Let’s Do It Again!

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!

Irrational powers

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

Endless Zeros

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

Dropping Objects

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

Putting Down Roots

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

Irrational Ideas

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