Last time… Read article we tackled derivatives with a “machine” metaphor. Functions are a machine with an input (x) and output (y) lever. The derivative, dy/dx, is how much “output wiggle” we get when we wiggle the input:
Now, we can make
The jumble of rules for taking derivatives never truly clicked for me. The addition rule, product rule, quotient rule — how do they fit together? What are we even trying to do?
Here’s my take on derivatives:
Why do analogies work so well? They’re building blocks for our thoughts, written in the associative language of our brains.
At first, I thought analogies had to be perfect models of the idea they explained. Nope.
“All models are wrong, … Read article
I’ve just added a new feature to the site: an Aha / FAQ section for each article.
You can add an aha! moment or question, and vote / discuss them individually. This extends aha.betterexplained.com, making mini-posts for key ideas in an article. Continue reading
How do you wish the derivative was explained to you? Here's my take.
Psst! The derivative is the heart of calculus, buried inside this definition:
But what does it mean?
Let's say I gave you a magic newspaper that listed… Read article
I see the dot product as directional multiplication. But multiplication goes beyond repeated counting… Read article: it’s applying the essence of one item to another.
Normal multiplication combines growth rates: “3 x 4″ can mean “Take your 3x growth and make
Logarithms are everywhere. Ever use any of the following phrases?
You’re describing numbers in terms of their powers of 10 — a logarithm. Ever mention an interest rate or rate of return? It’s
Hi all, I wanted to announce that Math, Better Explained is available on the Kindle store!
If you’re looking for a digital gift this holiday season, I know just the ticket 
. Continue reading
My favorite analogies explain a thought and help you explore deeper truths. Here’s a metaphor that captures my stance on learning:
Our goal is to hunt down problems. You can use arrows
The Pythagorean Theorem shows how strange our concept of distance is. Using the rule a2 + b2 = c2… Read article, we can trade some “a” to get more “b”.
Starting with
means “A 13-inch pizza equals a
