The Conventional Easel Painting Done by the Painters - Management Assignment Help

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Introduction

Blue Poles: Number 11, 1952 by artist Jackson Pollock was not the conventional easel painting done by the painters before him. A culmination of 10 years of Pollock’s development of his paint drip technique which was a contrast to the traditional way of painting using paint brushes with careful strokes depicting real life images. It involved a horizontally placed canvas which he would splash and “drip” paint over from an old paint can. It is also covered footprints and even small objects like coins and shattered glass. 20 years later Blue Poles: Number 11, 1952 was sold for nearly AUS $ 1.5 million to the National Gallery of Australia and is now said to be worth between $20 and $100 million. At the time newspaper articles such as Sydney’s Daily Mirror ran headlines such as: Figure 1: Front page of Sydney’s Daily Mirror newspaper after the painting was bought in 1973 by The National Gallery of Australia. Not only is there a striking similarity between Pollock’s patterns and those of nature, but there are also similarities between Pollock’s painting process and the process used by nature to build its patterns. In particular, contrary to popular belief, Pollock didn’t merely splatter a few blobs of paint on a canvas

Topology In the following section we will go through the basic definitions and examples within topology.

Definition 2.1 (Topological space) Definition 2.2 (Geometric Spaces) -has the following properties:

1. infinite 2. continuous 3. three-dimensional A Euclidean space is a geometric space with a finite number of dimensions, for example the xyz plane, where each dimension is given coordinates, where there exists a distance function, d, between any two points A and B. [2] Definition 2.3 (Metric Space) When this d between points A and B is of a non-negative value and in contained within an abstract set it becomes a metric space. The distance function within a metric function must satisfy these three properties:

2 1. Identification if the distance between point A and point B is zero ⇔ that the the two points are the same 2. Symmetry - The distance from A to B = the distance from B to A 3. Triangle inequality – the sum of the distance between A and B, and B and C is equal to the distance between A and C d(x,z)d(x,y)+d(y,z) Example 1 (Metric Space) [3] [4] Definition 2.4 (Topological dimension) a topological dimension has values in the reals, if X and Y are homeomorphic then they have the same dimensions [5] dim(X) properties of a lebesgue covering dimension are: Definition 2.5 (Homeomorphic) [6] A Homeomorphism is a bijection between spaces. If f : X → Y is homeomorphic then both f and f −1 must be continuous. [7] Definition 2.6 (Refinement)

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