Sunday Function

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Sunday Function

Here’s an odd little bit of math for you this Sunday. It’s defined in terms of recurrence. Recurrence happens when a function is defined in terms of itself. This happens more than you might think – one famous example is the Fibonacci sequence, which is informally defined by saying “To get the next term in…

Sunday Function

So I spent two weeks in Wyoming, participated in a wedding in Louisiana, moved two apartments worth of stuff, visited Louisiana again to get a marriage license for myself (20 days left!), collected data for an experiment demonstrating a new result we’re trying to get published quickly (hot topic, lots of competition), and so forth.…

Sunday Function

Again, apologies for the hideously scanty posting. Been in the lab doing some really interesting research which will with some luck get me in a really nice journal, as well as doing the various rounds of revision on the paper for some previous research. Also putting two talks together for a conference/school. That whole wedding…

Sunday Function

Happy birthday to the United States! It’s one of the younger countries on the planet and yet has still managed to have one of the oldest continuous systems of government. Not too shabby. Here’s hoping our current wobbles get straightened out and our next few Independence Days occur under more pleasant conditions. I’m not sure…

Sunday Function

A while back I mentioned the St. Petersburg paradox. It’s a hypothetical gambling scenario where you win money based on the outcome of a coin toss. If you get your first tails on the first throw, you get $1. If you get one head before your first tails, you get $2 dollars. If you get…

Sunday Function

Back in 2003, I was a college freshman sitting in my first college math class – Honors Calculus I. On what was probably the second or third day of class, the professor gave us a surprise quiz. It was something like: “Give the formal statement of the principle of induction”. It was my first graded…

Sunday Function

You’re a member of the French Resistance in the height of WWII. You’re part of a network of resistance members who have to work with other resistance members they’ve never met before. For instance, an agent from Paris might have to meet up with an agent in Normandy to work together on sabotage before the…

Sunday Function

Consider this not-so-difficult sum: It consists of just a string of fractions up to whichever N you happen to choose. Add them up, and you certainly and unambiguously have a number. If you chose to stop at N = 10, you’d find that f(10) = 1627/2520, which is about 0.645635. If you chose to stop…

Sunday Function

It’s been a while since we’ve done a Sunday Function, so let’s get back into the swing of things with a weird one. This is Thomae’s function, and using Wikipedia’s conveniently typeset definition: If you’re new to the concept of rational and irrational numbers, it’s pretty simple. A number is rational if it can be…

Sunday Function

Happy Easter, everyone! This Sunday Function is going to be short and sweet, since unfortunately I’ve got a lot to do before Monday. Let’s get down to business! Here’s a function I’ve made up out of thin air. It’s pretty arbitrary – in fact, it’s discontinuous at x = -1/2 and not differentiable at x…