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Q: Why would knowledge of geometry be helpful to the Greeks?

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Geometry solved their problem about land and guide in the sea, by measurement everything, and increased their knowledge by the ancient North africans and Middle Easterners about mathematics, construction, architecture, architecture, etc.

Either the civilization had some knowledge of geometry or they would not understand the term

Your knowledge in geometry would be a big help in studying trigonometry, because trigonmetry involves the ratio of the sides of a right triangle, something that is underpinned by geometry. The pythagorean theorem is crucial here. Also, the angles are important, and that is also underpinned by geometry.

The Greeks could learn that Greece is not as big as the circumference of the Earth. This would lead to new countries, like America.

The Greeks could learn that Greece is not as big as the circumference of the Earth. This would lead to new countries, like America.

It would give them an estimate of distances and of the scientific explanations of astral and earthly events and distances,

Greeks live in the country of Greece. Canadians live in the country of Canada. Any further comparison would require knowledge of specific people.

I understand that they knew that if a triangle had sides of length 3, 4, and 5, the triangle would be a right triangle. The Greeks generalized this into the Pythagorean Theorem.

The Greeks could learn that Greece is not as big as the circumference of the Earth. This would lead to new countries, like America.

They would take the geometry CST

Ummm....wat?

Descartes did not discover geometry - he invented analytical geometry, which enabled mathematicians to use algebra to solve problems in geometry and geometry to solve problems in algebra. The world would be less developed than now, as would be the case with most discoveries.