A Conversation for The Euler Equation

The Bridges at Konigsberg

Post 21


Well, in response to Kes's question from a few days back, there are some protocols to what I' talking about, you may refer to Avoid the flaky side if such is not your cuppa, but, the basics of structure are sort of similar. . .I emailed Joanna about all this nonsense. Basically I'd be content at this point to find one person who was willing to listen and understand what I am getting at.

A very few simple questions (and an exercise in circular logic perhaps):

Does anyone remeber and American Cartoon show called fangface? This would be his little typyface? ):> , see, he had one big pointy fang. Anyway:

Symettrical things are symmetrical to each other,either in SIZE, or SCALE, correct.

A symmetrical thing built off another Symmetrical thing would exhibit some of these characteristics? Right?

A Locus of points coinciding with all vertices of such a construction would form a sphere?


The Bridges at Konigsberg

Post 22

Joe aka Arnia, Muse, Keeper, MathEd, Guru and Zen Cook (business is booming)

The mathematical definition of symmetry: A construct is symmetrical under an operation if it is impossible to distinguish the before and after images.

The Bridges at Konigsberg

Post 23


So where doesthat leave the "Fractal geometry" term of 'Symmetry of Scale"? that which we call call "similarity" in terms of triangles of the same angles, but different proportions? Anyway, as you know, I have a basic slightly advanced US Maths background, and the text with with i most recently refreshed my Memories was entitled "Excursions in Modern Maths" and was designed for Lib Arts Majors for a course Entitled Advanced Maths for Liberal Arts Majors. I readily admit that i am in over my head, but I do know that the Koch Curve makes perfect sense. . .

The Bridges at Konigsberg

Post 24


"Thanks I'll walk across the bridges and take a look. BCNU"

Good luck... Konigsberg doesn't exist any more as such. Up until May 1945 the city USED to be the capital of East Prussia, which formerly was the extension of Germany into what is now Poland. For nearly eight hundred years it had been the symbol of the great German drive East to claim "lebensraum" at the expense of her Slavic neighbours (Hitler didn't come out of a vacuum, he was capitalising on general German feelings about Poles and Russians that had been around for a long time. Where do you think the Germanic languages, including English, get the word "slave" from?)

After the Germans had spent six years being particular nuisances to their neighbours, especially their eastern ones, the Poles and the Russians were agreed on one thing - no more. While the Poles were not especially overjoyed to exchange German domination for Russian, they agreed on one thing - no more bloody Prussians this far East. So most of what was formerly East Prussia was absorbed into Poland (its German inhabitants were shown the same courtesy they had shown to the Poles, ie, not very much, and forcibly shipped West into what later became East Germany.) The top right hand corner, with Konigsberg in it, was annexed to the Soviet Union, and the city was renamed.

All symbols of German domination in Konigsberg, including the crusader castle, were blown up by the new management: all seven of the bridges had been destroyed in the fighting anyway.

I think the city, today, is still a Russian enclave out on the far end of the Gulf of Leningrad. I'm not sure how many of the bridges they managed to rebuild, though...

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