Aspect ratio

I hate it when I see someone watching television in the wrong aspect ratio; for some reason it really bugs me.

Aspect ratio is always given as horizontal:vertical. Television programmes are usually produced in one of two formats: “regular” 4:3 and “widescreen” 16:9.

If you watch a 4:3 programme with a widescreen television on its 16:9 setting everything looks stretched – people look short and fat.

A widescreen television should be using the 4:3 setting to watch a 4:3 programme. This wastes some screen real estate with black bars at each side of the screen, but it prevents distortion.

Likewise, a 4:3 television should be using the 16:9 setting to watch a 16:9 programme. This creates the familiar “letterboxing” effect at the top and bottom:

For movies a ratio of 2.35:1 is very common but others are frequently used. Ben Hur was shot in an incredible 2.76:1.

Philips have gone as far to produce a “cinema-ratio” TV:

Teaching statistics with Fruit Gums

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Fruit Gums can be used to demonstrate the concept of standard deviation.

Calculating standard deviation is easy, it’s simply:

Which, with the right teaching, and enough practice, anyone can learn to do. Understanding what standard deviation means is far more difficult.

I bought three boxes of Fruit Gums …

… and sorted them by flavour.

I collected the data in Excel which yielded the following spreadsheet:

The issue of standard deviation is summed up in the question: “What is the largest and smallest number of each flavour that you can expect to find in each box?”

Lime is a special case. The were seven lime fruit gums in each box, meaning the standard deviation was zero. You could therefore – based on this sample alone – expect to find seven lime fruit gums in each box.

The standard deviation of a sample is a measurement of its spread, it tells you the mean distance from the mean.

For lemon fruit gums the mean is 19.0 plus or minus a standard deviation of 2.2. You could therefore expect to find – on average, based on this sample alone – between 16.8 and 21.2 lemon gums in each box. A box containing 25 lemon gums would be way outside the expected average contents.

The only outlier in this dataset is the first box’s orange gum count; based on the data collected we would expect a maximum of 21.2 orange gums. Clearly more fruit gums research is required.

Why grit roads?

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Almost every day I walk past this yellow grit container. I’ve never really paid attention to it before, but it’s certainly in the news at the moment.

Why do we grit roads?

The term “grit” is a bit of a misnomer and an ambiguous term. The “grit” used on roads is actually rock salt, known properly as halite.

Halite is the mineral form of sodium chloride, the same salt that’s used to season food. Most of the UK’s halite comes from Winsford Rock Salt Mine in Cheshire in the North West. You can see the yellow gritting vehicles at the bottom of the map below.


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Gritting roads is all about melting points. Water begins to freeze below 4°C, so if the ambient temperature is anywhere below 4°C any water on the roads will turn to ice, which is very slippery and cannot be pushed away by tyre tread.

Spreading salt on the roads causes it to mix with the water to produce brine. The saltier the brine, the lower the melting point. For example: a mixture of 30g of salt per 1000g of water lowers the melting point to −1.6°C. Now imagine the ambient temperature is 0°C: any pure water on the road will freeze but the salty water will remain a liquid.

Unfortunately there is a limit to salt’s usefulness. To make the melting point as low as possible you must add as much salt as possible and supplies are limited. Even a completely saturated solution, a totally impractical measure using a huge amount of salt (23.3% salt by weight) only has a melting point of −21.1°C, making the use of rock salt pointless below this temperature. Realistically it would be impractical and very difficult for councils to use rock salt to cope with temperatures much below −10°C.