| In differential geometry [ ] In the , the question of a triangle's angular defect is understood as a special case of the where the curvature of a is not a function, but a with the in exactly three points — vertices of a triangle | Spherical geometry [ ] Main article: Angles between adjacent sides of a triangle are referred to as interior angles in Euclidean and other geometries |
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| Ultimately, the answer was proven to be positive: in other spaces geometries this sum can be greater or lesser, but it then must depend on the triangle |
A has three angles, one at each , bounded by a pair of adjacent.
16| The parallel postulate is equivalent to the Equidistance postulate, Playfair axiom, Proclus axiom, the Triangle postulate and the Pythagorean theorem | : In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides |
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| The sum of the angles can be arbitrarily small but positive | The influence of this problem on mathematics was particularly strong during the 19th century |
In a , the of angles of a triangle equals the 180 , , two , or a half-.
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