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the claim

In spherical geometry any two great circles intersect, so parallel lines do not exist.

the verdict
SUPPORTED
the evidence backs this
Recorded sources
3 sources for · 0 against

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Is it true that in spherical geometry any two great circles intersect, so parallel lines do not exist?

Yes. A reference article on parallel lines states that in spherical geometry all geodesics are great circles and all great circles intersect, so no parallel geodesics exist; a mathematics Q&A proves two distinct great circles meet at antipodal points.

Verdict: SUPPORTED · 3 sources for, 0 against · Last checked

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Evidence for · 3
Parallel (geometry)
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Parallel (geometry). (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Parallel_(geometry)

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More for · 2
Two great circles intersect at two antipodal points (Spherical Geometry)
2020
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Two great circles intersect at two antipodal points (Spherical Geometry). (2020). math.stackexchange.com. https://math.stackexchange.com/questions/3699056/two-great-circles-intersect-at-two-antipodal-points-spherical-geometry

On the weak spherical incidence
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On the weak spherical incidence. (n.d.). zbmath.org. https://zbmath.org/3981949

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