PPT-Fractals everywhere

St Pauls Geometry Masterclass II Who are we Mairi Walker Final year maths PhD student at The Open University Studying links between geometry and numbers A lso interested in the history of maths. Menyuk University of Maryland Baltimore County Baltimore Maryland 21250 Received 8 October 1999 We describe a principle that can be used to generate selfsimilarity and fractals in almost any nonlinear system in nature that supports solitons given th FractalFoundationorg Copyright 2010 Fractal Foundation all rights reserved Fractal Rivers Teachers Intro NM Math Standards KG42 Find and describe geometric shapes in nature or architecture K12A13 Recognize reproduce describe extend and creat Amgad. Hussein, Maria . Tokarska. , Edward . Grinko. , . Dimitar. . Atassanov. , Megan Varghese, Emilio . Asperti. GEOMETRY. "Clouds are not spheres, mountains are not cones, coastlines . are not . Using Mata and . Stata. . to Draw Fractals. Seth Lirette, MS. Inspiration. Types . Of. Fractals. Escape-time. . Fractals. Formula iteration in the complex plane. Iterate many times. If doesn’t diverge to infinity, it belongs in the set and you mark it.. By. Leslie Ryan. Common Terms. Iteration-. To . repeat a pattern multiple times, usually with a series of steps. . Reflection-. An image that is thrown back from light, heat, or sound. Like an image you see in a mirror. . Modelling. Fractals. Fractals. A fractal is a mathematical set that typically displays self-similar . patterns. Fractals . may be exactly the same at every scale, . or they . may be nearly the same at different scales. : NEW PARADIGMS IN LINEAR WAVE PHYSICS Maria Mylova , James M. Christian, and Graham S. McDonald m.mylova @edu.salford.ac.uk & j.christian @salford.ac.uk Materials & Physics Research Centre , Universi Everywhere you go, everywhere you look, you see people using their smartphones and tablets—and that includes the workplace. The use of these devices for business purposes is growing exponentially Basic Concept. Entities are composed of features that are reproduced at different scales.. And whole entities can be described as a sum of smaller features that have the same characteristics. . Typically based on lines and examines line segments that have the same pattern.. Newton’s method. Need initial guess and derivative. Quadratic convergence. Proof via . taylor’s. theorem. x_n+1 = . x_n. – f(. x_n. )/f(. x_n. ). Derivation from point-slope y = m*(x – x_0) + y_0:. Part 1: In which we attempt to describe what a fractal is, because people will ask (but perhaps they will not really want to know the answer).. Then I introduce the 2. nd. most photogenic fractal of the class, and attempt to convince you it is cool anyways.. Fractals. Self Similarity. They appear the same at every scale, no matter how much enlarged.. Fractals. Fractal curves have infinite length within a finite region. Koch curve. Koch Snowflake. Dragon Curve. (wave hands around room). They’re on the walls and in the halls.. (point to walls). They’re on the chairs and on the stairs.. (point to chair). They’re on the toilet seats and on your feet.. (point to feet). Status is ubiquitous in modern life, yet our understanding of its role as a driver of inequality is limited.  In Status, sociologist and social psychologist Cecilia Ridgeway examines how this ancient and universal form of inequality influences today’s ostensibly meritocratic institutions and why it matters. Ridgeway illuminates the complex ways in which status affects human interactions as we work together towards common goals, such as in classroom discussions, family decisions, or workplace deliberations. Ridgeway’s research on status has important implications for our understanding of social inequality. Distinct from power or wealth, status is prized because it provides affirmation from others and affords access to valuable resources. Ridgeway demonstrates how the conferral of status inevitably contributes to differing life outcomes for individuals, with impacts on pay, wealth creation, and health and wellbeing. Status beliefs are widely held views about who is better in society than others in terms of esteem, wealth, or competence. These beliefs confer advantages which can exacerbate social inequality. Ridgeway notes that status advantages based on race, gender, and class—such as the belief that white men are more competent than others—are the most likely to increase inequality by facilitating greater social and economic opportunities. Ridgeway argues that status beliefs greatly enhance higher status groups’ ability to maintain their advantages in resources and access to positions of power and make lower status groups less likely to challenge the status quo. Many lower status people will accept their lower status when given a baseline level of dignity and respect—being seen, for example, as poor but hardworking. She also shows that people remain willfully blind to status beliefs and their effects because recognizing them can lead to emotional discomfort. Acknowledging the insidious role of status in our lives would require many higher-status individuals to accept that they may not have succeeded based on their own merit many lower-status individuals would have to acknowledge that they may have been discriminated against. Ridgeway suggests that inequality need not be an inevitable consequence of our status beliefs. She shows how status beliefs can be subverted—as when we reject the idea that all racial and gender traits are fixed at birth, thus refuting the idea that women and people of color are less competent than their male and white counterparts. This important new book demonstrates the pervasive influence of  status on social inequality and suggests ways to ensure that it has a less detrimental impact on our lives.