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
Does .999… = 1? The question invites the curiosity of students and the ire of pedants. A famous joke illustrates my point:
A man is lost at sea in a hot air balloon. He sees a lighthouse approaching in the … 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
I’ve struggled with how to write about calculus. The standard techniques seem to be:
Puzzles can help develop your intuition -- figuring how to navigate a grid helped me understand combinations and permutations.
Suppose you're on a 4 × 6 grid, and want to go from the bottom left to the top right. How… Read article
The Monty Hall problem is a counter-intuitive statistics puzzle:
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… Read article, but not the purpose. Integrals help us
Counting isn’t easy. Suppose your boss wants you to work from 8am to 11am, and mop floors 8 to 11. Simple – it’s one floor per hour, right?
Nope! There are 4 floors to mop (8, 9, 10 and 11)… Read article
We’re taught that exponents are repeated multiplication. This is a good introduction, but it breaks down on 3^1.5 and the brain-twisting 0^0. How do you repeat zero zero times and get 1?
You can’t, not while exponents are repeated multiplication.… Read article
