MA 256 Creative Geometry
Name ___________________________________
Activity 8: Modular Arithmetic Designs
Class Time (circle one) Monday Wednesday
ROTATIONAL SYMMETRY
1) Create a picture that contains rotational symmetry set in realistic context. Attach your
results.
http://www.myoats.com/create.aspx
2) What is a Mandala?
http://en.wikipedia.org/wiki/Mandala
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3) What types of symmetry does a Mandala have?
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Classroom Activity 1:
4) Use MyOats to create a simple Mandala. Attach the results.
MODULAR ARITHMETIC
5) What is modular arithmetic?
http://en.wikipedia.org/wiki/Modular_arithmetic
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6) When was modular arithmetic introduced and by who?
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7) Two integers a and b are said to be congruent modulo n, if
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8) Complete the following modular congruences.
27 is congruent to what in mod 4?
57 is congruent to what in mod 6?
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133 is congruent to what in mod 8?
357 is congruent to what in mod 14?
9) List five applications of modular arithmetic.
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10) Complete the mod 4 addition table.
http://www.cut-the-knot.org/blue/Modulo.shtml
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Classroom Activity 2
11) Create a mod 4 arithmetic design with a standard grid. Attach results.
(see instructor for handout)
www.wou.edu/~burtonl/prep/cayley.ppt
Modular Art and Q-R Code designs. (power point)
12) What are Polar Equations?
http://en.wikipedia.org/wiki/Polar_equation
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Classroom Activity 3
13) Use the Grapher program to create a mod 4 arithmetic design using polar equations.
Show 2D and 3D views. Attach results.
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MATHEMATICAL MODULAR MODELS
14) Create a Mathematical Rose. Give an explanation and uses of a mathematical rose.
http://en.wikipedia.org/wiki/Rose_(mathematics)
http://mathworld.wolfram.com/Rose.html
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15) Create a Logarithmic Spiral. Give an explanation and uses of a Logarithmic Spiral.
http://mathworld.wolfram.com/LogarithmicSpiral.html
http://www.redbubble.com/people/sgeek/works/8104141-scape
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16) Create an Archimedean Spiral. Give an explanation and uses of an Archimedian Spiral.
http://en.wikipedia.org/wiki/Archimedean_spiral
http://mathworld.wolfram.com/ArchimedesSpiral.html
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17) Explain the difference between an Archimedean Spiral and a Logarithmic Spiral.
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MODERN MODULAR ART
18) What is a modern description of modular art?
http://dumbonyc.com/2010/03/25/modular-art-collection-pop-up-studio/
19) Explain one approach to creating modular art.
http://www.art-rethought.com/
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Classroom Activity 4
Create a math-based modular design in a real-world setting.
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