This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 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. REGULAR PROBLEMS 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, ) is the line at distance p from the origin which is normal to angle . 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 . So the measure or area of a set S of lines is just Measure( S ) = Z S 1 d p d ....
View Full Document