Is there an equation to describe regular polygons?

So a blog reader, Michael Gmirkin, sent me an in-depth email about the possibility of the existence of a super equation that can describe any regular polygon. I wasn’t sure. For reference, you might want to check out these 2 blog posts about the equation for a square: question, answer.

I was going to just ask you here. Then I remembered there’s a Stack Overflow equivalent for maths. So I went there and asked the question. So if you know the answer, you can comment here, or go to the maths StackExchange site and earn yourself some points.

You can assume that the centre of the regular polygon in at the origin (0,0). Researching a little on the topic, I also learnt about the apothem, which is also the shortest distance from the centre to a polygon’s side. The “normal” radius is the distance from the centre to one of the regular polygon’s vertex.

If you trace 2 circles, one with the apothem and one with the radius, you get an inscribed circle and circumscribed circle respectively.

Query bundling – an interruption handling tip

Ok, I feel really bad about this. Months ago, when I first had the idea of writing a self-help ebook *gasp*, I asked Ben Barden for a tip on how he handles interruptions. He gave one, and I’m ashamed to say it’s been sitting in my todo list for, well, months.

I’m often asked to do something when I’m already busy with something else. One way I deal with this is to request “query bundling” – basically, if someone expects to have a number of queries, it is far better if they collate the tasks and send them to me in one go, than to interrupt me every time they have a question. In some cases, certain requests can be related to others, so it’s actually quicker and easier to do a few of them at once.

– Ben Barden

I can understand this. When I first started working, I had tons of questions. How did this program work? Why are the programs scheduled in this order? When do we tell the users their reports are ready? What, why is that again?

After a while, I had this feeling that I’m interrupting my senior colleague too much. So without prompting, I started bunching questions together, and when I had to ask, I’ll unleash a few of them at one go. I’d also try to wait to ask when he’s not too busy, but that’s kind of subjective. He’s always busy. And not the useless kind of busy either.

Ben Barden is a musician, blogger and PHP developer. Find out more about him at his site

Answers to philosophical questions must be reasoned

My friend wrote a short guide on what makes a question philosophical. The 3 conditions for a question to pass the philosophical test are interesting.

Has not been answered by science

The obvious reason is that, if it’s answered by science, there’s no point in answering it (philosophically).

For example, “Can penguins fly?” is answered by science. It’s “no”. Their bodies aren’t made for flying. Although…

More than one possible answer

If there’s only one answer, there’s no point in answering it.

For example, “Is 1+1 = 2?” has the answer “yes”. There’s no other answer.

Unless you’re talking about base 2…

Cannot be answered by conducting an experiment

“Can common salt be produced by mixing two liquids together?” can be answered with experiments. After laborious testing, you find that if you mix sodium hydroxide and hydrochloric acid, you get sodium chloride (and water), or more commonly known as salt.

If a question can be answered with experiments, then there’s no point arguing about it. Just do the experiment to test the answer.

So I conclude…

that my friend doesn’t like science. *smile*

No, it’s that when a question can only be answered by reasoning it through, then it’s considered a philosophical question.