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
Math seems to get magical in groups. Maria Droujkova organizes the awesome Math 2.0 interest group… Read article, which I found out about recently — I’m bummed I didn’t hear about it till now! There’s a mailing list, webinars with prominent
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
Git is a fast, flexible but challenging distributed version control system. Before jumping in:
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
It's
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: