# Math 110 Math Apps Art

## Class Resources and Handouts

Course Syllabus (Section 01, TTh 9:30-10:45)Course Syllabus (Section 02, TTh 2:00-3:15)

## Homework

Homework 1, Due 9/13/18Homework 2, Due 9/27/18

Homework 3, Due 10/9/18

Homework 4, Due 10/18/18

Homework 5, Due 10/30/18

Homework 6, Due 12/3/18

Homework 7, Due 12/6/18

Homework 8, Due 12/13/18 (this handout would help)

### Course Updates and Materials

Check here for a summary of what we covered each day, links to useful tools, and class handouts.

Date | Summary | Resources |

Aug 23 | Course Introduction | |

Aug 28 | An overview of essential Euclidean geometry: the impact and structure of The Elements, and how we can use simple tools to construct useful geometric shapes | Euclid's The Elements Handout PDF Euclidean Geometry Lecture Slides PDF |

Aug 30 | Definitions and properties of polygons: What is a polygon? How are they classified? For a summary, see the first few slides in the Polyhedra Slides PDF for September 4 | |

Sep 4 | A review of polygon definitions, and an introduction to the definitions and classifications of polyhedra. Platonic and Archimedean solids. The Classification Theorem | Polyhedra Lecture Slides PDF Platonic Solids in 2D |

Sep 6 | Conic Sections: The circle, ellipse, parabola, and hyperbola can all be realized as the intersection of a cone and a plane. No slides, but experiment with the applet to see how to create each curve. | Conic Section Applet |

Sep 11 | Mathematical Envelopes: Their definition, and some well known curves and shapes that can be "formed" by their envelopes. | Envelopes Lecture Slides PDF Complete Graph Applet Cardioid Envelope Applet Circular Envelope Applet |

Sep 13 | Projections: We lose valuable information about an object when we lose a dimension, but we can find some clever ways of overcoming this obstacle, and sometimes use it to our advantage. | Projection Slides PDF |

Sep 18 | Perspective Projection: Vanishing points; 1, 2, and 3-point perspective | Perspective Slides PDF |

Sep 20 | Anamorphic Art: Using perspective grids to create realistic 3D effects; cylindrical anamorphic art | Anamorphic Art Slides PDF |

Sep 25 | Number Systems: Converting from Base 10 to other bases, Converting from other bases to base 10, and a little history behind the numbers we use today (and why they're pretty good, but not perfect) | Number Systems Slides PDF |

Sep 27 | Colors as Numbers: RGB, Hex, and HSL color codes | Colors as Numbers Slides PDF Applet: Quick Base Conversion Calculator Applet: How pixels display RGB colors Applet: HEX Color Palettes Applet: Colors with RGB, HEX, HSL |

Oct 2 | Exam I | |

Oct 4 | No Class - Fall Break | |

Oct 9 | Vectors and Matrices, Part I: What is a vector? What are some operations we can perform on vectors? | Vectors and Matrices Part I Slides (HTML) |

Oct 11 | Vectors and Matrices, Part II: What is a matrix? What operations can we perform with them? What will we use them for? | Vectors and Matrices Part II Slides (HTML) |

Oct 16 | No slides, but we talked about functions on vectors, and how we can find a matrix of a transformation (reviewed at the beginning of slides for Oct 18) | |

Oct 18 | How to find and apply linear transformations to stretch, rotate, and otherwise change images in the plane | Linear Transformation Slides (HTML) Applying a Linear Transformation |

Oct 23 | No Class - Advising Day | |

Oct 25 | Common color transformation matrices, HSL colors and color schemes | Transforming Colors and Color Schemes Slides (HTML) |

Oct 30 | A final look at linear transformations in three dimensions, and why it turns out we need four | Transformation of Three Dimensions Slides (HTML) |

Nov 1 | Exam II | |

Nov 6 | A brief summary of the novella Flatland, some ways of understanding the fourth dimension, and an introduction to the artistic approaches to visualizing it | Flatland and the Fourth Dimension Slides (HTML) |

Nov 8 | The influence of theories regarding the fourth dimension on the art world; A brief review of Euclidean geometry | Cubism Slides (HTML) Review of Euclidean Geometry Slides (HTML) |

Nov 13 | The Mathematics of Non-Euclidean Geometry | Non-Euclidean Geometry Slides (PDF) |

Nov 15 | MC Escher and Non-Euclidean Geometry | Escher Slides (PDF) |

Nov 20 | Rigid Motions | Rigid Motions Slides (HTML) |

Nov 27 | Finite Symmetry Groups | Finite Symmetry Group Slides (HTML) |

Nov 29 | Wallpaper and Frieze Groups | Wallpaper Group Slides PDF Wallpaper Group Applets |

Dec 4 | No slides! We summarized the tiling patterns we've seen, and saw a final method on creating them. | |

Dec 6 | Last topic - fractals | Iterative Function Systems Automata (One Line) Cellular Automata (Game of Life) |