What is the strangest coincidence that you have ever come across?

That has ever happened to you?

Coincidence is an idea that can sometimes be treated mathematically.

For example, take the Birthday problem.
You discover that two of the people on a football pitch during a match have the same birthday.
Does this count as a coincidence?

You have to send a document to someone you do not know somewhere else in the country.
You send it to the person you know who is most likely to know this person. They do the same.
How many postings will there be until delivery, on average?

Paul Erdos was mathematician who gave his colleagues an Erdos number.
If they had written a paper with him, their Erdos number was one.
If they had written a paper with someone who had written a paper with him, then their Erdos number was two, and so on.

We can use this idea in all sorts of ways.
Imagine a chain of people such that every person in the chain has shaken the hand of the people on either side of them.
The Handshake-Number for two people is the number of people in the shortest possible such chain.
Might there be two people with no Handshake-Number?
How could you reduce your average Handshake-Number dramatically?

It is easy to manufacture coincidence if you try.

If you are determined to find numerical significance
in how the measurements of the Blackpool Tower relate to each other,
you can do!

But is there a force in nature heading in the direction of coincidence?
The psychotherapist Jung developed the idea of synchronicity:
that events have a tendency to occur in apparently coincidental ways.

Twins are said to know if their partner dies,
even if they are on opposite sides of the world at the time.

Coincidence can happen in mathematics:
although sometimes the apparent coincidence can be explained.

For example, pick three numbers a, b, and c in arithmetic progression, then three more, d, e and f, also in arithmetic progression.

Now solve the simultaneous equations ax + by = c, dx + ey = f.
What results for x and y do you get? Try this a few times. Is this coincidence?

On the other hand, look at the decimal form of the number e.

e = 2.718281828...

Is the repetition of 1828 a coincidence?

Two more examples: a solar eclipse is remarkable because the moon almost exactly covers the sun.
This is because the sun is about 400 times wider than the moon,
and also about 400 times further away from us. A coincidence?

The east coast of Latin America and the west coast of Africa appear to fit together.
Is this coincidence?