On a globe (model of the Earth), the lines of longitude (meridians) all pass through the North and South poles. What does this tell us about parallels in spherical geometry, in contrast to Euclid's fifth postulate?

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Accepted Answer

Two distinct 'straight lines' (great circles) always meet, so no parallels exist. On a sphere, great circles (the 'straight lines') such as meridians all intersect at the poles, so no two are parallel. This violates the fifth postulate, giving spherical (non-Euclidean) geometry.

On a globe (model of the Earth), the lines of longitude (meridians) all pass through the North and South poles.
What does this tell us about parallels in spherical geometry, in contrast to Euclid's fifth postulate?

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More Class 9 The Fifth Postulate practice

On a globe (model of the Earth), the lines of longitude (meridians) all pass through the North and South poles.What does this tell us about parallels in spherical geometry, in contrast to Euclid's fifth postulate?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 The Fifth Postulate practice

On a globe (model of the Earth), the lines of longitude (meridians) all pass through the North and South poles.
What does this tell us about parallels in spherical geometry, in contrast to Euclid's fifth postulate?