Welcome to the Theory of Everything forums.
You are currently viewing our boards as a guest which gives you limited access to view most discussions and access our other features. By joining our free community you will have access to post topics, communicate privately with other members (PM), respond to polls, upload content and access many other special features. Registration is fast, simple and absolutely free so please, join our community today!
If you have any problems with the registration process or your account login, please contact contact us.
| | | | | Raider of the lost time
Status: Offline Posts: 5,147
Thanks Given: 659
Thanked 103x in 102 Posts
Join Date: Nov 2003 Rep Power: 72 | rational polygons -
01-31-2008, 02:16 PM
The area of a rectangle is the product of its length (L) and its width (W). However, the largest area of a quadrilateral inscribed in a circle is a square or the same as a rectangle with length equal to width, L=W. If the circumscribed circle has unit radius then the area of the inscribed square is 2 square units and the sides are irrationals square root of 2. if an inscribed rectangle has unit width then the length is again an irrational square root of 3 whose area is also square root of 3 square units. Without further proofs, it is logical to assert that no rational quadrilaterals can be inscribed in a circle. However, for general polygons, it can be demonstrated that a regular rational hexagon of unit sides can be inscribed in a unit circle.
In nature, this distinctive pattern can be observed in the structure of snowflakes or snow crystals. If it can be experimentally measured that the sizes of these hexagonal structures are consistently of the same size then it proves the existence of global symmetry for earthbound unit circles. On the other hand, if these structures are of different sizes then global invariant symmetry does not exist even though local invariant symmetry does.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| |
|  | | | | | Moderator
Status: Offline Posts: 7,204
Thanks Given: 334
Thanked 621x in 593 Posts
Join Date: Aug 2005 Rep Power: 90 |  Re: rational polygons -
01-31-2008, 02:21 PM
Quote:
Originally Posted by AntonioLao  The area of a rectangle is the product of its length (L) and its width (W). However, the largest area of a quadrilateral inscribed in a circle is a square or the same as a rectangle with length equal to width, L=W. If the circumscribed circle has unit radius then the area of the inscribed square is 2 square units and the sides are irrationals square root of 2. if an inscribed rectangle has unit width then the length is again an irrational square root of 3 whose area is also square root of 3 square units. Without further proofs, it is logical to assert that no rational quadrilaterals can be inscribed in a circle. However, for general polygons, it can be demonstrated that a regular rational hexagon of unit sides can be inscribed in a unit circle.
In nature, this distinctive pattern can be observed in the structure of snowflakes or snow crystals. If it can be experimentally measured that the sizes of these hexagonal structures are consistently of the same size then it proves the existence of global symmetry for earthbound unit circles. On the other hand, if these structures are of different sizes then global invariant symmetry does not exist even though local invariant symmetry does. |
If my memory serves me well I believe snowflakes are all different in shape,although
there does appear a certain symmetry with them.
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself?
Last edited by mkirkpatrick : 01-31-2008 at 02:22 PM.
Reason: spelling error.
| |
| | | The Following User Says Thank You to mkirkpatrick For This Useful Post: | | | | | | Raider of the lost time
Status: Offline Posts: 5,147
Thanks Given: 659
Thanked 103x in 102 Posts
Join Date: Nov 2003 Rep Power: 72 | Re: rational polygons -
01-31-2008, 02:26 PM
Quote: |
Originally Posted by mkirkpatrick snowflakes are all different in shape,although there does appear a certain symmetry with them. | You are correct. It is the hexagonal symmetry I'm interested in.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| |
| | | | | | Moderator
Status: Offline Posts: 7,204
Thanks Given: 334
Thanked 621x in 593 Posts
Join Date: Aug 2005 Rep Power: 90 | Re: rational polygons -
01-31-2008, 02:31 PM
Quote:
Originally Posted by AntonioLao You are correct. It is the hexagonal symmetry I'm interested in. |
What will this tell you?
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself? | |
| | | | | | Raider of the lost time
Status: Offline Posts: 5,147
Thanks Given: 659
Thanked 103x in 102 Posts
Join Date: Nov 2003 Rep Power: 72 | Re: rational polygons -
01-31-2008, 02:39 PM
Quote: |
Originally Posted by mkirkpatrick What will this tell you | the existence of local as well as global gauge symmetry independent of length.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| |
| | | | | | Moderator
Status: Offline Posts: 7,204
Thanks Given: 334
Thanked 621x in 593 Posts
Join Date: Aug 2005 Rep Power: 90 | Re: rational polygons -
01-31-2008, 02:43 PM
Quote:
Originally Posted by AntonioLao the existence of local as well as global gauge symmetry independent of length. | Surely we are surrounded by perfect symmetry,albeit mostly invisible,local and otherwise.
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself? | |
| | | | | | Raider of the lost time
Status: Offline Posts: 5,147
Thanks Given: 659
Thanked 103x in 102 Posts
Join Date: Nov 2003 Rep Power: 72 | Re: rational polygons -
01-31-2008, 02:49 PM
Quote: |
Originally Posted by mkirkpatrick mostly invisible | In mathematics, if a transformation does not exist between two domains then they are conversely invisible to each other.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| |
| | | | | | Moderator
Status: Offline Posts: 7,204
Thanks Given: 334
Thanked 621x in 593 Posts
Join Date: Aug 2005 Rep Power: 90 | Re: rational polygons -
01-31-2008, 02:53 PM
Quote:
Originally Posted by AntonioLao In mathematics, if a transformation does not exist between two domains then they are conversely invisible to each other. | Can they then still effect on another?
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself? | |
| | | | | | Raider of the lost time
Status: Offline Posts: 5,147
Thanks Given: 659
Thanked 103x in 102 Posts
Join Date: Nov 2003 Rep Power: 72 | Re: rational polygons -
01-31-2008, 03:03 PM
Quote: |
Originally Posted by mkirkpatrick Can they then still effect on another | That could be the quantum nonlocality that many are talking about. I' afraid I dont understand it. My idea is based on the existence of unit circle of gauge invariance, in fact two circles linked together into a Hopf ring. Transformations exist and they commute between zero and infinity but not taking the exact values of zero and infinity.
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| |
| | | | | | Moderator
Status: Offline Posts: 7,204
Thanks Given: 334
Thanked 621x in 593 Posts
Join Date: Aug 2005 Rep Power: 90 | Re: rational polygons -
01-31-2008, 03:09 PM
Quote:
Originally Posted by AntonioLao That could be the quantum nonlocality that many are talking about. I' afraid I dont understand it. My idea is based on the existence of unit circle of gauge invariance, in fact two circles linked together into a Hopf ring. Transformations exist and they commute between zero and infinity but not taking the exact values of zero and infinity. |
I don't fully understand it either,but it "feels" right!
regards michael.
Humilty,coupled with boldness,surprises truth to
reveal herself? | |
| | | The Following User Says Thank You to mkirkpatrick For This Useful Post: | | |
Currently Active Users Viewing This Thread: 1 (0 members and 1 guests) | | | | Thread Tools | | | | Display Modes |  Linear Mode | | |
