Fun Math - The 7 Bridges

I have been teaching high school math for over 30 years and also at the University. Many of my students have returned and told me that i was the best math class they ever took. Mainly because i forced them to think and because i made math fun.

One of my tricks is to introduce math concepts by using history. So here is a collection of my favorite Math stories or discovery.

Today in class we were discussing mathematical modeling. And the first person that came into my mind was Euler. The greatest mathematician of all time. Now you can image if most students do not even know who was president during the Vietnam War, how are they going to know Euler !!

We just celebrated his 300 year anniversary. He is pictured on the 10 Franc in Switzerland where they put people who have contributed to civilization, not Presidents like in the US. But then of course we are lucky we have George Washington on the one dollar bill or no one would know who our first president was.

So one of the most interesting Geometry questions in history is the famous "Seven Bridges of Koningsberg". What ? Say what ? Never heard of it ? It is amazing that high school students who have had a FULL year of Geometry and never heard of Euler nor the famous problem of the 7 bridges. I am sure the Europeans students know of Euler and they probably also know who was the American president during the Vietnam War. But then US students do not know the Circumference of the Earth either !! What do they teach them in Geometry then. Don't they know that Geo-metry means the "measure of the earth" and that the Greeks knew the Circumference of the earth before Christ was born. (let me see was that 2,000 years ago or 3,000 years ago...where is my calculator)

Worse yet when we try to discuss the circumference of the world, the first thing they ask is "will this be on the test". Never mind that we live in Florida and that the space shuttle circles the earth every 90 minutes (from Red October a classic movie). I show it in class every year...at least the good parts.

Getting back to the 7 Bridges. It is hard to describe it here with no drawings and if you are really interested, i am sure you know how to google search it. I will put a link at the bottom for the over 50 crowd.

Euler told his students that they need to make a mathematical model of it. To get away from the real world rivers and bridges that get in the way of the thinking.

Then we have a discussion of the well known barn picture that must be drawn with straight lines and in one smooth motion. Again hard to demonstrate here (maybe my son will show me how to draw on this blog....i will try to add the picture to the margin).

One can quickly see that there are "odd" vertices and "even" vertices. And in order for the game to work you must start on the bottom (an odd vertice) and end at the other bottom also an "odd" vertices. And it you have one odd, you must have another odd. And only 2 odd vertices will work.

Well the 7 Bridges has 4 odd vertices so it is impossible.

Then it gets real exciting when the town decided to add a Bypass Bridge (number 8 bridge) outside of town. Now there are only 2 odd vertices and it can be done.

And it is DONE !! every hour on the hour by tour buses in Koningsberg.