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Author Topic: Is this a solution for trisecting an angle?  (Read 1905 times)

Offline f.point

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Is this a solution for trisecting an angle?
« on: 27/05/2015 11:04:09 »
Solution trisecting (n-sections) and n-proper construction of the polygon using divider and straightedge.

The ball shall be awarded in two equal parts, obtained half contains two areas, the circle (represents a planar geometry) and a semi-sphere (represents spherical geometry), the circle is the boundary between the circuit and semi-sphere
View photo (below)
CIRCLE
within a given arbitrary angle BAC,straightedge (straightedge is flexible, it can draw on a sphere)
straight line the BA to extend the circle to give the point D
SPHERE
straightedge connect points B and D, you get the curve BD
straightedge and divider - a procedure divisions curve into two equal parts is the same as the process of division shall exceed the level in two equal parts, we get the point E
straightedge - connect points C and E and get the curve CE


Proportion longer exists in plane geometry, I found that the process can be applied to the sphere
choose point G
divider EC, from point G we get a point Hdivider EC, from point H we get a point I
divider EC, from point E twe get a point Jdivider EC, from point J get the point K
divider EC, from point K get the point L
straightedge point L and point I and connect, we get curve LI
EG divider, from the point L we get a point P
EG divider, from the point P and get the point Ostraightedge join the dots E and P and proceed to the circle, we get the point Q
straightedge merge points E and O and proceed to the circle, we get the point R
CIRCLE
straightedge connect point A and point Q, we get straight line AQ
straightedge connect point A and point R, we get straight line AR

these have carried out the production of a given trisection angle, is obtained from the rest of the (n-section, a regular n-polygon) ...

Now proclaim everywhere that I decided 2- millennium math problems
« Last Edit: 30/05/2015 13:32:41 by chris »


 

Offline evan_au

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Re: final solution
« Reply #1 on: 27/05/2015 12:50:44 »
I had a quick skim, but it's a long time since I did any geometry...

Quote from: f.point
straightedge is flexible, it can draw on a sphere
Traditionalists will have a problem with this step; Euclid's style of geometry was originally done in a "Euclidean" space (ie not curved).

However, there is a modern equivalent to the straight line in a non-Euclidean geometry: The geodesic. On a sphere, all geodesics are segments of great circles.

Quote
straightedge point L and point I and connect, we get curve LI
I have a slight problem with this step. Curve LI is like lines of latitude, and is not a geodesic, so it can't be considered a "Straight line in a curved geometry", or drawn with a straight edge (even a bendy one).

I guess you could draw LI easily enough with a compass...
 

Offline f.point

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Re: final solution
« Reply #2 on: 27/05/2015 14:49:57 »

Traditionalists will have a problem with this step; Euclid's style of geometry was originally done in a "Euclidean" space (ie not curved).

in the rules says that you should use an unmarked straightedge and dividers, I respect the rules, no one next to me did not find that the proportion of arc can be solved in sphere,
 

Offline Airthumbs

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Re: final solution to trisecting an angle
« Reply #3 on: 30/05/2015 04:49:20 »
Is trisection of a triangle considered ethical?  Triangles have rights too you know!  :-)
 

Offline alancalverd

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Re: final solution to trisecting an angle
« Reply #4 on: 30/05/2015 08:10:07 »
No!

1. Since EG is arbitrary, you could select EG such that it is not a rational fraction of the great circle. Then the entire construction is invalidated.

2. A chord on a great circle subtends a smaller angle than the same chord on a small circle.

Sorry, mate, but the proof that an angle cannot be trisected by Euclidean construction, remains supreme.
« Last Edit: 30/05/2015 08:16:11 by alancalverd »
 

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Re: final solution to trisecting an angle
« Reply #4 on: 30/05/2015 08:10:07 »

 

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