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to the spherical case, the sum of the angles of a hyperbolic triangle is less than 180°, and can be arbitrarily close to 0°. Thus one has an angular defectAs in the spherical case, the angular defect and the area determine each other: one haswhere and is the constant curvature. This relation was first proven by Johann Heinrich Lambert. One sees that all triangles have area bounded by .

As in the

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