This one strikes me, and apparently others, as highly counter-intuitive, but it’s true because of mathematics! Take any two places in the world; call these points A and B. Take any two paths between A and B that are the same distance; call these paths C and D. Let C(x) be as far down path…
Author: Clio
Reflection
“There’s a shadow in the mirror with a glimmer of the one that was.” My creative juices are like a gas-powered lawn mower that’s been kept a few too many seasons. I pull the cord and the engine kicks over a few times and I think that it’s the time that things will engage, but…
Pseudocode for the Russian peasant method of binary
Just for fun… Here’s the pseudocode for the method of building a binary number from a decimal number, based on the Russian peasant method of multiplication: function mybin(mydec) { mybin = “”; do while mydec > 0 { if mydec is odd: { mydec = mydec – 1; mybin = “1” + mybin; } else: mybin…
Russian peasants, number sense, and bases
Russian peasants do too much work There is a method of multiplication called the Russian peasant method. I’ve seen it mentioned here and there, but I was not explicitly educated in the process; it struck me as being more trouble than it was worth, and I didn’t previously bother to dig farther into it. I…
The Wayward Airline Passenger
This problem was brought to my attention on G+, but I wasn’t satisfied with the solution presented. There are actually two versions, the one that was originally presented on G+ and the corrected one that matches the standard version. I’ll discuss the standard version first. Standard version: All seats on an airplane are assigned. However,…
The History of Factorials: Kramp
In an earlier post, I argued that the definition of factorial (\(n!\)) is the number of ways that a number of n distinct objects can be arranged. I have recently been told that, no, the formal definition of factorial is as generally offered by sources such as Wolfram and Numberphile: The product of all integers from…
Infinity and String Theory
There’s a Numberphile video that’s hurting people’s brains. It claims to prove (several ways, including in a companion video) that \[\sum_{n=1}^{\infty} n = -\frac{1}{12}\] This is, of course, highly counterintuitive. The video itself is misleading in that the speakers refer to the sum of all natural numbers, when this is not in fact the sum…
January 8
A day late, but not quite a dollar short: That was the story of his life, it seemed. Running behind but still somehow managing to eke out just enough to be considered a success. Or, at least, not a failure. He didn’t know how many times he’d been here before, sitting on the edge of…
January 7
There was a little girl who thought she’d challenge the world to change, to become the way she wanted it to be. She had grown tired of the angry way it had decided to march onward, day after day, and decided that it needed to learn to walk backwards, or at least sideways. She told…
January 6
once, when i was glass and the morning sun was still high in the sky i could see the rainbows shimmering through my skin the road was long in front of me but i looked forward to the walk once, when i was steel and the noontime clouds crept and dawdled i could see the…