Amur
08-29-2006, 10:54 AM
Generally it feels like there is an embedded 2-dimensional geometrical aspect within the mind which is hardwired into the brain in some-sense. At the point of writing it feels almost like I could communicate and transmit with 2-dimensional regular geometrical images alone, as it comes so naturally. This only indicates that there is a vast potential hidden within geometry alone. As far as I've come I haven't yet found a negative effect of looking at self-similar geometrics.
If looking at geometrical self-similar forms, we can easily give the point(s) numerical values from 0(void) up to OO(circle).
0->void, 1->point, 2->line, 3->triangle, 4->square, 5->pentagon, 6->hexagon, 7->heptagon, 8->octagon, 9->enneagon, 10->decagon and so on. It is easily noticable that the self-similar form becomes very quickly something which resembles a circle. If we take a 20-pointed icosagon it's quite near to a circular shape already. The circle naturally has the biggest area, from where it is easy to conclude that every self-similar shape can exist within the circle.
They all seem to have more or less their own attribute to them. The next builds upon the previous ones with 1,2 and 3 being quite crucial. Unfortunately I don't know much about the area yet.
A line (http://en.wikipedia.org/wiki/Line) between 2 points(A, B) is always the shortest distance possible between those 2 points.
An equilateral triangle (http://en.wikipedia.org/wiki/Triangle) between 3 equally distanced points(A, B, C) is the hardest structure which exists. The angles in the triangle round up so that from wherever an impact comes it is always supported by the 2 other points. Perhaps this has some correlance with the Tetragons appliance to the element of Fire. The triangle is a representation correllation between 1 point related to a Line(2 points).
The square (http://en.wikipedia.org/wiki/Square_(geometry)) is the first 2D representation of a line-field. I don't know much properties about the square, other than living inside too 'squarish' houses makes one a square head *grin*. Perhaps even the building geometries affect peoples consciousness. Though a pure square for me is a symbol for cleanliness/tidyness/order. Another viewpoint could be the 4-directions. When constructing a sphere with 2 circles, the point where the circles meet has 4 directions to follow.
The pentagon (http://en.wikipedia.org/wiki/Pentagon) has some peculiar properties. When connecting the points with each other through lines it gives the perfect representation of the value phi (http://en.wikipedia.org/wiki/Golden_ratio). Which is considered to be one of the pattern which nature readily follows. In many ancient aspects, phi was considered to be the seat of Beauty itself. Here's the pentagram (http://en.wikipedia.org/wiki/Pentagram).
The Hexagon (http://en.wikipedia.org/wiki/Hexagon) has 120 degree angles between the points and saves space in relativity to it's strength. It is generally used by bee-hives as it has superior size/strength and heat properties(if I remember correctly). hexagram (http://en.wikipedia.org/wiki/Hexagram) is generally 2 polar equilateral triangles on top of each other. One could say that it is a defense against both Heaven and Hell.
The Heptagon (http://en.wikipedia.org/wiki/Heptagon) I don't know much about more than that the number 7 has had alot of mystic and magickal meanings attached to it. The heptagram (http://en.wikipedia.org/wiki/Heptagram) has been used to go with the number 7 in all the mystical meanings. If I remember correctly there's alot of seven mystery in the bible. Following the lines of an obtuse heptagram makes me confused atleast. Just doesn't make sense lol.
The Octagon (http://en.wikipedia.org/wiki/Octagon) corresponding to the number 8. One can get the points of the octagon by putting 2 squares on top of each other with one turned half the side distance to either way.
The Enneagon (http://en.wikipedia.org/wiki/Enneagon)
The Decagon (http://en.wikipedia.org/wiki/Decagon)
The Circle (http://en.wikipedia.org/wiki/Circle) has many symbolisms attached to it, whereas most of them have attached the circle to infinity itself as it has no beginning nor end. It is equal into all directions and it is said to be a representation of Justice also. Anything travelling towards the circle has the same feedback from the circle regardless from which direction it comes. Naturally a fully mathematical infinite-sided polygon(circle) is impossible in this world as it will always come down to some resolution. It might be interesting to note that all the planets and stars are something which resembles a circle. Gravity itself acts through a circular principle, pulling on every point in a likewise force at the circle.
I'll continue this later when more information has come and time gives away for it.
If looking at geometrical self-similar forms, we can easily give the point(s) numerical values from 0(void) up to OO(circle).
0->void, 1->point, 2->line, 3->triangle, 4->square, 5->pentagon, 6->hexagon, 7->heptagon, 8->octagon, 9->enneagon, 10->decagon and so on. It is easily noticable that the self-similar form becomes very quickly something which resembles a circle. If we take a 20-pointed icosagon it's quite near to a circular shape already. The circle naturally has the biggest area, from where it is easy to conclude that every self-similar shape can exist within the circle.
They all seem to have more or less their own attribute to them. The next builds upon the previous ones with 1,2 and 3 being quite crucial. Unfortunately I don't know much about the area yet.
A line (http://en.wikipedia.org/wiki/Line) between 2 points(A, B) is always the shortest distance possible between those 2 points.
An equilateral triangle (http://en.wikipedia.org/wiki/Triangle) between 3 equally distanced points(A, B, C) is the hardest structure which exists. The angles in the triangle round up so that from wherever an impact comes it is always supported by the 2 other points. Perhaps this has some correlance with the Tetragons appliance to the element of Fire. The triangle is a representation correllation between 1 point related to a Line(2 points).
The square (http://en.wikipedia.org/wiki/Square_(geometry)) is the first 2D representation of a line-field. I don't know much properties about the square, other than living inside too 'squarish' houses makes one a square head *grin*. Perhaps even the building geometries affect peoples consciousness. Though a pure square for me is a symbol for cleanliness/tidyness/order. Another viewpoint could be the 4-directions. When constructing a sphere with 2 circles, the point where the circles meet has 4 directions to follow.
The pentagon (http://en.wikipedia.org/wiki/Pentagon) has some peculiar properties. When connecting the points with each other through lines it gives the perfect representation of the value phi (http://en.wikipedia.org/wiki/Golden_ratio). Which is considered to be one of the pattern which nature readily follows. In many ancient aspects, phi was considered to be the seat of Beauty itself. Here's the pentagram (http://en.wikipedia.org/wiki/Pentagram).
The Hexagon (http://en.wikipedia.org/wiki/Hexagon) has 120 degree angles between the points and saves space in relativity to it's strength. It is generally used by bee-hives as it has superior size/strength and heat properties(if I remember correctly). hexagram (http://en.wikipedia.org/wiki/Hexagram) is generally 2 polar equilateral triangles on top of each other. One could say that it is a defense against both Heaven and Hell.
The Heptagon (http://en.wikipedia.org/wiki/Heptagon) I don't know much about more than that the number 7 has had alot of mystic and magickal meanings attached to it. The heptagram (http://en.wikipedia.org/wiki/Heptagram) has been used to go with the number 7 in all the mystical meanings. If I remember correctly there's alot of seven mystery in the bible. Following the lines of an obtuse heptagram makes me confused atleast. Just doesn't make sense lol.
The Octagon (http://en.wikipedia.org/wiki/Octagon) corresponding to the number 8. One can get the points of the octagon by putting 2 squares on top of each other with one turned half the side distance to either way.
The Enneagon (http://en.wikipedia.org/wiki/Enneagon)
The Decagon (http://en.wikipedia.org/wiki/Decagon)
The Circle (http://en.wikipedia.org/wiki/Circle) has many symbolisms attached to it, whereas most of them have attached the circle to infinity itself as it has no beginning nor end. It is equal into all directions and it is said to be a representation of Justice also. Anything travelling towards the circle has the same feedback from the circle regardless from which direction it comes. Naturally a fully mathematical infinite-sided polygon(circle) is impossible in this world as it will always come down to some resolution. It might be interesting to note that all the planets and stars are something which resembles a circle. Gravity itself acts through a circular principle, pulling on every point in a likewise force at the circle.
I'll continue this later when more information has come and time gives away for it.