Tammi K Posted March 27, 2017 Share Posted March 27, 2017 (edited) 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 March 29, 2017 by Tammi K Quote Link to comment Share on other sites More sharing options...
Mike in SA Posted March 27, 2017 Share Posted March 27, 2017 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). 3 Quote Link to comment Share on other sites More sharing options...
chiguirre Posted March 27, 2017 Share Posted March 27, 2017 If it doesn't have to be geometry, how about Number Theory or Counting and Probability from AoPS? 1 Quote Link to comment Share on other sites More sharing options...
kiana Posted March 27, 2017 Share Posted March 27, 2017 What about Coxeter's Geometry Revisited? Quote Link to comment Share on other sites More sharing options...
Monica_in_Switzerland Posted March 27, 2017 Share Posted March 27, 2017 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) 1 Quote Link to comment Share on other sites More sharing options...
Monica_in_Switzerland Posted March 27, 2017 Share Posted March 27, 2017 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. Quote Link to comment Share on other sites More sharing options...
almondbutterandjelly Posted March 27, 2017 Share Posted March 27, 2017 Ooh, if I had to do that, I would get the Zometools Geometry stuff. Fun! Quote Link to comment Share on other sites More sharing options...
Emerald Stoker Posted March 27, 2017 Share Posted March 27, 2017 (edited) 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 March 27, 2017 by Emerald Stoker 1 Quote Link to comment Share on other sites More sharing options...
2_girls_mommy Posted March 27, 2017 Share Posted March 27, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
gstharr Posted March 27, 2017 Share Posted March 27, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
Sebastian (a lady) Posted March 28, 2017 Share Posted March 28, 2017 (edited) I have a WW2 era book with military application problems. Thinks like navigation, gunnery, targeting and paratroop drops. Eta link https://catalog.hathitrust.org/Record/000586385 Edited March 28, 2017 by Sebastian (a lady) 1 Quote Link to comment Share on other sites More sharing options...
Joules Posted March 29, 2017 Share Posted March 29, 2017 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. 1 Quote Link to comment Share on other sites More sharing options...
J-rap Posted March 29, 2017 Share Posted March 29, 2017 It's topics like this that make me wish I could homeschool my kids all over again! Quote Link to comment Share on other sites More sharing options...
Tammi K Posted March 29, 2017 Author Share Posted March 29, 2017 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! 1 Quote Link to comment Share on other sites More sharing options...
Tammi K Posted March 29, 2017 Author Share Posted March 29, 2017 Great ideas! Thanks everyone. We are going to do several of them. Quote Link to comment Share on other sites More sharing options...
Tammi K Posted March 29, 2017 Author Share Posted March 29, 2017 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. Quote Link to comment Share on other sites More sharing options...
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