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
Euler's identity seems baffling:
It emerges from a more general formula:
Yowza -- we're relating an imaginary exponent… Read article to sine and cosine! And somehow plugging in pi gives -1? Could this ever be intuitive?
Not according to 1800s mathematician Benjamin
Brevity is my favorite aspect of effective communication. We’re limited creatures, only able to handle a few thoughts at once — make them count!
Concise writing helps us share ideas, but we hamstring ourselves by trying to appear “substantial”. Let’s… Read article
A reader recently suggested I write about modular arithmetic (aka “taking the remainder”). I hadn’t given it much thought, but realized the modulo is extremely powerful: it should be in our mental toolbox next to addition and multiplication.
Instead of… Read article
I loved drawing as a kid. A recent "aha!" was realizing how similar the process of good drawing is to good learning -- they depend on recognizing and mastering underlying structures. My philosophy in 3 words:
Pencil, then ink.… Read article