To get an idea of what is possible using algebra to make art, look at a few of the designs available in the Desmos Art Gallery (

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1 Desmos.com is a beautiful free online graphing calculator designed to help students learn algebra. You can use it in a browser (Chrome/Firefox/Explorer/Safari/Opera) on a computer, or there is also a free app. In this project, you will use Desmos (and your knowledge of equations) to make art. This isn t just a fun math activity but actually a very useful technological skill: major computer programs like Flash, InkScape, AutoCAD, and Illustrator use exactly this technique to describe the shapes in the images they create. To get an idea of what is possible using algebra to make art, look at a few of the designs available in the Desmos Art Gallery ( We are going to jump right in. Below are two of my own. Twenty-six functions and a few mistakes, this is what my end result was. The third one is one of my favorites from another student. I used linear, quadratic, and circular functions. Circles and Ellipses (ovals) follow similar properties to quadratics in vertex form. The example we are going to explore is below look at my final result in comparison to my hand drawing

2 Try to develop 11 additional equations that create the picture below two are provided. 1 7 Linear: Quadratic: ( ) Circle: ( ) ( ) Ellipse/Oval: ( ) ( ) Equation Equation Type/Shape Equation Restriction (Domain/Range) 1 Linear * Quadratic ( ) *

3 PreCalculus Name -Drawing is clearly constructed 4pts 3pts 2pts 1pt 0pts Organization and Neatness -Sketch is clearly labeled and graph segments dissected -Missing 2 or more -Document is assembled with care Sketch Equations and Line Information -Evidence of mathematical is present -Drawing contains at least 15 linear segments -Drawing contains at least 10 non-linear segments -Each line from the drawing is represented in equation form -Each line's domain/range (start and stop point) is given -Sketch screenshot Missing 3-4 Missing 3-4 Missing 5-6 components Missing 5-6 components Finished Document ( ) -Equations included, labeled, and restrictions provided -Graph is an accurate representation of the paper sketch -Link to the Desmos Drawing in the document OR Document with sketch and final graph is not shared with Mr. Mijajlovic -Document is shared with Mr. Mijajlovic Total Points Earned: / 24

4 Advanced Algebra Name -Drawing is clearly constructed 4pts 3pts 2pts 1pt 0pts Organization and Neatness -Sketch is clearly labeled and graph segments dissected -Missing 2 or more -Document is assembled with care Sketch Equations and Line Information -Evidence of mathematical is present -Drawing contains at least 10 linear segments -Drawing contains at least 5 non-linear segments -Each line from the drawing is represented in equation form -Each line's domain/range (start and stop point) is given -Sketch screenshot Missing 3-4 Missing 3-4 Missing 5-6 components Missing 5-6 components Finished Document ( ) -Equations included, labeled, and restrictions provided -Graph is an accurate representation of the paper sketch -Link to the Desmos Drawing in the document OR Document with sketch and final graph is not shared with Mr. Mijajlovic -Document is shared with Mr. Mijajlovic Total Points Earned: / 24

5 Linear: Quadratic: ( ) Circle: ( ) ( ) Ellipse/Oval: ( ) ( ) Equation Equation Type/Shape Equation 1 Restriction (Domain/Range)

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7 Mijajlovic_Art with Demos Example Sketch Sketch with my Mathematical Evidence Equations Equation Equation Type/Shape Equation Restriction (Domain/Range) 1 Linear * + 2 Linear * + 3 Linear * +

8 4 Linear * + 5 Linear * + 6 Linear * + 7 Linear * + 8 Linear * + 9 Ellipse ( ) ( ) 10 Quadratic ( ) * + 11 Quadratic ( ) * + 12 Circle ( ) ( ) 13 Linear * + Final Graph Link to Final Graph on Desmos