Transcript Fractals
Fractals A lesson for 3rd grade Rose Horan Click on me! Cali the alligator! Where do you want to go? • History of Fractals • Definition of fractals • Examples • Fractal or Not Game? • NCTM Standards • Fractals Everywhere • Fractal Food • Virtual Manipulative • References Click on the pink arrows!! History of fractals: • The word “fractal” did not exist until 1975 • Benoit Mandelbrot is considered to be the “fractal father of geometry” History of Fractals cont: • Mandelbrot needed a name for his shapes, dimensions and geometry. • Mandelbrot’s son was home from school. • Mandelbrot was going through his son’s Latin Dictionary. “He came across the adjective fractus, from the verb frangere, to break. The resonance of the main English cognates – fracture and fraction – seemed appropriate. Mandelbrot created the word (noun and adjective, English and French) “fractal.” Definition of Fractals: •Rough or fragmented geometric shapes that can be subdivided in parts, each of which is a reduced size of the whole •Any pattern that reveals greater complexity as it is enlarged •Closer you come the more detail you see •Repeating pattern •Self similar •World within worlds A coast line is good example. The closer you get to the coastline, the more detail you see. The area also increases. Examples: This pattern is repeating. There is a world within worlds. Fractal or Not? • Which items are fractals? Click on them: NCTM Standards • Recognize geometric shapes and structures in the environment and specify their location. • Create mental images of geometric shapes using spatial memory and spatial visualization. • Recognize, name, build, draw, compare and sort 2 and 3 dimensional shapes. All of these items have fractals on them: Greeting Cards Coffee Mugs Clothing Pictures Jewelry Notebooks More items that have fractals…. Mouse Pads Magnets Clocks Tile Boxes Stickers Ornaments Posters Tote Bags Examples found in nature:Snowflakes Shells Tree Branches Ferns Clouds Cloud Nebula More Nature Examples: River systems Stalagmites Lightning Mountain Ranges Leaf Veins Close up view of a fractal The closer you come to the object the more detail you see. Close up view of fractal food Broccoli The closer you come to the object the more detail you see. Definition of Fractals: •Rough or fragmented geometric shapes that can be subdivided in parts, each of which is a reduced size of the whole •Any pattern that reveals greater complexity as it is enlarged •Closer you come the more detail you see •Repeating pattern •Self similar •World within worlds Click on the question mark to go back to the game TRY AGAIN!! YOU CAN DO IT!!! Click on the dog if you need extra help. Click on Sun to go back. TRY AGAIN!! YOU CAN DO IT!!! Click on the dog if you need extra help. Click on Sun to go back. TRY AGAIN!! YOU CAN DO IT!!! Click on the dog if you need extra help. Click on Sun to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. CORRECT!!! AWESOME JOB!! Click on the girl to go back. For more practice Try Virtual Manipulative: • http://nlvm.usu.edu/en/nav/frames_asid_136_g_2_t_3.html?open=instructio ns • http://nlvm.usu.edu/en/nav/frames_asid_135_g_2_t_3.html?open=instructio ns • http://nlvm.usu.edu/en/nav/frames_asid_137_g_2_t_3.html?open=instructio ns • Click on the links above and check out the websites! Write two (2) paragraphs about what you learned and how fractals are in everyday life. Click on Cali! Click on Cali! References • • • • • • • • • • • • • • • • http://standards.nctm.org/document/chapter4/numb.htm http://growabrain.typepad.com/growabrain/2004/09/growabrain_frac.html http://www.west.asu.edu/achristie/548/02WQ/linda/Fractals_files/image004.gif http://www.allegria.com.au/Prod_Fractals.html http://www.dcrimages.com/cgi-bin/store/fractal.cgi/ovalstickers/dcrimages.16563370 http://mathworld.wolfram.com/Fractal.html http://www.cafepress.com/spiritkeep01.8500187 http://www.dcrimages.com/cgi-bin/store/fractal.cgi/clocks/dcrimages.16534955 http://www.dcrimages.com/cgi-bin/store/fractal.cgi/mousepads/dcrimages.16427367 http://www.healingdaily.com/detoxification-diet/broccoli.jpg http://www.ybdigitals.com/images/Resize%20of%20Wide%20clouds%20D%204-1Hz.jpg http://www.sciencemuseum.org.uk/antenna/motherland/images/tree.jpg http://nlvm.usu.edu/en/applets/controller/query/query.htm?qt=fractals http://images.google.com/imgres?imgurl=http://classes.yale.edu/fractals/Panorama/Nature/NatFracGallery/Gallery/ LightningS.gif&imgrefurl=http://classes.yale.edu/fractals/Panorama/Nature/NatFracGallery/Gallery/Gallery.html&h= 100&w=100&sz=10&tbnid=8TDlu7zefFgJ:&tbnh=77&tbnw=77&hl=en&start=78&prev=/images%3Fq%3Dfractal%2 Blightning%2B%26start%3D60%26svnum%3D10%26hl%3Den%26lr%3D%26sa%3DN http://www.bucka-lassen.dk/flacroz/pictures/0604_5_Nullarbor_coast_line.jpg http://images.google.com/imgres?imgurl=http://www.byers.us.fm/Fractals/Animations/300/design857.gif&imgrefurl =http://www.byers.us.fm/Fractals/Animations/Headers/Tubes.htm&h=225&w=300&sz=379&tbnid=x_ScR8WaKSw J:&tbnh=83&tbnw=111&hl=en&start=17&prev=/images%3Fq%3Dcartoons%2Bdancing%26svnum%3D10%26hl% 3Den%26lr%3D