## How Do Optical Illusions Work12 optical illusions Optical Illusions and the Fibonacci Sequence Big Ideas Unit of Instructionillusions that can be created using the Fibonacci sequence.Geometry Concept Learn to recognize and use the Fibonacci sequence and its applications After examining many uses of optical illusion in archNCTM 9-12 Standardsterconnect and build on one another to two- and three-dimensional geometric guments about geometric relationships. objects and the units, systems, and Use representations to model and interpret physical, social, and mathematical Geometry and Art: Optical Illusions and the Fibonacci Sequence Section 7 Page Idaho Content Standards G.4.1.1 Analyze properties and det G.4.1.2 Explore congruence and similari G.4.1.3 Establish the validity of geometric conjecture using inductive and G.4.4.1 Draw and construct representat 9-12.VA.3.1.1 Select and appl 9-12.VA.3.1.4 Select and visualize visualenhance meaning in artwork.Background Vocabulary Contrast Optical Illusion Diagonal Line Reflection Dynamic Fibonacci sequence Square Plane Horizontal Line Symmetry LineOp Art Math Instruction (pre- or post-project) Ruler measurement skills Geometry and Art: Optical Illusions and the Fibonacci Sequence Driving Question Project Objective To gain an understanding of the Fibonacci seoptical illusions.Questions to be Answered What is Op Art? What are optical Illusions? What is a Fibonacci sequence? Why is a Fibonacci sequence important? How can a Fibonacci sequence be used to create an optical illusion? Materials Materials Required 8.5 X 11 inch paper Drawing paper Black markers of various size tips Erasers (acrylic or kneadable) , Al. Incredible Visual Illusions. Arcturus, 2006.Seckel, Optical Illusions.2005 Section 7 Page Geometry and Art: Optical Illusions and the Fibonacci Sequence Lesson Outline Description of Overview of Op Art, Fibonacci Checkerboard Art Work Day Day led discussion about patterns t Ask students to help identify t The teacher will show a variety of optical illusions, and identify them as optical Definitions of Optical Illusions Split the students into four or five groups.For each group, pass out a folder of resource materials on optical illusions. Ask each group to come up with a definition of what they collectively think are illusions. In twenty minutes they select a spokesperson from the makes their presentation. Each group presents and the class votes on the best definition and uses that All the above suggested topics get covered with this approach except the Split students into groups of five
.
Distribute a variety of samples of the Have each group make a presentation about tDay Two: Fibonacci Checkerboard Art Presentation on Leonardo Fibonacci and the Fibonacci Checkerboard Divisions quare plane into equal square units (see figure Section 7 Page Geometry and Art: Optical Illusions and the Fibonacci Sequence If those horizontal and vertFibonacci numbers, interesting designs result. This is a Fibonacci checkerboard (see Sequential Fibonacci units can be used symmetricallyresulting design can still be colored (or shaded) in an alternating checkerboard fashion Fibonacci Checkerboard Art can be applied to other geometric shapes such as The teacher, using the overhead, and the students, using pencil and paper, will to create a simple square Fibonacci Assign the students to create an optical illusion based on a Fibonacci sequence. Caution students to use careful measurements with a ruler. Students will need to work on rough designs so they will be ready to work on a finished project. Assign and review requirements for the reflection paper. 15 minutes Day Three: Student Work Time Answer any student ques Working time with the teacher answering qure day in class to work with teacher invest extra time in their projects.Assessment Rubric udents may get an optical illusion or line design. bonacci sequence in their project Content: 15 points Section 7 Page Geometry and Art: Optical Illusions and the Fibonacci Sequence Background Material for Optical Illusions Many optical illusions “appear” in a certain way and are hypothesized to indicate a ry. One may make certain codirected a trading post east of Algiers in North Africa. This is where he learned about the Hindu-Arabic number system.Fibonacci is most known for spreading the Hindu-Arabic numeral system, rather than the Roman numeral system, through his “Book of ing just the numerals 0-9, addition and subtraction system. It also taught lattice multiplication, fractions, and decimals (aFibonacci’s book proved the Pythagorean Theorsystem, and it became the standard text for solved, a problem involving the growth of Optical illusions may be created in many waSection 7 Page Geometry and Art: Optical Illusions and the Fibonacci Sequence Ideas for Further Independent Student Project Fibonacci Spiral is a mirrored duplicatipattern found in sunflowers.Edna Andrade, Islamic tile designs, and Celtic inspired by Julian Beever; create an optical illusion room with distorted perspectives; create a Celtic knot made out of a variety of with floor tiles set in the Fibonacci sequence. Section 7 Page Geometry and Art: Optical Illusions and the Fibonacci Sequence Fibonacci Checkerboard Art can be applioptical illusions as well. on on Fibonacci Numbers, check http://www.fibonacci.net/Numbers and the Golden Section.” You will then be accessing one of the world’s truly re information on Fibonacci FASCINATING RUN Fascinating Activities with Intriguing Numbers Fibonacci Checkerboard Art FASCINATING FIBONACCIS Mystery and Magic in Numbers Hammel Garland (P |

© 2012 **labroda**