It has been known since at least Euclid’s time that there are an infinite number of prime numbers. Here is his basic proof: Imagine that there is a finite set of prime numbers, P. Let N be the product of all the elements of P, plus 1. N’s factors do not include any element of…
Author: Clio
My Muse
I smothered my muse with a down-filled pillow And left her corpse stretched out, Naked and prostrate, On the futon in the spare room. I held her in my dreams for a fortnight, Then discarded the memory, Wretched and withered, To the wraiths that live behind the house. But her siren call kept singing to…
The Rubik’s Cube and task completion
Part of my shtick as a Geometry teacher is the Rubik’s Cube. I have a 3^3 and a 5^3 in my room; I’d had a Void as well, but it’s wandered off (perhaps due to my own doing). The students will distract themselves with the cubes; some of them will ask me to do it….
Your Song
I wrote your song last night In words of sulfur and strychnine Writ in blood on onion skin I set it on fire And watched the smoke curl Up Up Up And Nevermore Now I’m humming the melody Softly to myself Thinking only Of you — ptkh 10.21.14
Urban Boneyard
The city is filled with the carcasses of yesterday’s homes, Once lovely bones picked clean by the copper vultures, Empty frames where glass held back the wind and rain In years now gone and done This was a young couple’s dream for a future together That was a family pausing on the ladder to take…
Simplify Radicals: Python code
I’m exploring if it’s possible to create a function in GeoGebra that would take an integer as input and create a simplified radical as output. For instance, it would take \(20\) as input and return \(2\sqrt{5}\) as output. I don’t know a way, so if someone does, please tell me. (Edit: There is the SurdText…
Sleepy snowdrift
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
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,…