Mercyhurst UniversityMath DeptDr Williams Home

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 1, Due 9/13/18
Homework 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.

Aug 23Course Introduction
Aug 28An overview of essential Euclidean geometry: the impact and structure of The Elements, and how we can use simple tools to construct useful geometric shapesEuclid's The Elements Handout PDF
Euclidean Geometry Lecture Slides PDF
Aug 30Definitions 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 4A review of polygon definitions, and an introduction to the definitions and classifications of polyhedra. Platonic and Archimedean solids. The Classification TheoremPolyhedra Lecture Slides PDF
Platonic Solids in 2D
Sep 6Conic 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 13Projections: 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 18Perspective Projection: Vanishing points; 1, 2, and 3-point perspective Perspective Slides PDF
Sep 20Anamorphic Art: Using perspective grids to create realistic 3D effects; cylindrical anamorphic art Anamorphic Art Slides PDF
Sep 25Number 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 codesColors 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 2Exam I
Oct 4No Class - Fall Break
Oct 9Vectors 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 11Vectors 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 16No 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 18How to find and apply linear transformations to stretch, rotate, and otherwise change images in the planeLinear Transformation Slides (HTML)
Applying a Linear Transformation
Oct 23No Class - Advising Day
Oct 25Common color transformation matrices, HSL colors and color schemesTransforming Colors and Color Schemes Slides (HTML)
Oct 30A final look at linear transformations in three dimensions, and why it turns out we need four Transformation of Three Dimensions Slides (HTML)
Nov 1Exam II
Nov 6A 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 8The influence of theories regarding the fourth dimension on the art world; A brief review of Euclidean geometryCubism Slides (HTML)
Review of Euclidean Geometry Slides (HTML)
Nov 13The Mathematics of Non-Euclidean GeometryNon-Euclidean Geometry Slides (PDF)
Nov 15MC Escher and Non-Euclidean GeometryEscher Slides (PDF)
Nov 20Rigid MotionsRigid Motions Slides (HTML)
Nov 27Finite Symmetry GroupsFinite Symmetry Group Slides (HTML)
Nov 29Wallpaper and Frieze Groups Wallpaper Group Slides PDF
Wallpaper Group Applets
Dec 4No slides! We summarized the tiling patterns we've seen, and saw a final method on creating them.
Dec 6Last topic - fractalsIterative Function Systems
Automata (One Line)
Cellular Automata (Game of Life)