Pythagorian Geometry behind the Vergina Star ??

[Andrew]

Everybody knows Pythagorians for their great theorem of the hypotenousa in a rectangular triangle. Maybe less known is their relationship with the incommesurance of the square root of 2 (1,414...).
In the Thread about the Macedonian symbols it is well proven that the Vergina Star of the Temenids was in reality a more diffuse symbol among Greeks. How did Greeks designed it so accurately. How can you devide a circle accurately in 16 parts ?? Can the Pythagorean Geometry help us in that task ??

YES !!!!

And it helps by giving us exactly the angle that is 1/16 of a circle (2π/16 = π/8) . Now the tangent of that angle is tan(π/8) = SqRt(2) - 1

http://img386.imageshack.us/img386/6093/16starom3.png (http://imageshack.us)

[Tsontos]

I dont think so. Sunburts of 16 rays are common across different continents in the Ancient world.

[Promethean Fire]

I dont think so. Sunburts of 16 rays are common across different continents in the Ancient world.


What has that got to do with the geometry??:huh:

Across different continents, i would be interested to see these perfect sunbursts of 16 rays, honestly because i havent seen them anywhere as ancient as in Greece.

[kostas68]

Wasn't Pitagora the greatest makedonski mathematical?I read such a scopian theory but i can't remember where it was written.Probably it was in the monkey-news forum and the genious who claimed that wrote also something like...Hermes trici-veliki !(yes,he meant <Hermes trismegistos>!)

[Andrew]

I dont think so. Sunburts of 16 rays are common across different continents in the Ancient world.

Don't forget that Pythagoras travelled in the east for 20 years ..He went to Babylon ,Egypt ..some say he even reached India (I don't believe that) ...
The babylonians knew the irrationality of SqRt(2) ,but never made a systematic theory.
The Egyptians knew the Pythagorian theorem long before Pythagoras , but they knew it as the "5,4,3" theorem ..that is to obtain a rectangular angle form a triangle with hypotenoysa 5 and other sides 3 and 4. Again no systematic theory . Pythagoras and the Pythagorians generalized it to be applicable in ALL the rectangular triangles.
So I'm not denying that you can find the star in the oriental cultures . It's the precision that interests me , as Promethean Fire added !!


And Kwstas68 :clap2: :clapping: :clap2: The Skops probably say that also Pythagoras was a great "Makedonsky" philisopher-Mathematician :p:p:p

[Flipper]

Basicaly the Pythagoreans were so far out that they're shocking me. They were not just scientists but great spiritual people as well.