Let y : S' - R2 be the given piecewise analytic curve. Fixing a line T,...

 

Transcribed Image Text:

Let y : S' - R2 be the given piecewise analytic curve. Fixing a line T, Emch considers all secants of y that are parallel to T and calls the set of all midpoints of these secants the set of medians M7. Under some genericity assumptions he proves that for two orthogonal lines T and T-, M, intersects M7 in an odd number of points. Nowadays one could write this down homologically. These intersections correspond to inscribed rhombi, where the two intersecting secants are the two diagonals of the rhombus. Now he rotates T continuously by 90 degrees and argues that M, n M7- moves continuously, where at finitely many times two intersection points can merge and disappear or two new intersection Let y : S' - R2 be the given piecewise analytic curve. Fixing a line T, Emch considers all secants of y that are parallel to T and calls the set of all midpoints of these secants the set of medians M7. Under some genericity assumptions he proves that for two orthogonal lines T and T-, M, intersects M7 in an odd number of points. Nowadays one could write this down homologically. These intersections correspond to inscribed rhombi, where the two intersecting secants are the two diagonals of the rhombus. Now he rotates T continuously by 90 degrees and argues that M, n M7- moves continuously, where at finitely many times two intersection points can merge and disappear or two new intersection

Answer rating: 100% (QA)

This question deals mainly with three aspects Rhombus degeneracyand mean value theorems First of all ... View the full answer