A great mathematician you'd be lost without!

Leonhard Euler

1707 - 1783

Euler (pronounced 'oiler') was a Swiss mathematician who has contributed a huge amount to much of the maths that is used today. In fact we probably wouldn't have Sat Nav if it wasn't for Euler!

Although it may seem he was around a long time ago, compared to Pythagoras (570 BC!) it's pretty recent...

He made a real difference in lots of areas of maths from algebra to number theory and to geometry, where he effectively 'invented' a whole new area of maths that's called 'Graph Theory' and which has led on to 'Topology' which is a way of looking at shapes, where shapes are considered the same if they can be squished or stretched to be the same as long as no holes are filled in and no new holes are made. So in topology a teacup is considered to be the same topology as a doughnut! (because they both have 1 hole in them)

In Year 12 Further Maths we're looking at Euler's Graph Theory, we'll be looking to see how it can be used for very practical purposes. Car Sat Navs rely on the theories that were first started by Euler and if you have ever used Google Maps to find your way, you have Euler (and a few others) to thank!

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It all started with a problem about bridges in the Prussian town of Konigsberg (what is now Kaliningrad in Russia). On a Sunday afternoon people would go for a walk over the 7 Bridges of Konigsberg going through the different areas of town. The challenge was... is it possible to visit all the areas of town by crossing over each bridge once and only once?
Have a go...!

It was Euler who first proved that it was in fact impossible... Read more about it here... and it was his new way of thinking about the problem which created the mathematics of Graph Theory and then Topology...

Have you ever tried to draw the house with the cross without taking your pen off the paper and without retracing any lines? what about the one on the right? These are examples of graphs

It's thanks to Euler that we know when it is and when's it's not possible to do this. Can you make a 'graph' that you can draw without retracing and one that you can't?