Now to find a mathematician who reads Latin...
Friday, October 13, 2006
Leonard Euler and the Bridges of Konigsberg
Have just found Euler's original paper on the "Bridges of Konigsberg" problem (can you cross all the bridges exactly once?):
Now to find a mathematician who reads Latin...
Now to find a mathematician who reads Latin...
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9 comments:
Tony, Euler only shows it is not possible.
Indeed he does.
I am pondering on why a Christian Mathemetician wants a Latin speaking Mathemetician to read a Latin Book written by non Roman Mathemetician, and conclude it must be a Mathemetician thing known only to Mathemeticians as Euler was the worlds greatest Mathemetician who, in this book touched upon topology Mathemeticians - er - sorry, mathmatics.
Do you know the hymn to this Mathemetician probem Tony?
............................
Seven bridges spanned the River Pregel,
Many more than might have been expected,
Konigsberg's wise leaders were delighted
To have built such very splendid structures.
Crowds each ev'ning surged towards the river,
People walked bemused across the bridges,
Pondering a simple sounding challenge
Which defeated them and left them puzzled.
Here's the problem; see if you can solve it!
Try it out at home on scraps of paper,
Starting out and ending at the same spot,
You must cross each bridge just once each evening.
Eulerian graphs all have this restriction:
THE DEGREE OF ANY POINT IS EVEN.
That's the oldest graph result
That mankind has ever known.
All the folk in Konisberg were frantic!
All their efforts ended up in failure!
Happily, a learned mathematician
Had his house right there within the city.
Euler's mind was equal to the problem
"Ah", he said, "You're bound to be disheartened,
Crossing each bridge only once per outing
Can't be done, I truly do assure you.
Laws of Nature never can be altered,
We can't change them, even if we wish to.
Nor can flooded rivers or great bridges
Interfere with scientific progress.
War brought strife and ruin to the Pregel,
Bombs destroyed those seven splendid bridges.
Euler's name and fame will, notwithstanding,
Be recalled with Konigsberg's for ever.
Thanks to Euler, Graph Theory is thriving.
Year by year it flourishes and blossoms,
Fertilising much of mathematics
And so rich in all its applications.
Colleagues, let us fill up all our glasses!
Colleagues, let us raise them now to toast the
Greatness and the everlasting glory
Of our Graph Thry, which we love dearly.
............................
Ok, I don't pretend to be a Mathemetician, but one and one have to make two, so, do you intend to solve this puzzle or want to find out how Euler came to his Mathemetical conclusion Tony?
Yes, I love Graph Theory dearly -- where did the poem come from?
Ever heard of Bohdan Zelinka? He wrote the 'Graph Theory Hymn'which you read there. I forget who wrote the music, but no doubt it would be online. It is a real song.
You may like to learn to play the tune on your guitar in a bit of spare time.
Dico in linguam Latinam et Mathematicus sum.
Thanks for the pointer, I will read it with interest although I will not be expecting Virgil or Ovid. :)
To answer Bev's questions, it might be instructive to consider Europe in the 17th century.
At that stage all Mathematicians and Scientist communicated in Latin as it was the Lingua Franca of Europe and educated people. Until the second half of the 19th century all Mathematicians wrote in Latin: then the curse of Nationalism struck. Note, however, that Euler's contempory Emmanuel Kant wrote in incomprehensible German (even native speakers have difficulty deciphering it).
What this means is that I can read the first half of Gauss' works, but not the second as he wrote them in German.
The loss of Latin as an academic language is very sad and I think that we would have been preserved much nonsense if it had not been lost.
I am a little confused why Bev would have thought that Euler was Italian.
Ursus
Thanks, Ursus.
I think I want to translate "Geometriam Situs" as "Geometry of Place" (i.e. topology.
And I see Regiomonti Borussiae = Königsberg.
Thankyou Ursus for your kind explanation!
I did know Euler was not Italian of course, but at the time of the comment had forgotten his nationality.
I too agree the loss of Latin is a great blow in the academic world, nevertheless, the academic world shall (hopefully) continue as more and more turn to learning Latin as a language.
Tony, one can only think of topology when one thinks of the Seven Bridges of Konisberg as I believe Euler tapped into topology in the book mentioned.
Let me think back ... if I recall correctly, topology does not recognise the circle and the square but does recognise the figure eight and relies basically on connective issues.
Fascinating subject to study up on! It leads me straight to something dear to my heart. Nature.
Topology... isn't that when you can't tell the difference between a coffee cup and a doughnut?
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