# Spherical GeometryWatch

#1
I hate Spherical Geometry.

Can anyone show me what you a) get from formula (2) in Question 2 of this sheet when you let a,b,c become small, and b) how to show that the trinagle inequality holds for spherical triangles using (1)?

http://www.maths.ox.ac.uk/current-st.../geometry4.pdf

Thanks
0
12 years ago
#2
To show that sina/sinα = sinb/sinβ = sinc/sinγ you need to know that sinx ≈ x for small x... the usual formula follows.

cos a = cos b cos c + sin b sin c cos α

cos a ≥ cos b cos c - sin b sin c (because cosα is between 0 and 1)

cos a ≥ cos (b+c) (trig identity)

a ≤ b + c (inequality sign changes because arcosine is monotonically decreasing on 0 to pi)
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