On the fifth day at sea, I was set adrift in a rowboat and left to my own devices. In the boat, I had an oar, rations for three days, and an umbrella. There was no cell phone, which was just as well, because I was out of reach of any towers anyway. There was…
Author: Clio
January 4
There is solace in silence Quiet that seeps in from the shadows Sleek as a cat, padding softly across tiles There is solace in silence Snowflake settling on autumn leaves Swirled by chilling winds There is solace in silence But at the same time, Not — ptkh 010414
January 3
You were the Buddha. That’s what you’d told us when you’d gone to China and the children had gathered around you, this towering behemoth of a man with a round belly and an expansive smile. When you were lying there, flat, stomach distended from post mortem gasses, I tried to be sad at your loss….
January 2
There is a paper wasp nest dangling from a tree on our easement, high above the street. It is easily the size of a human head, even desiccated as it is from winter months of disuse. Back in autumn, after the leaves had fallen and made the nest visible to anyone who walked by, I…
January 1
At some point, walking along the snow-flocked train tracks in the winter evening’s half-light, I became aware. By this I mean: All that I was was now. I had no past to dwell within, chiding myself, steeped in regrets. I had no future lingering in the wings like a Dickens villain, ready to set me…
Probabilities: Consecutive numbers
On a mathematics community on Google+, Michal Nalevanko asked the question (paraphrased here, including my assumptions): Let us say there is a lottery game in which twenty numbered balls are pulled from a pool of eighty. What is the probability that three or more numbers will be consecutive? It is assumed that the numbers are…
The Quadratic Formula and the Shortcut
Background There are two common ways for finding roots of quadratic equations, that is, equations of the form \[ax^2 + bx + c = 0\] The one that’s usually taught first is a shortcut that works best when \(a = 1\) and two factors of \(c\) have a sum of \(b\): In fact, that’s exactly…
The square of a sum and the sum of cubes
Let’s start with a fun fact: Take the first \(n\) integers. Add them and then square the result; call this \(S\). Take the cube of each and add those numbers; call this \(C\). It will always be the case that \(S = C\). For instance, take \((1, 2, 3)\): \[(1 + 2 + 3)^2 =…
The Grandfather Tree
I never thought I would give you permission to cut down that giant oak tree in the back of the property, the one that had led my grandfather to buy this land in the first place. It had been tall even when he’d seen it as a young man only a year into his first…
Factorials and the meaning of “is”
In a YouTube video, James Grime of NumberPhile makes the claim that the meaning of the factorial is \[n! = \prod_{i=1}^n i\] for n > 0, and proceeds to explain why 0! = 1 using a recursive proof. This echoes what Wolfram Mathworld has to say on the subject: “The factorial n! is defined for a…