Conics art for camt 2011

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  • 1. The Start of Something BIG CONICS Art Foldable
  • 2. Start Something BIG.. Create a multifaceted foldable CONIC Art Practice Create Your Own CONICS Art
  • 3. Foldable From the ziploc bag: Next take the full sheet Take one full sheet First, fold it hotdog and one half sheet of style and make a crease cardstock Open the fold and fold You will also need to in the two edges share the scissors towards the center First, take the half crease—this will result sheet and fold it in 3 parallel creases and hotdog style 4 columns Then cut along the crease and lay aside Repeat this process hamburger style—this will result in a table with 4 rows and 4 columns
  • 4. Now cut and weave… Take the full sheet (yellow) and fold in half hamburger (taco; horizontally) style Cut from the FOLDED edge along each of the 3 creases UP TO the vertical crease This will result in 3 slits in the middle of your paper Now weave the two strips alternately through the slits
  • 5. CenterRadiusEquationTangentAxis of SymmetryEquationDirectionFocusDirectrixCenterEquationVerticesFociCo-verticesCenterEquationVerticesFociCo-verticesAsymptotes
  • 6. Center The equation of a circle with center (0,0) andRadius radius, r, isEquation x2 + y2 = r2TangentAxis of SymmetryEquationDirectionFocusDirectrixCenterEquationVerticesFociCo-vertices c 2 = a2 – b 2CenterEquationVerticesFociCo-verticesAsymptotes c 2 = a2 + b 2
  • 7. TangentHORIZONTAL VERTICALHORIZONTAL VERTICALHORIZONTAL VERTICAL
  • 8. CenterRadiusEquationTangentAxis of SymmetryEquationDirectionFocusDirectrixCenterEquationVerticesFociCo-vertices c 2 = a2 – b 2CenterEquationVerticesFociCo-verticesAsymptotes c 2 = a2 + b 2
  • 9. HORIZONTAL VERTICAL
  • 10. Now let’s try Note: These equations have been solved for y= from the standard form on the foldable. Most students use Green some CONIC art! Globs to practice and refine their artwork in standard form before solving for y= e.g.Y1 was: x2 + y2 = 9 Take your calculator You should see a smiley face on your Go to the y= screen calculator. Type the following equations: Use Zoom 4:Zdecimal to see the design ( Y 1 = {− 1,1} 9 − x 2 ) better The final step is to turn AxesOff Use Y 2 = . 5 x 2 − 2( − 1 .5 ≤ x and x ≤ 1 .5 ) the Format (2nd ZOOM, then scroll down to AxesOff) ( )Y 3 = {− 1,1} (1 − ( x + 1) 2 / .25) * 1 + 1 Y 4 = {− 1,1} ((1 − ( x − 1) / .25) * 1) + 1 2Y 5 = {− 1,1} ((1 − x / 9) * −4 ) /( −3.5 ≤ x and x ≤ 3.5) 2
  • 11. Now it’s your turn… Use what you have learned and design your own CONIC Art You may use the foldable to design your own equations or just modify the dragonfly equations While you are working I will display some of my students’ works…