New shoes

This Christmas marked the first time I had spent significant time with my brother and sister since their entry into the London marathon was confirmed. Wanting to run with them, I ran a steady 10 miles with my brother on Christmas Eve and combined a swift half hour with an easier 30 minutes with my sister on Christmas morning – on the beach along the South Coast. I have run on Christmas morning for the last few years and I find it helps to ease the guilt felt from over-indulging on various foods. Although I probably need more than an hour’s worth of running.

It had also been my intention to run on Boxing Day but, unfortunately, I was suffering a sore back, so decided to rest. However, this would mean that in order to burn off many excess calories (and to save having two consecutive rest days), I had to run the following day; the day I was to drive the four hour journey home.

Wanting to make an early getaway, I planned to run for about an hour, covering close to 10 miles. This particular run would take me into the New Forest as far as I have previously ventured so, when I had been running for 35 minutes, I decided to follow a new road – just to see where it went. The road soon became a track, which subsequently became a path. Then it disappeared. Yes, that’s right, it disappeared. But I could see traffic up ahead along a busy road, so I crossed the marshy land to investigate and discovered a designated cycle track.

With time on my side, I continued my investigation and, after about another half an hour, found myself in the next village. Thinking I ought to turn around, as time was getting on, I returned along the road from where I had come and decided to see if one of the tracks off the road would provide an adequate ‘short cut’.

The track that I chose became a path but, again, disappeared. Concerned that time was short, I continued by heading in the direction that I suspected I wanted. I passed through woods, followed fence lines, and tried to locate paths in order to try and identify some sort of ‘landmarks’, but soon found myself with barren heathland in every direction as far as I could see. By this stage, I had no option, but continue to follow my instinct. I ran up and down hills, passed through streams, more marshes and bogs, with hardly any change in my surroundings.

By now, I had been running for almost two hours; I needed to get back, so that I could drive home. Finally, I saw a house, which had to be on a road and, continuing in the same direction, I ended up within 100m of exactly where I wanted to be. I don’t think that’s too bad an effort considering I was running for more than two miles without knowing my location (without GPS, map, compass or otherwise).

However, by the time I returned, I had been running for more than two and a half hours – 90 minutes longer than intended. This means that the run would be my longest since July, the last long run of 2011. It is also probably time to throw out my fourth pair of 1000+ mile trainers, which look like they’ve been running with TFP a few too many times.

No room at the inn*

The last week of term is here, and I am determined not to fall into the mould of showing films that students could equally watch during the holidays.

Instead, we will discuss infinity through the Hotel Hilbert (see here for a description), Zeno and other paradoxes (see here for others) and propose that it will never be Christmas.

Yours, Scrooge.

*Perhaps Mary and Joseph should have tried Hilbert’s Hotel

Planning for Christmas

With Christmas approaching, lessons in class are often littered with appropriately themed resources. However, I have a somewhat scrooge-like reputation to protect, so am not too frivolous in my giving.

I don’t spend time or money decorating the classroom, nor do I introduce Christmas into the theme of lessons, unless it has a real purpose; there’s no room for ‘painting Father Christmas by numbers’, even if maths problem have to be solved in order to work out the number first.

But there are a few places where Christmas and maths naturally coalesce. The first is applying mathematics to the journey that Father Christmas must travel on Christmas Eve. There are plenty of opportunities to apply maths in this instance; to the speed of travel, the size of the sleigh, the minimum number of reindeer required and so on. But, unfortunately, Father Christmas and physics are not the best of friends so, in order to avoid an unhappy ending, I steer clear of this one.

Some people may be familiar with the desk calendars that are printed onto 3-D shapes, similar to that shown in the image below. This page [navigate from here if the link has expired] has a number of different options that are more exciting than what is essentially a cuboid – although I would encourage students to generate their own nets.

Moving away from ‘making things’, the American bank, PNC, has developed a Christmas Price Index – based on the amount it would cost to buy items from the song ‘The Twelve Days of Christmas’ (see here). I tend to start with a calculation of the number of presents, which is a source of surprise for many, before a calculation of the cost of buying all of those items – more than $100 000. The list of possible directions from here is endless, aided by the PNC supplying data as far back as 1984.

Note: The trend and the pie chart, below, refer to the PNC Christmas Price Index, which are both based on the cost of Day 12 alone, not the total cost of all days.