Please follow instructions and do all questions. Please choose any problem.Also this is the final project and needs to be completed on the date provided no extensions. So if you cant complete by than please just say so.
Final Project Due Tuesday by 11:59pm Points 0 Submitting a file upload File Types pdf Submit Assignment We were able to cover quite a bit of ground in this course, but really there are way more topics in mathematics than could ever be fit into a single semester and many of these find their way into artistic expression. For this project you can pick one of the topics we missed to learn a little about and create your own original artwork based on it! Dependent on project selected. To make it clear, you can pick ANY math topic that can be made into art that you would like to learn more about but that we haven't already done a project on. I would like for you to let me know your topic before you get started just to make sure you have a clear idea of what is expected for the project, exactly what type of art-work you are planning to do, and to help you find resources and materials. Below are two lists of topics that are pre-approved and come with ideas for what you could do as an art project for them. The first list is topics that we covered in the course but did not have a specific project on and the second list is topics that I *wanted* to cover in the class but we did not have time for. Feel free to select one of these if you would like, you can select the topic with a different project if you want. I have learning resources for all of these art projects already available. If you have questions about the suggestions, contact me and I'll be glad to clear them up. Topic ideas covered in course Covered in the Course Topic Art Project Suggestion Euclidean Constructions Create a picture by hand using a compass and straight edge. Use the Euclidean constructions we learned to get precise angles, shapes, and lengths in your picture. The Golden Ratio Create a picture or sculpture purposely using the Golden Ratio in all aspects of it's creation. This would need to be a bit more in depth than what was done for the Golden Ration homework and use the Golden Ratio throughout for "proper" proportioning and subject placement. Plane Symmetries Create a mandala from physical objects that shows many symmetries. Objects could be things like seeds, dried beans and spices, different colored sands, crayons, or anything else available to you. The material choices here are pretty flexible, I've even seen a nice mandala made from junk and trash (it was a statement about recycling or something I think). Inversion Create a simple tiling pattern in Euclidean space, overlay the pattern with a piece of paper that has a circle on it, and invert the pattern over the circle using a straight-edge and compass and the inversion techniques we learned. Non-Eulclidean Geometry Draw a picture using straight edge and compass in the Poincaré model of hyperbolic space or on a sphere using spherical geometry. This might be a difficult project, I haven't tried it yet. Fractals Create your own linear or shape based planar fractal and sketch it by hand to a large number (six or more) of iterations. The fractal would need to be drawn large enough to have the resolution to show detail at the iteration level shown. Modular Arithmetic Create a string art sculpture using modular arithmetic to determine string placement. Topic ideas not covered in course Not Covered in the Course Topic Brief Topic Information Art Project Suggestion Tangent Lines Tangent lines are lines that have the same slope as a curve at a given point and touch the curve Create a string-art sculpture where the strings follow tangent lines of a shape to create the shape. If we had two more weeks in the semester, this would have been one of your module projects! ∞ Final Project Continue Learning Introduction Materials Needed Project Examples at that point. They are a Calculus concept, but by ignoring some of the background can be simplified to be easily understood by any student. Tangent lines are briefly discussed in section 5.4 of your textbook with some art examples. Three Dimensional Fractals Fractals in three dimensions can be formed in much the same way as fractals in two dimensions, but and result very intricate shapes. Three dimensional fractals and related topics are discussed in section 5.5 of your textbook. Create the first three iterations of the Menger Sponge out of modeling clay. This idea could easily be changed for a different fractal, but the Menger Sponge is particularly simple to create. Homotopy of Spaces The chapter on topology is one I'm particularly disappointed we couldn't get in this semester because it's my favorite field of study and possibly the reason this class exists! Topology is essentially what geometry wold be if the world was made from modeling clay so nothing was rigid. A homotopy is a way to change one shape into another in such a way that the fundamental properties of the shape are preserved. Homotopy is discussed in section 6.1 of your book. Create a 3-D shape from modeling clay and show the steps of a homotopy into another shape. For a (too) simple example of this, a coffee mug can be turned into a doughnut through homotopy. Non- Orientable Manifolds A non-orientable manifold is a shape constructed in such a way that there is no concept of left and right in it. A simple example of this would be a Möbius band which can be created by taking a long strip of paper, putting a twist in it, and taping the ends together. Non-orientable manifolds are discussed in section 6.3 of your textbook. Create a never-ending frieze pattern on a Möbius band. Care would need to be taken to have the "ends" of the pattern meet up correctly at the taped edge of the band. Modular Origami Origami is the art of folding paper into intricate shapes without cutting or gluing the paper. It is an active field of Create an origami icosahedron from Sonobe units. This requires 30 units and some precision folding because sloppy folds will make it difficult to "close" the final sculpture. This link is to a PDF that shows how to make a Sonobe unit: study in mathematics right now. Modular origami is created by making repeated small units that fit together to make more complex shapes. You can find more about modular origami here: https://www.origami- resource- center.com/modular- origami.html (https://www.origami- resource- center.com/modular- origami.html) PDF from Matthew Arthur (http://mathewarthur.com/origami/how-to-make-a-sonobe- unit.pdf) And this link shows how to assemble the units into an icosahedron, though their result is a bit sloppy. Instructions from MathCraft (https://mathcraft.wonderhowto.com/how-to/modular- origami-make-cube-octahedron-icosahedron-from-sonobe- units-0131460/) Irrational Numbers Irrational numbers are numbers that cannot be written as a fraction or terminating decimal. Some irrational numbers you might be familiar with are (pi), (the Golden Ratio), (Euler's constant), and . Irrational numbers are everywhere. Create an original musical composition based on an irrational number. This would require a bit more than just picking out the (numbered) notes of the number on a piano. A good example of what you'd want here is in this video: What Pi Sounds Like (https://youtu.be/wK7tq7L0N8E) (https://youtu.be/wK7tq7L0N8E) Note that there are other ways to use irrational numbers to make art such as this idea of using to make a cityscape Cityscape from Pi (https://youtu.be/2hUNNwZBJ4g) (https://youtu.be/2hUNNwZBJ4g) Create your own original artwork based on a mathematical topic that we have not covered in class. When you have decided on what topic you would like and what project you want to do, send me the details through email so I can approve the topic, give specific instructions for turning in the project, and help you find resources. You should submit your topic and project idea to me no later than Monday, December 2nd. As usual, your project will be submitted as a pdf file. Sculptures or 3D models created will need to be photographed from various angles and the photos pasted into the document being submitted. Drawings or paintings can be scanned or photographed to be pasted in. Musical or theatrical compositions can be recorded and uploaded to YouTube and then submitted as a link in the document being submitted. Besides the photos of your work (or link to your work), you will need to explain your creation in the submitted document. This explanation should include the following: 1. A short description of your math topic. This description does not have to be exhaustive, around a page should do for this part of the project. 2. A description of the creation of your artwork. This description should include how you made the art and explicitly explain how your mathematical topic was used in the creation of the work. Two or three paragraphs should be sufficient for this part of the project, but you can use more space if you need it. 3. Any extra information needed to fully explain your creation. This part depends entirely on what was created and if you feel there needs to be extra explanation. Save the completed document as a PDF file and submit. The grade for this project is based on clear explanation of your topic and artwork construction, proper use of the mathematical techniques needed to create your artwork, and correct representation of the mathematical topic in your work. Creativity will also be a small part of your grade as with our other projects. Project Instructions