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In the same paper, Dehn also constructed an example of a non-Legendrian geometry where there are infinitely many lines through a point not meeting another line, but the sum of the angles in a triangle exceeds
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Infinity and the mind. The science and philosophy of the infinite
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states that the sum of the angles of a triangle is at most
419:"Die Legendre'schen Sätze über die Winkelsumme im Dreieck"
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is violated. They were introduced by Max Dehn (
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The non-Legendrian geometry consists of the points (
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are any (possibly infinite) elements of the field Ω(
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