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

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

Euler's identity seems baffling:

It emerges from a more general formula:

Yowza -- we're relating an imaginary exponent to sine and cosine! And somehow plugging in pi gives -1? Could this ever be intuitive?

Not according to 1800s mathematician Benjamin… Read article

So many math courses jump into limits, infinitesimals and Very Small Numbers (TM) without any context. But why do we care?

Math helps us model the world. We can break a complex idea (a wiggly curve) into simpler parts (rectangles):… Read article

Integrals are often described as finding the “area under the curve”. This description is misleading, like saying multiplication is for finding “the area of a rectangle”. Finding area is a useful application, but not the purpose. Integrals help us combine… Read article

Accepting that numbers can do strange, new things is one of the toughest parts of math:

• There’s numbers between the numbers we count with? (Yes — decimals)
• There’s a number for nothing at all? (Sure — zero)
• The number

Pi is mysterious. Sure, you “know” it’s about 3.14159 because you read it in some book. But what if you had no textbooks, no computers, and no calculus (egads!) — just your brain and a piece of paper. Could… Read article