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Guest
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 Posted: Sun Feb 06, 2005 9:57 pm Post subject: pentagram vcs hexagram! |
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| how about exponential function(hor),negative exponentional function(set) and logarytm(Ausar)? what do they do in 3D? and what is the relation, what do you KNOW?
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Guest
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| Posted: Sun Feb 06, 2005 10:17 pm Post subject: |
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| elaboration of the Theme: Mathyla Ghyka, rumunian mathematician said: "ALL SHAPES IN THIS UNIVERSE ARE JUST PENTAGRAM AND HEXAGRAM!"
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Sun Apr 10, 2005 12:19 pm Post subject: A very 2D view... |
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[quote="Anonymous"]"ALL SHAPES IN THIS UNIVERSE ARE JUST PENTAGRAM AND HEXAGRAM!"[/quote]
Surely in 3D the 2D triangles have it.
ONE point above a triangle logically creates a tetrahedral frame, with the addition of 3 equal lines.
The Pentagram is a 2D representation of 5 tetrahedrons and the hexagram a 2D representation of 12 tetrahedrons, 6 above and 6 below.
The oscillating triangle frame hypothetically, can create space for a double tetrahedron which can be described as 3^2 or 3*3. The 9 equal lines make a double tetrahedral frame. This shape creates space inside for a 10th line +.
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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angeloflight5
Joined: 12 Mar 2005
Posts: 6
Location: Atlanta, GA, USA
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| Posted: Sat May 07, 2005 12:49 am Post subject: 3-dimensional Pentagram |
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You say that a 2D pentagram drawn into 3D is 5 tetrahedrons, right? Can anyone draw this for me?
Also, I'd like to see a hexagram, which you say is 12 tetrahedrons in 3D.
The 3D hexagram I can imagine, I think. But the 3D pentagram is what I'm having trouble visualizing. I see that the two 5's are the same. How come, when the hexagram in 3D is 6x2 but the pentagram is not 5x2?
The pentagram in 3D is also fuzzy to visualize for me also because it is basically only two triangles crossed together, only one point from the each of the two triangles is connected, the beginning point and the ending point. The two triangles are not true triangles, however. They look like the old Star Trek logo.
Just curious.
angeloflight5:11:1:11
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Sat May 07, 2005 8:49 am Post subject: Re: 3-dimensional Pentagram |
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| angeloflight5 wrote: | You say that a 2D pentagram drawn into 3D is 5 tetrahedrons, right? Can anyone draw this for me?
The 3D hexagram I can imagine, I think. But the 3D pentagram is what I'm having trouble visualizing. |
The pentagram is hard to do see from 2D. BUT to see it in 3D, go to your local War Hammer shop and buy 5 tetrahedral dice. Stick the middle of one edge of each dice together with blue tack in a circle. Or:
Cheeper version is to get pipe cleaners and thin straws or Qtips and glue, it requires 30, same size pieces (the sum visible on the purchased tetrahedral dice). Make 5 tetrahedrons and fit together.
The 2D above view shows a pentagram.
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Also, I'd like to see a hexagram, which you say is 12 tetrahedrons in 3D.
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Again to demonstrate 12 tetrahedrons are needed, the frames constructed from a total of 72 same size pieces. The number of X's in each square in a square grid of 6x6.
The tetrahedrons are face side paired. The view of the 2D hexagram creates points above and below.
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I see that the two 5's are the same. How come, when the hexagram in 3D is 6x2 but the pentagram is not 5x2?
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The 5 are in a circle, the 12 are above and below a flat plane, similar to placing a piece of paper between all paired tetrahedrons.
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The pentagram in 3D is also fuzzy to visualize for me also because it is basically only two triangles crossed together, only one point from the each of the two triangles is connected, the beginning point and the ending point. The two triangles are not true triangles, however.
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When the 5 tetrahedrons are placed in the circle there is a slight gap between them, which causes an oscillation.
The 5 points can be seen as the three points of a triangle with an additional one above and one below. 3+1+1=5 points=9 lines=a double tetrahedron.
Imagine at one point the lines or 'arms' of a single triangle open, one going up, one other going down. Remembering the position of the broken point a double tetrahedron can be made. This transformation has 9 equal lines in it's framework, the number of squares in a grid of 3x3 squares.
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They look like the old Star Trek logo.
Just curious.
angeloflight5:11:1:11 |
If you look at equal squares you will find that they have the same number of squares as equal triangles have triangles.
I believe we will be star treking sooner than later.
Ant
http://www.stargrail.co.uk
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Sat May 07, 2005 9:06 am Post subject: Re: 3-dimensional Pentagram |
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| Ant wrote: |
72...The number of X's in each square in a square grid of 6x6.
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Sorry, meant to say the number of I's crossed in a square grid of 6x6.
Ant
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angeloflight5
Joined: 12 Mar 2005
Posts: 6
Location: Atlanta, GA, USA
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| Posted: Sun May 08, 2005 2:07 am Post subject: pentagrams and hexagrams |
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Hahaha. *laughing to myself here* Thanks, Ant.
You gave me more than I guess I was expecting. Wow. 
Now lemme just go nab some of those pipe cleaners. haha. What, 102 of them, u say? :p
Lemme go make these things now. ^_^
Joy, joy. lol
angeloflight5:11:1:11
(previously known as "akhu1004" or "divine_evolution777" in the Yahoo! Group)
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Sun May 08, 2005 9:28 am Post subject: Re: pentagrams and hexagrams |
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| angeloflight5 wrote: | Hahaha. *laughing to myself here* Thanks, Ant.
Lemme go make these things now. ^_^
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If you do, you don't need so many.
I have studied magic squares and now concider them a 2D representation of a 3D image. The first magic square is a saturn square a grid of 3x3 squares.
Each square contains two measures of the square root of 2. Which creates 18 lines, as 9 crosses.
The 18 lines create a quantum matrix of 5 tetrahedrons which can be described as a stellated tetrahedron.
Some years ago I had an unexpected realisation when I removed the center tetrahedron.
If you do get round to it you need 18 thin straws, cut them to about 3 inches. Get enough pipecleaners to make 36 at 2 inch length pieces.
Bend each pipe cleaner length in half, half of two lengths of pipe cleaner placed in each end of the straw pieces. Three pipe cleaner pieces to each stellated tetrahedrons corner. Six pipe cleaner pieces at the joints of the center tetrahedron.
Once a stellated tetrahdron is made, it is easy to see the cube frame that forms by removing the middle tetrahedron. A cube made by removing the one inside five tetrahedral frames.
The stellated tetrahedron show the math of 2+2= 4, 5 or 6.
A cube made in this way could be described as five tetrahedral frames minus one. Or could be described as adding one to account for the expansion to the cube.
If you do start playing with them good luck, hope you enjoy it. In the meantime here is a picture of some of the shapes that have been abstracted from equal square math.
Ant
| Description: |
| This is the shapes extracted from the numbers within an equal square of 3x3. |
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Mon May 09, 2005 7:30 pm Post subject: More magic square shapes |
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Cwantum 5 and 6 Cubes.
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Sun Jun 12, 2005 6:51 pm Post subject: Re: A very 2D view... |
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| Ant wrote: |
The oscillating triangle frame hypothetically, can create space for a double tetrahedron which can be described as 3^2 or 3*3. The 9 equal lines make a double tetrahedral frame. |
When space is represented as cubes, the shape of an equal square based
Pyramid contains the same cubic space as a double triangle based Pyramid.
To explain:
(Ignore the dots, they have been added to stabilize the number grouping).
Side view, where each digit indicates how many cubes deep.
....1...........1
...21.........22..........1.........1
..321.......333.........21.......22...........1.......1
.4321.....4444........321.....333.........21.....22.........1.....1
54321...55555.......4321...4444.......321...333.......21...22
.4321....................321...................21.................1
..321......................21....................1
...21........................1
....1
Totals:
55 55 30 30 14 14 5 5
Double Triangle Pyramids reformed create single square based Pyramids. They also reform to a stellated octahedron or Merkabah shape.
They can be viewed as above so below... and as below so above...
Ant
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Ant
Joined: 03 Apr 2005
Posts: 58
Location: Berwickshire Scotland
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| Posted: Mon Jun 20, 2005 11:43 am Post subject: Re: A very 2D view... |
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| Ant wrote: |
Surely in 3D the 2D triangles have it. |
When the triangle edge opens at one point, one arm can go up, the other can go down, the third can remains still. This oscillating triangle frame, can create space for a double tetrahedron. The shape known as a hexahedron. Imagine the red buds in the group of single hexahedrons closing to form a triangle.
There are 9 equal lines in a hexahedron, the number of squares in a 3 square and the number of triangles in a 3 triangle.
111.....1
111...111
111.11111
The hexahedron fits inside a icosahedron.
Ant
| Description: |
| A hexahedron in a icosahedron. |
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| Description: |
| A hexahedron or stellated triangle. |
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