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My IA topic is 'Exploring the 17 plane crystallographic groups in Alhambra Palace' 

 

I visited AlHambra Palace, that is located in Granada Spain last summer, and was really impressed by the complexity of its architectures and wall patterns. And the influence of math in art really struck me. I also really want to major in Architecture so that added to my interest, and Islamic Architecture is a big interest of mine.
Alhambra palace has been said to contain all 17 crystallographic groups (wallpaper patterns): which is the classification of two-dimensional patterns, based on the symmetries in the patterns.

My aim is to investigate and prove the presence of the 17 crystallographic groups from the pictures I took last summer of wall patterns and mosaics found in Alhambra Palace.  

 

I am really interested in this exploration, especially that I think I'd be able to show a lot of personal engagement, given its connection to what I'll major in, my personal interest and the fact that I'll be using pictures I took my self (for the most part).

 

However my concern is were it falls under, which is most likely geometry. And I was wondering if this will not cut the HL standard, does it seem too easy, since it doesn't touch on an HL topic from the syllabus?

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As much as I like the topic, if it's not about the syllabus topics, you might be on a slippery slope. How exactly, in math terms, would you plan to prove the presence of the groups?

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As much as I like the topic, if it's not about the syllabus topics, you might be on a slippery slope. How exactly, in math terms, would you plan to prove the presence of the groups?

 

The math involved would be applying the rules of symmetry and translation (reflection, rotation) and find geometric patterns present in Alhambra that meet all 17 groups, here's is an image of the different classification groups:

http://www.cienciateca.com/17spgps.gif  

http://black.mitplw....teen_groups.png

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The math involved would be applying the rules of symmetry and translation (reflection, rotation) and find geometric patterns present in Alhambra that meet all 17 groups, here's is an image of the different classification groups:


http://www.cienciateca.com/17spgps.gif  


http://black.mitplw....teen_groups.png

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