Тригонометрия гиперболической плоскости положительной кривизны. Ромакина Л.Н. - 37 стр.

UptoLike

Составители: 

ch B
(cc
0
a(BB
0
)) ch C
(bb
0
a(CC
0
))
R b
0
(t : 1 : b
0
3
) c
0
(1 : t : c
0
3
) B
0
(1 : t : 0) C
0
(t : 1 : 0)
BB
0
(tb
3
: b
3
: t
2
1) CC
0
(c
3
: tc
3
: t
2
1)
(bb
0
a(CC
0
)) =
c
3
(1 t
2
)
c
3
(1 + t
2
) 2tb
3
, (cc
0
a(BB
0
)) =
b
3
(1 t
2
)
b
3
(1 + t
2
) 2tc
3
.
b
3
> 0 c
3
> 0 t (0; 1)
1
=
2
= 1
ch B = i
b
3
(1 + t
2
) 2tc
3
t
p
4(b
3
tc
3
)(c
3
tb
3
) (t
2
1)
2
,
ch C = i
c
3
(1 + t
2
) 2tb
3
t
p
4(b
3
tc
3
)(c
3
tb
3
) (t
2
1)
2
,
sh B = i
(1 t
2
)
p
b
2
3
t
t
p
4(b
3
tc
3
)(c
3
tb
3
) (t
2
1)
2
,
sh C = i
(1 t
2
)
p
c
2
3
t
t
p
4(b
3
tc
3
)(c
3
tb
3
) (t
2
1)
2
.
˜a ABC
˜a = πρ/2
ch A = cth
˜
b
ρ
cth
˜c
ρ
, cth
˜
b
ρ
= th
˜c
ρ
ch A,
ch A = ch B ch C, sh B = i sh
˜
b
ρ
sh A, ch
˜c
ρ
= i sh
˜
b
ρ
sh C.
ABC C =
πi/2
ch
˜c
ρ
= cos
˜a
ρ
ch
˜
b
ρ
, ch
˜c
ρ
= cth A cth B,
ch A = i sh B cos
˜a
ρ
, sin
˜a
ρ
= sh
˜c
ρ
sh A, sh
˜
b
ρ
= i sh
˜c
ρ
sh B.
ABC
b
0
c
0
a (t : 1 : b
0
3
)