

Vector Calculus

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Total twist, twist at a point

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Follow the best tradeoff


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Flux per unit volume

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Mario Kart speed boost

Cross Product

All the uneven parts

Engineering / University Math

Linear Algebra

Math with mini-spreadsheets

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Fourier Transform

Patterns have circular ingredients


Fancy, programmable multiplication

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#1: There's a staging area

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A quickstart guide

Web Development

Faster Javascript

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Don't redownload until expired

Gzip Compression

Zip files before sending

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Get past the gotchas

Understanding MVC

Fat models, thin controller, thin view

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1-page summary


Treat a script as data

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Attacker spoofs a legit request

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Use firebug

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Low-level Programming


You'll never run out. Ever.

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Byte Order

Computers speak different languages


Not every char is 2 bytes

XOR Swap

Cleverness, not for real life

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Symbol Tables

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Telnet is an IM conversation


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Pareto Principle

Sometimes 80% is enough

Stock Market

A transparent store

Accounting Basics

Everything is owned by someone

Interest Rates

A formula for every type of interest

Debt & Leverage

Invested debt multiplies return

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Know Thyself

If you're Hulk, be Hulk.

Simplicity vs. Complexity

Complexity, not power, is the enemy.

Notes on Happiness

Passion, foolishness, dancing

Brevity is Beautiful

Zero guilt.