Prove:- The defect of a triangle in (LG) is an area function.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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VI. Prove:- The defect of a triangle in (LG) is
an area function.
****************
VI
Transcribed Image Text:*************** VI. Prove:- The defect of a triangle in (LG) is an area function. **************** VI
Expert Solution
Step 1

For a triangle, the function defect defined is defined as, Defect = π-α+β+γ where the angles alpha, beta, and gamma are measured in radians.

We need to show that the defect of a triangle in (LG) is an area function. 

In other words, we need to show that defect of a hyperbolic triangle is equal to area (A) of the triangle.

Here, two cases arises.

(i) A hyperbolic triangle with one ideal vertex (γ=0) and interior angles α and β.

(ii) A hyperbolic triangle with all interior angles α, β, and γ.

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