This is the final stage (or nearly so), of changing the value(s) for r, the radius of the sphere:
clearvars,clc
global r
for r=8.450000001
AB = 7.2; AC = 9.6; AD = 15.6; BC = 12; BD = 15.6; CD = 15.6;
ab=2*asind(AB/2/r);
ac=2*asind(AC/2/r);
ad=2*asind(AD/2/r);
bc=2*asind(BC/2/r);
bd=2*asind(BD/2/r);
cd=2*asind(CD/2/r);
ADC=acosd((cosd(ac)-cosd(ad)*cosd(cd))/(sind(ad)*sind(cd)));
ADB=acosd((cosd(ab)-cosd(ad)*cosd(bd))/(sind(ad)*sind(bd)));
BDC=acosd((cosd(bc)-cosd(bd)*cosd(cd))/(sind(bd)*sind(cd)));
s=sum([ADC ADB BDC]);
disp([r s s-max([ADC ADB BDC])] )
% disp([ACD ACB BCD]);
% disp(' ')
end
As can be seen, the radius seems to be 8.45.
The output
8.450000001 359.995768766871 179.999999837267
Shows the sum of angles ADC + ADB + BDC on the spherical surface is then 360°, which is necessary as the projected lines AD, BD and CD radiate from a point.
Below 8.45 the result of the total angles is complex. The total decreases rapidly beyond r=8.45:
r total angles about
point D
8 540 - 260.51354176315i
9 232.14298538851
10 178.032033381028
11 156.064985198326
12 143.936238873283
13 136.242783331235
14 130.947978166925
15 127.100223233904
16 124.192262348986
17 121.928170964417
18 120.123527806478
19 118.657435458096
20 117.447395576806
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Posted by Charlie
on 2024-04-30 12:15:00 |
spherical trig and varying r
