h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Totally counter-intuitive. Such fun.

A great way to freak out primary school teachers whose maths skills are sometimes slightly suspect.

(Not picking on primary teachers - they do a great job and we need more of them)

I agree - a very nice entry. Well done.

Many thanks - it's a good "ice breaker" at training courses, and could probably be used to start a fight in a pub !

loved the article, loved the logic and the cool looking equations contained, even though i didn't understand the equations, it wasn't neccesary. you could still get the point from the explanations to make it make sense. Well reasoned. p.s. i'd hate to be the guy who had to work out all of that math. ok, except i'd love to have been him at the moment of realisation of the implications of his discovery.

Thanks - I don't know where I found out this piece of information, although I certainly didn't work it out for myself.

If you fancy a challenge, try this one

Prove that the largest area which can be enclosed by a fixed length of string is a circular one. I had to do this in high school - the original question was to do with one of those "a farmer has a field" questions ("A farmer has a rectangular field with a wall along one side, and wants to enclose a rectangular area within the field using a length of rope, using the wall as one side of the rectangle. If the length of rope is 30 feet, what is the maximum area he can enclose?")

I gave the answer (100 square feet) without giving any explaination, and when asked "Why must it be a square enclosure?" I said that it was obvious, which didn't impress my teacher, so he made me prove that the largest rectangle for a fixed perimeter must be a square.
Like a mug, when I gave him the proof I then said, "Of course the largest area for a fixed perimeter would be a circle.", he made me prove that, too. (This was nowhere near as easy and I doubt if I could do it now, 35 years later!).

Any road up, glad you liked the article.

Do you think you could now, as it's 40 years later?

Ask again in a couple of years.

(you were expecting someone to say that, eh?)

Other than googling a solution, I doubt that this old man is up to the challenge! If anyone else wants to try, from memory I proved that the area of a regular polygon increases (for a fixed perimeter) as the number of sides on that polygon increases. Since a circle is (sort of) a regular polygon with an infinite number of sides, then I concluded that this was proof that a circle provides the biggest area.