IDS 123 - A World of Patterns:  Mathematics in Nature and the Arts

Course Description:   This interdisciplinary course focuses on the underlying mathematical principles of number, ratio, and pattern in nature and their relationship to the arts.  In this course we will examine the development of quantification throughout history.  We will also analyze how numbers, ratios, and patterns form the basis in a variety of academic disciplines and human endeavors, e.g. biology, chemistry, painting, sculpture, architecture, and music.
 


 

Spring 2008 
M/W 1:00 p.m. - 2:15 p.m.
STC 102

 

Prof. William Stargard 
Office Hours:  Tuesday 8:30 - 10:00,
                        Wednesday 11:15 - 12:30, and by appointment  
Haldan 207   731-7070                                          
stargarw@pmc.edu
                                                          
Prof. Joan Weinstein 
Office Hours: 
Monday and Wednesday 11:30 - 12:00;
                         Monday 2:30 - 4:00, and
by appointment
Dane 305   731-7184

weinstej@pmc.edu
       
   

Spring 2008 Syllabus and Course Information

  1/16

Introduction
    
How do you use numbers?
     Moranis: My Days are Numbered

Assignment 1

  1/21 Martin Luther King, Jr. Day - no classes  
  1/23 Numbers and Measurement
     How do you use quantitative reasoning?
     Numbers in art and architecture

     Number systems
 
  1/28 Numbers and Measurement
     More about number systems
 
  1/30 Numbers and Measurement
     The Ancient Maya

     Maya numeration system
Assignment 2
  2/4 QUIZ 1
Numbers and Measurement
     More about the Maya numeration system
Assignment 3
  2/6 Fibonacci numbers
     Fibonacci rabbits
     The rise of quantification in the West
Project 1 - due February 20
Extra Credit Assignment - due February 27
  2/11 Number and Ratio  
  2/13 Number and Ratio
     Fibonacci Numbers and Art
Study questions
  2/18 Presidents' Day - no classes  
  2/20 QUIZ 2
Number and Ratio
     The Golden Ratio
Drawing a Golden Spiral
  2/25 Number and Ratio
     The Golden Section and Golden Rectangle
     Leonardo's Annunciation
     Perugino's Madonna and Child
 
  2/27 Guest lecturer, Visual Arts Professor Carole Rabe
     Perspective
Part 1 of the midterm - due Wednesday, March 5
  3/3 Painting and the Golden Section
     Renaissance Perspective
     Masaccio, Holy Trinity
     Masaccio, Holy Trinity (diagram)
     Alberti - Perspective
Study questions
  3/5 MIDTERM EXAMINATION  
  3/10 Spring Break  
  3/12 Spring Break  
  3/17 Review of the Midterm Exam  
  3/19 Canons of Proportion  
  3/24 The Golden Ratio and the Human Body Extra Credit Project - due April 2
     Mondrian, Composition in Red, Yellow, and Blue
     Seurat, Bathing at Asnières
    
Piero della Francesca, Baptism of Christ
  3/26 Guest lecturer, Music Professor Mahala Beams
Mathematics and Music
 
  3/31 Mathematics and Music  (includes homework assignment)
Music in the West
 
 
  4/2 QUIZ 3
Introduction to Fractals
Handout on Fractals:  The Colors of Infinity
 
 
  4/7 More about Fractals
 
Homework:  write four measures of music in 4/4 time
  4/9 More about Fractals
The Finite State automata
 
Homework:  write out the results of the sixth fold
  4/14 The Dragon Curve
The Koch Curve
Project 2 - due April 23
Drawing the Dragon Curve
Triangle paper
Graph paper
 
  4/16 Guest lecturer, Biology Professor Susan Bear In-class response
Study questions
  4/21 R. Buckminster Fuller and the Geodesic Dome
Quiz on Fractals
 
  4/23 Mathematics in Nature and Science More study questions

Final Examination
Tuesday, April 29
1 - 3 pm
STC 102