Recent Posts by Ian Lucas

Taking your IB Diploma? Here’s a revision plan…

I don't want to be too prescriptive about how you should revise – everyone's different, everyone remembers stuff in different ways – but you should definitely prepare a revision plan. If you don't, then it will be a matter of luck whether or not you'll be ready in time for the exams. Most of you will have at least some holiday time before the exams, and it's imperative you make the most of it – you're on your own, and it's ...

A Mathematical Card Trick

Card tricks fall into several categories, and my favourite are those which look amazing but actually have some pretty simple maths behind them. Here's one of the simplest! 1.     Take an ordinary pack of cards and shuffle it. Deal out 26 cards, face up, and remember the 7th card. 2.    When you've dealt out the 26 cards, pick up the pile and turn them face down on the table, to one side. (If you're brave, shuffle them first, but make ...

Ancient Babylonians Do It Again!

Babylon – in ancient Mesopotamia, now Iraq – hosted one of the earliest recorded civilisations. Partly because they became a trading nation, they developed some of the earliest mathematical techniques. We already know that they were aware of what we now call Pythagoras' Theorem (in a numeric sense, since algebra didn't exist), but the some of the secrets of a tablet known as Plimpton 322 have been unravelled to show that they had developed a highly sophisticated form of trigonometry, ...

Sampling Methods

In statistics, a population is the complete set of data which is to be analysed. A population may consist of people (e.g. those living in a particular city), or living things (e.g. the population of all humpback whales), but could be any set of objects with something in common (e.g. all cars travelling on a particular road in a 24 hour period). Usually, it isn't possible to analyse a complete population. Why? It would take too long It would be too ...

Sam Lloyd, Master of Puzzles

Sam Lloyd was born in Philadelphia in 1841, but lived most of his life in New York. He was primarily a chess player and composer of chess problems, but he also delighted in mathematical puzzling. Actually, not just mathematical puzzles, but word puzzles; picture puzzles; tangrams; he composed thousands of them. In fact, it was one of his pictorial puzzles which grabbed my attention at a very early age, and possibly sparked my enjoyment of such puzzles. Have a look ...

Help with your IB Mathematics

Whether you are in the first weeks of your diploma course, or whether you are halfway through, there are always going to be some parts of the maths syllabus that make you scratch your head! Over the past couple of years some of the blogs I have written have concentrated on specific topics which I know can benefit from further explanation. I thought it would be helpful to list those blogs here: a reference for those that are new to ...

Games with Dots

Do people still play pencil and paper games these days? I grew up with them in my family – all sorts from number games, word games, drawing games. A number of the mathematical games involve spots or dots and, believe me, they can be fiendishly difficult to win against a good opponent. The simplest of all is boxes. A square grid of dots is created (the bigger you make it, the longer the game). The first player joins two  adjacent dots with either ...

MacTutor History of Mathematics

In my wanderings around the internet I came across a superb resource for anyone interested in, or needing information about, mathematicians, the history of mathematics, mathematical chronologies – even a 'famous curves' index. This is the MacTutor History of Mathematics site, created by John J. O'Connor and Edmund F. Robertson of the University of St. Andrews in Scotland. Under 'Mathematicians of the Day' there's an index of those who were born or died on every day of the year. I'm amazed ...

What Do You Get Asked in University Interviews?

Some universities interview applicants. In the UK, the Oxford and Cambridge interviews are an important part of the application process, Imperial College and UCL tend to interview the majority of applicants. In the US, many Ivy League colleges also carry out interviews. But what should you expect, and how can you prepare? Interviewers stress that they are not testing knowledge, which would be unfair, given that applicants come from many different backgrounds and educational systems. The purpose, says Oxford, is to ...

Putting the “Wow” into Magic Squares!

I'm sure that at some time in your life you've come across a magic square; usually a 4 x 4 table filled in with numbers where every row and column adds to give the same total. Here's an example where the total is 34 and, as a bonus, the two leading diagonals add to give 34 as well.           Well, that's quite nice, but hasn't really got the wow factor, has it? The next one has, though: same numbers, filled in differently.           It's ...

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