Impressum  Copyright © Klaus Piontzik  
German Version 
4  The angle approach
4.1  Angle differences
However,
temporary, a quantitative analysis can be reached also by
other methods. The angle approach takes the coordinates
of the extreme values (total intensity) and forms the
differences first between the latitudes and then with the
longitudes. For simplicity only the extreme values 1 (chapter 2.4) have been illustrated for the following analysis. Der Einfachheit halber sind im Folgenden nur die Extremwerte 1 aus zur Auswertung abgebildet worden. 
forming the difference of the latitude coordinates for the extreme values
Name  NorthMaximum  SouthMaximum  Anomaly  Minimum 
SouthMaximum  118,8625  
Anomaly  2,65  121,5125  
Minimum  82,9375  35,925  85,5875  
Saddle point  50,3875  55,475  53,0375  32,55 
forming the difference of the longitude coordinates for the extreme values
Name  NorthMaximum  SouthMaximum  Anomaly  Minimum 
SouthMaximum  118,925  
Anomaly  156,75  37,825  
Minimum  45,2875  164,2125  157,9625  
Saddle point  164,5625  45,6375  7, 8125  7, 8125 
If one looks these angle
differences more exactly, than can be shown that
practically all appearing angles are multiples
of certain basic angles. Most angles lie close to values which are a multiple of 7.5 degrees. And one receives 7.5 degrees, if the full circle is disassembled in 48 sections. The number 48 again is a multiple of the number 3 as well as the number 4. Already from it will consist evidently that here oscillation figures can appear with the number 3 or 4 or a combination of both numbers. 
4.2  Angle forming
To allow a better comparison, the angle spectra are constructed at first for the 3rd, 4th and 5th partition from 0 degrees up to 180 degrees. 
48163264128
corners
Multiple of 2,8125
2,8125  5,625  8,4375  11,25  14,0625  16,875  19,6875  22,5 
25,3125  28,125  30,9375  33,75  36,5625  39,375  42,1875  45 
47,8125  50,625  53,4375  56,25  59,0625  61,875  64,6875  67,5 
70,3125  73,125  75,9375  78,25  81,5625  84.375  87,1875  90 
92,8125  95,625  98,4375  101,25  104,0625  106,875  109,6875  112,5 
115,3125  118,125  120,9375  123,75  126,5625  129,375  132,1875  135 
137,8125  140,625  143,4375  146,25  149,0625  151,875  154,6875  157,5 
160,3125  163,125  165,9375  168,75  171,5625  174,375  177,1875  180 
3612244896
corners
Multiple of 3,75
3,75  7,5  11,25  15  18,75  22,5  26,25  30 
33,75  37,5  41,25  45  48,75  52,5  56,25  60 
63,75  67,5  71,25  75  78,75  82,5  86,25  90 
93,75  97,5  101,25  105  108,75  112,5  116,25  120 
123,75  127,5  131,25  135  138,75  142,5  146,25  150 
153,75  157,5  161,25  165  168,75  172,5  176,25  180 
510204080160
corners
Multiple of 2,25
2,25  4,5  6,75  9  11,25  13,5  15,75  18  20,25  22,5 
24,75  27  29,25  31,5  33,75  36  38,25  40,5  42,75  45 
47,25  49,5  51,75  54  56,25  58,5  60,75  63  65,25  67,5 
69,75  72  74,25  76,5  78,75  81  83,25  85,5  87,75  90 
92,25  94,5  96,75  99  101,25  103,5  105,75  108  110,25  112,5 
114,75  117  119,25  121,5  123,75  126  128,25  130,5  132,75  135 
137,25  139,5  141,75  144  146,25  148,5  150,75  153  155,25  157,5 
159,75  162  164,25  166,5  168,75  171  173,25  175,5  177,75  180 
4.3  Evaluation of the differences
The ascertained
differences between the magnetic extreme values are now
compared with the angle spectra constructed on top. Only the values from the 3rd, 4th or 5th partition, whose difference to the extreme value differences are smaller than ± 1 degree, are put down in a table. 
An analysis occurs at first which regard to the latitude coordinates: 
Difference evaluation of the latitude coordinates for the extreme values
Name  Difference  3corner  4corner  5corner 
NmaxSmax  118,8625    118,125  119,25 
NmaxAnomaly  2,65    2,8125  2,25 
NmaxMinimum  82,9375  82,5    83,25 
NmaxSaddle point  50,3875    50,625   
SmaxAnomaly  121,5125    120,9375  121,5 
SmaxMinimum  35,925    36,5625  36 
SmaxSaddle point  55,475  56,25  56,25  56,25 
AnomalyMinimum  85,5875  86,25    85,5 
AnomalySaddle point  53,0375  52,5  53,4375   
MinimumSaddle point  32,55  33,75  33,75  33,75 
And afterwards an analysis occurs with regard to the longitude coordinates: 
Difference evaluation of the longitude coordinates for the extreme values
Name  Difference  3corner  4corner  5corner 
NmaxSmax  118,925    118,125  119,25 
NmaxAnomaly  156,75       
NmaxMinimum  45,2875  45  45  45 
NmaxSaddle point  164,5625  165    164,25 
SmaxAnomaly  37,825  37,5    38,25 
SmaxMinimum  164,2125  165    164,25 
SmaxSaddle point  45,6375  45  45  45 
AnomalyMinimum  157,9625  157,5  157,5  157,5 
AnomalySaddle point  7, 8125  7,5  8,4375   
MinimumSaddle point  7, 8125  7,5  8,4375   
How is to be seen from
both tables, the 3rd 4th and 5th partition with enough
exactness (smaller than ±1 degrees) appears. In the
latitude, as well as in the longitude. However, the
geometrical or stereometrical consequence from this is,
that all Platonic solids can appear as
oscillation figures. And just with thus becomes
tetrahedron against dodecahedrondiscussion (what
concerns fields) simply superfluously. The consequence is likewise that the pure tetrahedron, octahedron or dodecahedron and icosahedron models deliver only partial views of the complete oscillation field, and, hence, are not entire. To the treatment of the concerning geologic models see chapter 13. 
4.4  The zero point
Most angles of the
extreme values lie close to values which show a multiple
of 7.5 degrees. The question which rises here, if within this oscillation structure a zero point exists, from which the whole field becomes representable? To answer this question it must be checked, how often 7.5 is included in the respective longitude data and which rest appears. 
The longitude coordinates for the extreme values 1
Name  Longitude  Longitude devide by 7,5  Rest 
NorthMaximum   96,125 degrees West  12  6,125 
SouthMaximum  +144,95 degrees East  19  2,45 
Great Anomaly  +107,125 degrees East  14  2,125 
Minimum   50,8375 degrees West  6  5,8375 
Saddle point  +99,3125 degrees East  13  1,8125 
If a zero point exists, than the rest shows the longitude of the zero point. It is the matter tf find factors (m) which deliver the identical rest for all points. It turns out the following result: 
The coordinates for the extreme values 1
Name  Longitude  m  Rest 
NorthMaximum   96,125 degrees West  11  13,625 
SouthMaximum  +144,95 degrees East  21  12,55 
Great Anomaly  +107,125 degrees East  16  12,875 
Minimum   50,8375 degrees West  5  13,3375 
Saddle point  +99,3125 degrees East  15  13,1875 
The coordinates for the extreme values 2
Name  Longitude  m  Rest 
NorthMaximum   96,04 degrees West  11  13,54 
SouthMaximum  +144 degrees East  21  13,5 
Great Anomaly  +106,5 degrees East  16  13,5 
Minimum   50,8145 degrees West  5  13,3145 
Saddle point  +99 degrees East  15  13,5 
The average from all rest corners amounts to 13,29 degrees. Up to 2 values all rests lie close to 13,5 degrees. Hence 13,5 degrees can be accepted here as longitude position of the zero point. 
In the consequence the longitude positions of the extreme values of the total intensity from the earth magnetic field are representable by the following formula:  
m is an element of the integers (...3,2,1,0,1,2,3...) and λ_{0} = 13,5 degrees of west.  
From now on this equation is called longitude position formula for the magnetic extreme values.  
With the
help of satellite geodesy in 1966 by C.A.Lundquist and G.
Veis determined the following parametres: (see in addition „Geodetic parameters for a 1966 Smithsonian Institution Standard Earth" von Lundquist, C.A., Veis, G., See also Torges „Geodäsie" page 77.) 



a_{1} is the great
equator halfaxis, a_{2} the small
equator halfaxis and λo the longitude of
the great halfaxis. 

With thus
the longitude positions of the extreme values from the
earth magnetic field stand in relation with the equator axes of a threeaxle ellipsoid. 

See also chapter 17. Also in modern publications is still maintained that the magnetic field disposes of no symmetrical structures. As to be seen in this chapter angle approach, however, this is right only the first sight and does not withstand a more precise examination. 
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