Sleepy snowdrift Slippery slope Dangling disheartened At the end of my rope Cracking the whip To drive the cart And watch the brickwork Fall apart The age of reason Trumpets change But reasons age And rearrange Somnolent sleeting Succulent slide Dolorous darkened Deliverance died – ptkh 8/18/14
Month: August 2014
Indeterminate vs. Undefined
Here’s something that seems to confuse many people: \[\frac{1}{0} \text{ is undefined}\\ \frac{0}{0} \text{ is indeterminate}\] If some number, any number at all, divided by zero is undefined, then why isn’t zero divided by zero likewise undefined? And what does “indeterminate” mean anyway? Let’s start with a more concrete question: What is division? Assume we…
The Six Basic Trigonometric Functions
I read an article today on the six basic trigonometric functions, and I thought there was a particularly important insight that I wanted to present in my own words. When I was in school, we learned the six basic trigonometric functions. Since I’ve been teaching, I’ve noticed that only three of these are emphasized: Sine,…
How Many Factors?
A post on G+ Mathematics asks: “How many of the positive divisors of 8400 have four or more positive divisors?” A divisor, or a factor, is an integer which evenly divides another integer; in other words, it is the opposite of a multiple (with the exception of 0). For instance, 8 has the factors {1,…