Mathematics Archives

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Maps are all lies – Representing a spherical earth on a flat world map

Is Greenland really bigger than Africa and Australia? Take a deep breath. The big map in your high school classroom, the atlas you’ve used to navigate during a road trip and even google maps are all lying to you. They all start with the same big lie, that the earth is flat, two-dimensional, like a pancake. When in fact, as humans have known for a very long time, at least since the time of ancient Greeks, that the earth is spherical (that people thought that the earth was flat at the time of Columbus is a myth). Well, not exactly spherical, …

Two goats and a car – The Monty Hall problem

Just a couple of weeks ago, I outlined the birthday paradox, a well-known counter-intuitive mathematical puzzle. Today, we’re going to explore another quite famous statistical problem, the one with the game show host, three doors, two goats and a car. The problem goes something like this. You’re at a game show on tv. There are three closed doors. Behind two of the doors there is a goat and behind one there is a car. The host of the game show asks you to pick one of the three doors. Once you do, the host opens one of the two unpicked …

The birthday paradox

Take a group of 23 people. What is the probability that two of them share the same birthday? Or let’s take a different approach. How many people do you need to make sure that the probability that two of them share the same birthday is close to 100%? On first glance, 367 seems like a probable answer (as there as 366 days during a year including February 29th). But while you would need as many to get to exactly 100%, you need much less to reach 99% probability.

How to take the perfect penalty kick

The Champions League final is coming up and there’s a chance that it will go to penalties. Will the teams have studied the behaviour of the keepers and the penalty takers of the opposing team? Have they inferred a trend? Will it even help at all? The question is though, can the keeper know which way the kicker will shoot? And if he does, does the kicker know that the goalkeeper knows? And what if the goalkeeper knows that the player knows that he knows?

Information Overload – The True Cost of Data

In the last few years we have produced more data than in all of human history. We live our lives constantly producing a stream of data, it controls our lives, not in a Matrix or Skynet kind of way, but every time we interact (text, call, tweet), conduct a transaction, perform an internet search, complete a national census or even simply give birth or die, you are creating data and contributing that in the right hands is valuable and powerful tool. A recent EMC study claims that less than 1% of global data is actually analysed.

Distribution of first digits: Benford’s Law

Take a large data set, like stock prices, electricity bills or population sizes of different countries. If you were to count how many times each digit appeared as the first digit (for 105 the first digit would be 1, for 34583 the first digit would be 3, etc.), what would be their distribution? You’d expect that each numeral would occur an equal amount of times. But you would be wrong.