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Need some 'special' topics for Geometry


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For reasons way too complicated to explain ( think Charter School requirements :001_rolleyes: ) my ds (10th grade) is doing a semester of Math- Special Topics rather than a traditional course.  He has already completed a typical geometry course but, for the purpose of checking a particular box in the requirement list, we need to come up with something 'special' or outside the traditional geometry class. 

 

Does anyone have any ideas what would be 'special' ?  Think enrichment or 'gifted' type topics in geometry.   It doesn't need to be advanced academics, college level, or anything difficult. It just needs to be outside the traditional box.

 

Any idea would be great. 

Edited by Tammi K
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Look for Kiselev's books - the second one (stereometry) takes things well outside the traditional box.  It covers vectors through Minkowski space (the same one used for Einstein's work on relativity).  It's quite small and dense, but is a good one.

 

I also like a couple of the Dover books, though they can be very formal - certainly college level.

 

Topics of particular interest: vectors (including cross/dot products), spherical geometry (includes discussion of "great circles" used to navigate the globe), spacetime, non-Euclidean geometry in general, trigonometry, or possibly topology (not technically geometry, but topologies may infer geometries).

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Symmetry

Rotations

In depth look at scale modeling

Fractals

MC Escher's art

Geometry in architecture

The golden mean

Area of polygons as number of sides increase compared to area of a circle

Volume of polyhedrons as number of faces increases compared to volume of sphere

Derivation of Pythagorean theorem (this is usually glossed over in regular géo class)

Geometric constructions (also routinely glossed over)

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Look for Kiselev's books - the second one (stereometry) takes things well outside the traditional box. It covers vectors through Minkowski space (the same one used for Einstein's work on relativity). It's quite small and dense, but is a good one.

 

I also like a couple of the Dover books, though they can be very formal - certainly college level.

 

Topics of particular interest: vectors (including cross/dot products), spherical geometry (includes discussion of "great circles" used to navigate the globe), spacetime, non-Euclidean geometry in general, trigonometry, or possibly topology (not technically geometry, but topologies may infer geometries).

Speaking of great circles, a project on map distortion would be great.

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Some links stashed away in my bookmarks:

https://babel.hathitrust.org/cgi/pt?id=mdp.39015000983471;view=1up;seq=5 (I think Sebastian recommended this once.)

https://www.tarquingroup.com/books/ages-16.html (some geometry topics there)

http://hyperbolic-crochet.blogspot.ca/ (is he crafty? grin)

https://www.geogebra.org/cms/ (learn a new program?)

https://books.google.ca/books/p/princeton?id=mYz7QIt3vQoC&printsec=frontcover&source=gbs_ViewAPI&hl=en&redir_esc=y#v=onepage&q&f=false (spherical trigonometry)

http://finitegeometry.org/sc/16/quiltgeometry.html (quilt geometry)

 

Hope you'll find something fun to do together!

Edited by Emerald Stoker
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Our Sunday paper just had an article about something one of our charter schools is doing in geometry, so yes, I actually have an idea. :) The project was that they had to build a "tin man" out of recyclables. The table showed empty water bottles, paper cups, etc. The students built kind of his skeleton with that. Then they had to figure out his surface area. So the final test on the project was when the teacher cut out aluminum foil to their dimensions and tried to cover the tin man with it. I thought that was pretty cool. 

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My son finished Thinkwell geometry just as his math circle was starting a geometry class. The math cicle uses a Russian book, geometry in problems, alexander shen. Tha was translated to english by ams. It tacklesvgeometry differently as it focuses on proofs. The kid loves the class. Said geometry this way helps him understand the traditioal way. P.s. i am unable to help him with anything in this book.

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Out of the box- Origami!  There are some excellent videos on the math of folding and uses in space and medicine.  Plenty of stories and details to research further.  I don't have time today, but I can dig up the titles of the videos we watched over the weekend.

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If it doesn't have to be geometry, how about Number Theory or Counting and Probability from AoPS?

 

Yep!  We did Number Theory for 1st semester. We were going to do Counting and Probability but ds wanted a break from AoP.  But, your right - great topics!

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Out of the box- Origami!  There are some excellent videos on the math of folding and uses in space and medicine.  Plenty of stories and details to research further.  I don't have time today, but I can dig up the titles of the videos we watched over the weekend.

 

Robert Lang - physicist and origami expert???   We just watched some video about him. Interesting guy.

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