What have you learned about math that you found interesting recently?

I've been looking into linear algebra, and I found a few intriguing things. Really anything you do with matrices is cool.

Last week I designed a roller-coaster using matrices to find a curve that best fit the roller-coaster I had imagined. To get the ideas for how tall or how steep each hill was, I used physics (dE = We, dp = Fdt, etc). With linear algebra, I could even account for friction without any messy and complex steps to change every hill.

I know this isn't specific enough to be your favorite, but I'm so happy to see a question that isn't homework I need to answer it!

I recently learned the "slide and divide" method of factoring quadratics.

Factoring quadratics isn't too hard when you have a coefficient of 1 on the first term.

Example:

x² + 7x + 12 = (x + 3)(x + 4)

But when the first coefficient is bigger, it gets harder. That's when the "slide and divide" method is helpful.

Example:

3x² + 4x - 4

Step 1: Slide the leading coefficient (3) to the end and multiply:

x² + 4x - 12 = 0

Step 2: Factor as usual:

(x + 6)(x - 2) = 0

Step 3: Divide the numbers by the number you slid in step 1:

(x + 6/3)(x - 2/3) = 0

Step 4: Simplify any fractions:

(x + 2)(x - 2/3) = 0

Step 5: Slide any denominators back in front of the x terms:

(x + 2)(3x - 2) = 0

I'm sure there are people out there that are going "whoopee, I learned that in 8th grade", but it was actually something that we were never taught. I always did it the long way and just recently someone asked about the "slide and divide" method and I had to go do some research to "learn" this trick.

So yes, even a top contributor in mathematics can learn something new in math...