Fall 2001
T-Th 10-11:50
Instructor: Dorothy Wallace
Office: 202 Choate House
Office Hours: 9-12 Wednesday or by appointment
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Math 5, Pattern Fall 2001 T-Th 10-11:50 Instructor: Dorothy Wallace Office: 202 Choate House Office Hours: 9-12 Wednesday or by appointment |
SYLLABUS
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Homework 6
Homework 7
Due Tuesday, Oct. 23
- 1. Your task is create a series of mandalas illustrating the idea of a group and its subgroups. These will all be derived from the same original image of a portion of Alhambra wall. You should be able to find at least three or four subgroups in one of the tiles, probably more.
- 2. Find the Alhambra photos.
Select a few that look promising and load them onto your machine, then import them into photoshop.- 3. Choose one and crop it to form a mandala. Save it as an 8 bit BW image. Clean it up a little using filters or by hand, until it will serve as a decent basis for a color image. Track what you did: which filters, what handwork, etc. Keep a log for each image you do.
- 4. Now save it as an RGB image. Your next job is to make it look good and to introduce color. Save your final image. One comment about color: the printed version tends to look different from what is on the screen. Generally colors are duller, so err on the bright side of what you intend. It varies with paper used too.
- 5. Math problem: Find a collection of subgroups of the group of symmetries of your mandala. You will need the multiplication table for the mandala, and you will look for smaller groups that can be made using just a few elements. Check for subgroups of all sizes to see if you can find one. Which sizes are possible? How would you color the mandala so that the result displays a given subgroup?
- 6. Create a separate image displaying each of the subgroups you found. Do at least 3 subgroups (some can be the same size) but not more than six. Three beautiful images are worth more than six average ones.
- 7. Pay attention to choice of background color, framing of image on page, etc.
- 8. Now print out these images to bring to class. Print two of each so you can hand one in. (You will need to locate a color printer, most likely in Kiewit.) I also want to see the associated math, so include the original group table for each image with an indication of which elements are in the subgroup you are illustrating. Finally, I would like copies of your logs for each image.
© 2001 Dorothy Wallace, Dartmouth College. All rights reserved.