WOLFRAM|DEMONSTRATIONS PROJECT

Basis for Pure Geodetic Angles

​
a
4
b
5
d
1
2
3
5
6
-1
tan
5
3
4
= π-
-1
tan
3
2
-
-1
tan
2
3

p
<p
>
3
7
-1
tan
3
2
13
-1
tan
2
3

19
-1
tan
3
4
31
-1
tan
3
3
2
37
-1
tan
2
3
5
43
-1
tan
3
3
4
61
-1
tan
2
3
7
67
-1
tan
3
8
73
-1
tan
4
3
5
79
-1
tan
5
3
2
This Demonstration illustrates the theorem: If
tan(θ)=(a/b)
d
, with square-free positive integer
d
and relatively prime
a
and
b
, and if the prime factorization of
2
a
+d
2
b
is
k
1
p
1
k
2
p
2
...
k
n
p
n
, then we have
θ=tπ±
k
1
<
p
1
>
d
±
k
2
<
p
2
>
d
±…±
k
n
<
p
n
>
d
for some rational
t
.