GEOMETRY OF SURFACES b3 course 2004 Nigel Hitchin
... equivalence relation. For example, in constructing the torus from the square we define (x, 0) ∼ (x, 1) and (0, y) ∼ (1, y) and every other equivalence is an equality. The torus is the set of equivalence classes and we give this a topology as follows: Definition 3 Let ∼ be an equivalence relation on ...
... equivalence relation. For example, in constructing the torus from the square we define (x, 0) ∼ (x, 1) and (0, y) ∼ (1, y) and every other equivalence is an equality. The torus is the set of equivalence classes and we give this a topology as follows: Definition 3 Let ∼ be an equivalence relation on ...
Do every problem. For full credit, be sure to show all your work. The
... Instructions: Do every problem. For full credit, be sure to show all your work. The point is to show me that you know HOW to do the problems, not that you can get the right answer, possibly by accident. ...
... Instructions: Do every problem. For full credit, be sure to show all your work. The point is to show me that you know HOW to do the problems, not that you can get the right answer, possibly by accident. ...
14.2 Flat Mirrors!
... Flat (Plane) Mirrors Simplest of all mirrors Light rays bounce off objects in front of the mirror and reflect from the mirror’s surface. An object's reflection is said to be located behind the mirror (not literally) The object distance (do) is equal to the image distance (di) ...
... Flat (Plane) Mirrors Simplest of all mirrors Light rays bounce off objects in front of the mirror and reflect from the mirror’s surface. An object's reflection is said to be located behind the mirror (not literally) The object distance (do) is equal to the image distance (di) ...
A quick proof of the classification of surfaces
... The classification of surfaces is one of the cornerstones of low-dimensional topology. The goal of this brief note is note is to explain an amazingly efficient proof of this result that is due to Zeeman [Z]. Most textbook sources for the classification are aimed at beginning students and include so mu ...
... The classification of surfaces is one of the cornerstones of low-dimensional topology. The goal of this brief note is note is to explain an amazingly efficient proof of this result that is due to Zeeman [Z]. Most textbook sources for the classification are aimed at beginning students and include so mu ...
