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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. Ultrastar Boy's/Men's Sports Solid Swim Jammers Swimsuit

Popular Articles

Intuitive Learning

ADEPT method

Learning starts with an analogy.

Why Learn Math?

Vocabulary for thinking

Math Intuition

Start with the cat, not its DNA

Bow & Arrow Intuition

First, have a good shot.

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

Mental Math Shortcuts

A few memorable conversions

Sum 1 to 100

Rearrange to simplify

Visual Arithmetic

Every operation is a transformation

Sense of Scale

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Fencepost Problem

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Number Systems

When the odometer ticks over

Everyday Logarithms

Counting digits

Modular Arithmetic

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Algebra & Counting


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Break down the tepee

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Map (distance matters) or non-map

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Choices multiply.


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How every shape changes

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Compare any quantities


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Pythagorean Rescale

Work from a unit triangle

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Angles from the mover’s perspective

Finding Pi

Surround that critter

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The Number e

Perfectly smooth growth

Natural Log

Time needed to grow

Imaginary Numbers

Numbers can rotate

Complex Numbers

Arithmetic goes 2d

Complex Multiplication

Scale & rotate


Grow numbers in the expand-o-tron

Think With Exponents

Logs are causes, exponents are effects


Visualize a dome, wall, and ceiling

Law of Sines

Every angle has an equal perspective.

Law of Cosines

Keep track of interacting parts.

Trig Identities

Draw the circles yourself.

Hyperbolic Trig

Mini exponentials and logarithms



See footprints, guess the animal


"Typical" depends on the relationship

Birthday Paradox

23 people, many possibilities

Bayes Theorem

Extra info? Adjust the odds.

Short Bayes’ Theorem

Adjust for false positives

Monty Hall

Original door vs. best of the other two

Calculus Course

Calculus Guide

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.

Calculus (Articles)

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0.999… = 1?

What's your number system?


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Make a model perfect


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Measurements depend on the instrument

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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Microwave the doughboy, quick

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Follow the best tradeoff


Amount of bananas crossing a surface


Flux per unit volume

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Mario Kart speed boost

Cross Product

All the uneven parts

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Math with mini-spreadsheets

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Patterns have circular ingredients


Fancy, programmable multiplication

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#1: There's a staging area

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Understanding MVC

Fat models, thin controller, thin view

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Treat a script as data

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Attacker spoofs a legit request

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Use firebug

Making Bookmarklets

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Low-level Programming


You'll never run out. Ever.

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Computers speak different languages


Not every char is 2 bytes

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Cleverness, not for real life

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Telnet is an IM conversation


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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.