3320hw4 - Math 3320 Problem Set 4 1 1. Find a formula for...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 3320 Problem Set 4 1 1. Find a formula for the linear fractional transformation that rotates the triangle 0/1, 1/2, 1/1 to 1/1, 0/1, 1/2 . 2. Find the linear fractional transformation that reflects the Farey diagram across the edge 1/2, 1/3 (so in particular, the transformation takes 1/2 to 1/2 and 1/3 to 1/3 ). 3. Find a formula for the linear fractional transformation that reflects the upper halfspace version of the Farey diagram across the vertical line x = 3/2 . 4. Find an infinite periodic strip of triangles in the Farey diagram such that the transformation 01 12 01 12 01 12 is a glide-reflection along this strip and the transformation = 12 25 is a translation along this strip. ab cd 5. Let T be an element of LF (Z) with matrix T −1 0 01 . Show that the composition 1 /0 , 0 /1 . T −1 is the reflection across the edge a/c, b/d = T ab cd 6. For a matrix A = same determinant. giving an element of LF (Z) , show that A and A−1 have the ...
View Full Document

Ask a homework question - tutors are online