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:
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
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
Seeing imaginary numbers as rotations… Read article was one of my favorite aha moments:
i, the square root of -1, is a number in a different dimension! Once that clicks, we can use multiplication to “combine” rotations of two complex numbers:
Yowza,
Sine waves confused me. Yes, I can mumble "SOH CAH TOA" and draw lines within triangles. But what does it mean?
I was stuck thinking sine had to be extracted from other shapes. A quick analogy:
You: Geometry is … Read article
Calculus examples are boring. "Hey kids! Ever wonder about the distance, velocity, and acceleration of a moving particle? No? Well you're locked in here for 50 minutes!"
I love physics, but it's not the best lead-in. It makes us wait… Read article
Similarity has bothered me for a long time. Why do all circles have the same formula for area — how do we know nothing sneaky happens when we make them larger? In physics, don’t weird things happen when you scale… Read article
A quick puzzle for you — look at the first few square numbers:
1, 4, 9, 16, 25, 36, 49…
And now find the difference between consecutive squares:
1 to 4 = 3
4 to 9 = 5
9 to … Read article
