Let P: SCU {o} be the stereographic projection introduced in our course. If y: [a, b]...

  

Transcribed Image Text:

Let P: S²CU {o} be the stereographic projection introduced in our course. If y: [a, b] → C is a continuously differentiable simple curve, that is, 7 is injective, then answer the followings: (a) Find the formula for the length of the curve ([a, b]) C C. Give the reason for your answer clearly. Hint: Use the notion of the chordal distance d(z, z)= 2|z-z' √/1+ |2|²√1 +2²2 Note that we can identify C with R² =R x R in the above. Let P: S²CU {o} be the stereographic projection introduced in our course. If y: [a, b] → C is a continuously differentiable simple curve, that is, 7 is injective, then answer the followings: (a) Find the formula for the length of the curve ([a, b]) C C. Give the reason for your answer clearly. Hint: Use the notion of the chordal distance d(z, z)= 2|z-z' √/1+ |2|²√1 +2²2 Note that we can identify C with R² =R x R in the above.

Answer rating: 100% (QA)

To find the formula for the length of the curve a b in the complex plane under the stereogr... View the full answer