{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

math4250homework3

# math4250homework3 - Math 4250/6250 Homework#3 This homework...

This preview shows pages 1–2. Sign up to view the full content.

Math 4250/6250 Homework #3 This homework assignment covers our notes on integral geometry (5) and on rotation index (6). Please pick 3 of the following problems. Remember that undergraduate students should average one challenge problem per assignment, while graduate students should average two challenge problems per assignment. 1. R EGULAR P ROBLEMS Do Carmo, p 47. #8, #12 ( There is a misprint in this problem! The ratio M 1 /M 2 = 1 / 2 , not 1 / 3 as stated in the text ), #13. In #12, DoCarmo asks for the “measure” of a set of lines. What is measure? We established a system of coordinates for the set of lines when we proved the Cauchy-Crofton formula: ( p, θ ) is the line at distance p from the origin which is normal to angle θ . In these coordinates, we can compute the “area” of a set of lines by integrating the function 1 over the set with respect to p and θ . So the “measure” or area of a set S of lines is just Measure( S ) = S 1 d p d θ.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

math4250homework3 - Math 4250/6250 Homework#3 This homework...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online