tag:blogger.com,1999:blog-1075593398139537131.post2080446650597157764..comments2023-09-21T01:38:02.574-07:00Comments on Without Geometry, Life is Pointless: Talking Habits of Mind: Part 1Avery Pickfordhttp://www.blogger.com/profile/10433339146333801163noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1075593398139537131.post-27447034208464074292018-09-17T01:52:14.666-07:002018-09-17T01:52:14.666-07:00Thanks for updating in details about the talking h...Thanks for updating in details about the talking habits of mind.. Most of the students are not interesting in the maths, especially me also not get much more score in the subject maths. But this post will give a new techniques to solve the maths problem. I love it very much and i hope it will useful to several students.<br />Regards<br /><a href="http://www.medscolony.com/tadalis.aspx" rel="nofollow">Tadalis</a><br />stephensamhttps://www.blogger.com/profile/15591895622825982386noreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-15396582391308875572011-11-28T18:14:01.973-08:002011-11-28T18:14:01.973-08:00@Avery,
I've got a pretty good understanding ...@Avery,<br /><br />I've got a pretty good understanding of both why a ruler and compass can't trisect an angle, and how to approximate that. <br /><br />Have you seen <a href="whole%20movement.com" rel="nofollow">Whole Movement.com</a>? I've seen some of the constructs that you can do with flimsy paper plates using this guy's directions... I have to say, it still wows me that I can make a tetrahedron and icosahedrons from paper plates...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-28052502480476746322011-11-28T12:29:56.158-08:002011-11-28T12:29:56.158-08:00@Andrew: The mirror reflects anything you've d...@Andrew: The mirror reflects anything you've drawn across the line formed by the mirror itself. Mathematically, the interesting question for me is, given specific tools, what can be built and what can't be built? For example, with a compass/ruler it is impossible to trisect an angle. Another common set of "tools" is the ability to fold paper. We were exploring what can and can't be made with our "tool" being this mirror.Avery Pickfordhttps://www.blogger.com/profile/10433339146333801163noreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-2765985156446727942011-11-28T02:58:11.839-08:002011-11-28T02:58:11.839-08:00What's the point of the math mirror? I do any...What's the point of the math mirror? I do any of my constructions now with a ruler and compass, rather than gridded paper, and while I don't always get measurable results, they're usually beautiful.<br /><br />I don't understand what the mirror in the picture is supposed to do....Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-89822666804966815672011-11-03T10:44:46.084-07:002011-11-03T10:44:46.084-07:00We thought about "other shapes" initiall...We thought about "other shapes" initially, but in the end, the problem is really not about the shape: it's about connecting two points. That's why the 3D version was a more interesting generalization.<br /><br />Both this problem and the one Joshua brings up start from a visual premise, and quickly take you into thinking about prime factorization. I first encountered the latter problem in Harold Jacobs' _Math A Human Endeavor_.<br /><br />On the last point in your post: it's not just that *society* values content more. It is in fact not possible to solve problems effectively without a well-stocked toolbox of content. <br /><br />The counterposing of those two sides of the coin is a classical mistake of both reformers and traditionalists. The art of teaching math is largely about navigating between those complementary poles.<br /><br />My comments about the same meeting cover different ground, and can be found at blog.MathEducationPage.org. <br /><br />Thanks for the kind words about my site! <br /><br />--HenriHenri Picciottohttps://www.blogger.com/profile/06875198126877279937noreply@blogger.comtag:blogger.com,1999:blog-1075593398139537131.post-60091017349597168892011-11-02T11:53:45.312-07:002011-11-02T11:53:45.312-07:00"other shapes or other paths" ... that r..."other shapes or other paths" ... that reminds me of the related problem of drawing your line at a 45 degree angle, bouncing off the sides repeatedly until you end in a corner. I wrote a short piece about it in the first Math Teachers' Circle newsletter: http://mathteacherscircle.org/newsletter/MTCircularSummer2011.pdfJoshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.com