Sunday Function

This is the graph of the line y = x: If you put your finger down on any point on that line, and then put another finger on another point on that line, you find that the total change in the y-coordinate divided by the total change in the x-coordinate between those two positions is…

Sunday Function

Sine, cosine, and tangent are of course the workhorse functions of trigonometry. You learn ’em in high school, and if you go on in math and science you never stop using them. Now on many occasions you might have the sine or cosine or tangent of some angle, and you want a way to invert…

Sunday Function

This Sunday I was at an event that involved a number of drawings for door prizes. There were perhaps 30 couples there – it was, not to beat around the bush, a wedding registry shindig at Bed, Bath, & Beyond. (Did I mention I’m recently engaged? I am. It’s the main reason for the endemic…

Sunday Function

Here’s a simple function that’s not so often found in mathematical physics, but it’s still a nice showpiece for exhibiting some interesting behavior: I’ve only plotted it for positive real x, because for x less than zero it starts spitting out complex numbers in a very unfriendly way. We’re only considering it along the domain…

Sunday Function

Step right up, Ladies and Gentlemen! Get your ticket to see the True Oddities of the Natural World! Do not be taken in by the Shameful Forgeries at Inferior Circuses, here you will see Genuine Curiosities from the Mists of Time! Beside these Archaic Functions, the Two-Headed Horse or Whatever is a Mere Bagatelle! So,…

Sunday Function

And now, two quick notes before we get to business: 1. God help me, but I’ve joined the Twitter bandwagon. Here I am, @BuiltOnFacts. Though it goes under this blog’s name, it is more of a “personal” account. So you’ll be reading some incomprehensible personal minutiae, random observations, wild assertions, and somewhat more politics that…

Sunday Function

…you’ve got to ask yourself one question: ‘Do I feel lucky?’ Well, do ya, punk? – Dirty Harry The laws of probability, like most of the mathematical rules that govern the world, are a relatively recent discovery. Ancient people like the Romans loved to gamble as much as we do, and they had at least…

Sunday Function

There’s an interesting contrast between the laws of nature and the laws which constitute our legal system. The laws of nature are compact and precise; written in standard notation without accompanying explanation, the fundamental laws fit on a few pages. The laws of the legal system span thousands of volumes and are frequently ambiguous and…

Sunday Function

We’ve spent more than a few Sunday Function features discussing the properties of the prime numbers. They’re just so important and interesting in number theory that they’re an irresistible target. Let’s set some scenery before getting to the actual function this week. There are an infinite number of prime numbers. Whatever gargantuan prime number you…

Sunday Function

Before her career took an unfortunate wrong turn, a young and talented Lindsay Lohan gave us a charming and popular comedy called Mean Girls. Time has been good to the careers of some of the others involved, Tiny Fey and Rachel McAdams perhaps most notably. But the film did something that very other movies have…