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Geometry and Matrices Hands On Activity

Geometry and Matrices Hands On Activity. The Reason You Might Actually WANT to Learn This Stuff By Christine Lauber. Computer Animation. National Standards. Materials. Geometry 9 – 12 Apply transformations and use symmetry to analyze mathematical situations

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Geometry and Matrices Hands On Activity

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  1. Geometry and MatricesHands On Activity The Reason You Might Actually WANT to Learn This Stuff By Christine Lauber

  2. Computer Animation National Standards Materials Geometry 9 – 12 • Apply transformations and use symmetry to analyze mathematical situations • understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices; • use various representations to help understand the effects of simple transformations and their compositions. Numbers and Operations 9 – 12 • Understand meanings of operations and how they relate to one another • develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices; • Compute fluently and make reasonable estimates develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases. • Quarter size sheets of graph paper • Graphing calculator • Computer Animation Activity Packet • PowerPoint presentation with examples

  3. Computer Animation • First cartoons were all produced by hand. • Each slight movement required a new picture to be drawn. • Today, computers have taken over!? • Can you name some of the computer animated films you have seen?

  4. What are the components of motion? • Think of how we move shapes on the Cartesian Plane. • Translation • Rotation • Reflection • Dilation

  5. The first step any animator needs to do is create a simple representation of their character. • On your graph paper, create a simple picture that involves 5-10 points and is NOT symmetrical. In the beginning….

  6. My image will be of a kite in the sky. My matrix looks like this. In order to create the picture in my TI calculator, I need to translate my matrix into L1 and L2.

  7. Reflects over the y-axis Reflects over the x-axis

  8. Reflects over the y = x axis Rotates counterclockwise 56°

  9. Now, change your image to a 3xn matrix by adding a last row of all 1’s

  10. Slides 2 to the right Slides 2 down

  11. Reflects over the y = x axis then slides 2 right Slides 2 right and 3 down

  12. What about rotating the image? Cos (5) -Sin (5) Sin (5) Cos (5) -2.6896, 1.9924, .8716, -5.9772 7.7952, .1743, -9.9619, -.5229 Cos (10) Sin (10) -Sin (10) Cos (10) -.5804, 1.9696, -1.7365, -5.9088 8.2258, -.3473, -9.8481, 1.0419 Who thinks they have an idea of how to rotate the image?

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