Welcome back once again. Today, I’m going to talk to you about recurrence relations. What are those, I hear you cry? It’s very simple. A recurrence relation defines the th term of a sequence in terms of the previous ones. For example, if is the th term of the Fibbonaci sequence, then we have the recurrence … More Let’s Do It Again!
Welcome back to one more Wandering Mathematician post. We’ve all heard the proof that is irrational (I think I might have done it myself, a while back), but today I’m going to present an entirely new way of proving it. In the process, I’m going to prove a whole lot more, such as the fact … More Irrational powers
You may or may not be familiar with the idea of a factorial. It’s very simple: factorial, written , is defined as . For example, and . There’s loads of interesting things to note about these, not least that is divisible by if . One of the most interesting things, though, is the number of zeros … More Endless Zeros
Hey there! I’m very excited because I’m trying a new experiment: I’m embedding a video into this blog! Here goes: It’s common knowledge that heavy objects and light ones fall at the same speed in a vacuum. This video is from the Apollo space program and demonstrates the effect. Today, I’d like to discuss why … More Dropping Objects
Welcome, one and all, to another week’s Wandering Mathematician! Today, I’m going to be telling you about a very useful little formula that used to be on the UK A Level syllabus but isn’t any more. The question is, given a quadratic equation , and given that this equation has solutions , what is ? … More Putting Down Roots
For some reason, I’d like to talk about pirates today. Actually, I don’t need a reason — pirates are cool. They just arrrr. I’m sorry. I’m so sorry. Anyway, let’s say we’ve got pirates, imaginatively named through . They’ve just captured gold pieces, and the question is how to divide them up. They’ve got some … More Piracy — It’s A Crime
What’s ? Any calculator will tell you that it’s about , but that doesn’t tell me what it is. Today, I’ll be talking about numbers like , , and so on. First, though, we need a quick reminder about definitions and then a couple of proofs. If you’re OK with rational and irrational numbers, you … More Irrational Ideas