The Generalized Circle Fractal: Exploration & Straightedge-Compass Construction

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Xuất bản 09/08/2016
Explore the fractal online at http://demonstrations.wolfram.com/GeneralizedStraightedgeAndCompassFractal/ I recently found this interesting fractal which could be created from a triangle in a very simple way. The basic idea is to start with an equilateral triangle, and keep the new finding midpoint triangles, and then adding the circles' of those triangles. Here, by the circles of a triangle' I mean the three circles centered around the vertices of the triangle, which have a radius equal to m times the edge-length of the triangle (where m=1). By repeatedly creating the new midpoint triangles, and their circles I created the interesting patterns described in my previous videos (see below for links). However, today I started to look at what happens when one changes the circle-radius multiplier m. If one creates a configuration of circles by running the original system for a given number of iterations, and then one alters the value of the multiplier' m one sees the circles change size and position in a beautiful way. In this video I give a rough outline of the idea behind the systems, then I show how the configurations of circles change as the multiplier is changed from 0 to 3, then I describe how these patterns can be made via a straightedge and compass construction (using GeoGebra). New Compass And Straightedge Fractal Explored In Color https://www.youtube.com/watch?v=QNuZ9yXdev0 A New Fractal Created With Compass And Straight Edge https://www.youtube.com/watch?v=SGDQkncxia0 http://www.geogebra.org/cms/en/ https://sites.google.com/site/richardsouthwell254/home
Computer Compass Mathematics Programming Language Paradigm Geometry Field Of Study Circle Midpoint Vertex Compass-and-straightedge Construction Exploration Taxonomy Subject Fractal Concepts/Theories Triangle Mathematical Concept Sierpinski Triangle Namesake Pascal's Triangle Namesake Benoit Mandelbrot Academic Stephen Wolfram Computer Scientist Mechanisns Euclidean Geometry Concepts/Theories GeoGebra Software computational geometry

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