Maricopa Community Colleges  MAT105   19896-19965 
Official Course Description: MCCCD Approval: 05/09/89
MAT105 19896-19965 L+L 3 Credit(s) 4.50 Period(s)
The Mathematics of Design
Study of classic Greek geometric constructions as elements found in nature and in artistic design. Applications in art and design. Prerequisites: MAT077 or equivalent or permission of instructor.
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MCCCD Official Course Competencies:
 
MAT105   19896-19965 The Mathematics of Design
1. Perform classic Greek constructions with compass and straight edge. (I)
2. Use construction methods to divide a line segment into a golden ratio. (II)
3. Describe how classic triangles appear in nature and in design. (III)
4. Apply triangles with specific ratios as design elements. (III)
5. Describe how dynamic rectangles appear in nature and in design. (IV)
6. Apply dynamic rectangles as design elements. (IV)
7. Describe the relationship of Fibonacci numbers to other geometric figures found in nature. (V)
8. Apply Fibonacci numbers as design elements. (V)
9. Describe how spirals appear in nature and in design. (VI)
10. Apply spirals as design elements. (VI)
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MCCCD Official Course Outline:
 
MAT105   19896-19965 The Mathematics of Design
    I. Basic Constructions
        A. Congruent line segments
        B. Congruent angles
        C. Segment bisector
        D. Angle bisector
        E. Perpendicular through a point on a line
        F. Perpendicular through a point not on a line
        G. Parallel lines
        H. Congruent divisions of a line segment
        I. Applications in art
      II. Unique relationships
          A. Golden section of a line segment
          B. Phi proportions of a line segment
          C. Pentagon within a circle
          D. Pentagon given a side
          E. Golden rectangle
          F. Similar rectangles
          G. Applications in art
        III. Special triangles
            A. 3-4-5 triangle given longer leg
            B. 3-4-5 triangle given the unit
            C. Triangle of price given a pentagon
            D. Triangle of price given a golden rectangle
            E. Harmonic triangle givena pentagon
            F. Harmonic triangle given an inscribed pentagon
            G. Right triangle in a semicircle given a circle
            H. Right triangle in a semicircle given a diameter
            I. Isosceles right triangle
            J. Golden triangle given a golden rectangle
            K. Isosceles triangle
            L. Equilateral triangle
            M. Applications in art
          IV. Dynamic rectangles
              A. Dynamic rectangles generated from a square
              B. Dynamic rectangles within a square
              C. rectangle given width
              D. rectangle given a circle
              E. rectangle given a golden rectangle
              F. rectangle given a width
              G. rectangle given a square
              H. @ + 1 rectangle given a square
              I. Reciprocal of a rectangle
              J. Applications in art
            V. Fibonacci numbers
                A. Dividing a line segment into palindromic sequence of Fibonacci numbers
                B. Applications in art
              VI. Spirals
                  A. Archimedean spiral
                  B. Golden spiral given a golden rectangle
                  C. Logarithmic spiral given a golden triangle
                  D. "Spiral" about a square
                  E. "Spiral" using alternate poles
                  F. Baravelle spiral within a square
                  G. Straight-line spiral in a square
                  H. Applications in art
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