1. ©G Dear 2009 – Not to be sold/Free to use
Spherical
Geometry
General Mathematics
HSC
Great Circles
and Small Circles
Stage 6 - Year 12
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©G Dear 2009 – Not to be sold/Free to use

2. Any circle passing through the poles.
Great Circles (1/4)
Any circle passing through the poles.
North Pole
Great Circle
(Equator)
Axis
South Pole

3. Length of Great Circles (2/4)
Diameter
Radius D
2r
C =
r = 20 cm
C = 2xx20
≈ 126 cm
D = 20 cm
C =  x 20
≈ 62.8 cm
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4. Any circle perpendicular to the axis.
Small Circles (3/4)
Any circle perpendicular to the axis.
Axis A
Series of
Small
Circles
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5. Small Circles (4/4) C = 2  r = 2 x  x 5 = 31.4 cm
To calculate the length of the small circle we need to know the length of its radius. r
C = 2  r
5cm
= 2 x  x 5
= 31.4 cm