D = 1600 (5H) metres (5H) miles H = 1.8m D = 4800m or 3 miles Sunset #8 (2009) Opies 12 miles is OK for a cruise ship with H = 29m The Tunnel of Eupalinos (530-520 BC)
10 yrs of tunneling 170m mean depth 1036m The Rough and the Smooth
Self-similarity Helge von Kochs Snowflake, 1904 Mandelbrots set (1980): the set of start points that stay at finite distances form the black region with its infinitely intricate boundary x x2 y2 + a ; y 2xy + b
Any part of the boundary contains copies of the whole set Jack the Dripper Jackson Pollock's Convergence (1952), 237.5cm393.7cm, oil on canvas 2009 The Pollock-Krasner Foundation/Artists Rights Society (ARS), New York.
Fract(ion)al Dimension Cover with N(r) squares of side r N(r) r D 1D2 Large D means greater intricacy: the line behaves like an area
Pollocks complexity increases with t Fractal signature ? Can you tell a Fake Pollock ?
Can a fractal analysis distinguish true from fake? YES Richard Taylor et al NO Kate Jones-Smith et al Controversial! String surface model: hyperbolic paraboloid
by Fabre de Lagrange, 1872 Two bars equally spaced, each turns on an arm perpendicular to itself and one arm swings on a pillar; these arms can be ranged in one plane, and also turned end for end. Henry Moore, Bird Basket, 1939
Jerusalem Chords Suspension Bridge Bzier-du Casteljau Curves Smooth curves in car design (Renault), VW, Mercedes computer graphics and font creation Postscript, Adobe illustrator, True Type, CorelDRAW Bzier-du Casteljau Curves
curve drawn The Gallery Problem camera How many cameras are needed to watch a gallery and where should they be placed?
Simple Polygonal Galleries Regions with holes are not allowed and no self intersections convex polygon one camera is enough an arbitrary n-gon (n corners)
? cameras might be needed 3-Colouring the Gallery Assign each corner a colour: pink, green, or yellow. Any two corners connected by an edge or a diagonal must have
different colours. Thus the vertices of every triangle will be in three different colors. A 3-colouring is always possible. Put cameras at corners of same colour Pick the smallest of the coloured corner groupings to locate the cameras. You will need at most [n/3] = [19/3] = [6.33] = 6 cameras (yellow or pink). Chvtal (1972)
Maths and Poetry Andrei Markovs invention of mathematical textual analysis (1913) The statistical theory of non-independent sequences of events Markov Processes ual Analysis of Textual Interconnectiv Interconnecti
Tess Tremlett - Community Engagement Manager. Introduction - Tess Tremlett, Community Engagement Manager, Forest of Dean District Council. Social Prescribing is a pathway available to all adults across Gloucestershire. ... (Friedli and Watson, 2004):
Buffet Presentation A buffet offers all dishes from a selected menu in a single attractive setting A buffet offers food service professionals the opportunity to exercise their creativity by identifying themes, and then creating menus, displays, and decorations with these...
On the night..... 6pm Arrive -pre-dinner drinks 7pm Dinner 8.15pm The UKGCVA Members Awards 1.The UKGCVA Best Innovation Award 2.The UKGCVA Trailblazer Award 3.The UKGCVA Exec Award 4.The UKGCVA Voice Award 5.The UKGCVA Trendsetters Award 6.The UKGCVA Socialite Award 7.The...
Kristine Dahl, prosjektkoordinator. Elin Paulsen, prosjektmedarbeidar. Barbro Os Noste, hovudtillitsvald . ... - Harald Sivertsen (5) Å ha sitt helse- og omsorgstilbod i Stad 2020 - Barbro Longva (6) Å ha eit meiningsfult og aktivt liv i Stad 2020
Intro. Although the resemblance between generations of organisms had been noted for thousands of years, it wasn't until the 1800s that scientific studies were carried out to develop an explanation for this.
Three types of media waves can travel through: Solids, Liquids, Gases. * Electromagnetic Waves: Waves that do not require a medium for travel (can travel through a medium or a vacuum). Examples: light, heat, x-rays, microwaves, radio waves, infrared waves....
www.enviroweather.msu.edu. Enviro-weather Mission. Enviro-weather is an interactive information system linking real-time weather data, forecasts, and biological and other process-based models for assistance in operational decision-making and risk management associated with Michigan's agriculture and natural resource industries.
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