[BlindMath] Geometry help

[John G. Heim]

Well, its not really an answer to the original question but one way to 
do geometry is to see it in your mind. In fact, in geometry, once you 
get beyond 2 dimensions, you're mostly doing it in your mind whether you 
can see or not. A math text book might make some attempts to show 
pictures of 3 dimensional objects, for example when showing how to 
calculate the volume of a sphere, but mostly that is left to the 
imagination of the student. When you get into the geometry of complex 
numbers, you might put the formulas on paper but you wouldn't attempt to 
draw the solution. And, of course, at higher levels, objects beyond 3 
dimentions are always imagined in one's head. Multi-dimentional geometry 
is a big deal these days because it is used in areas of physics like 
super string theory and super gravity theory.

My experience is that having to draw geometric figures is a liability. 
Some time ago I proposed a geometry problem on a chat list for 
mathematicians and the onese who did it in their head were much more 
successful than those that insisted in drawing it. Of course, I invented 
the puzzle myself and solved it without drawing it.

Again, it doesn't really answer the original question it's just that I'm 
uncomfortable saying you can't do geometry without a physical model. If 
you get far enough in math, you have to do that.


On 2/11/23 18:11, John Gardner via BlindMath wrote:
> The important message here is that you need to see the image to do geometry. If you cannot see it visually, you need to see it with your fingers. None of your present tools give an image. So you cannot do geometry with these tools.
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Robert Jaquiss via BlindMath
> Sent: Saturday, February 11, 2023 2:56 PM
> To: 'Blind Math list for those interested in mathematics' <blindmath at nfbnet.org>
> Cc: rjaquiss at earthlink.net
> Subject: Re: [BlindMath] Geometry help
>
> Hello:
>
>       There are three solutions I can think of:
> 1. APH sells the Draftsman system for creating raised line images. There are accessories that when used with the Draftsman allow the user to draw precise images. A student should be able to complete his/her homework or an aide can copy drawings from a board.
> 2. The SwellForm machine with SwellTouch paper from American Thermoform allows sighted teachers or aides to draw or copy images onto SwellTouch paper. When the SwellTouch paper is processed by the SwellForm machine, any black areas will raise.
> 3. ViewPlus Technologies sells embossers capable of creating raised images.
> Hope this helps.
>
> Regards,
>
> Robert
>
>
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Sonya Lawrence via BlindMath
> Sent: Saturday, February 11, 2023 5:31 AM
> To: blindmath at nfbnet.org
> Cc: Sonya Lawrence <sflawrence1 at gmail.com>
> Subject: [BlindMath] Geometry help
>
> Hello:
> I am interested in obtaining an accessibility plan to share with my son’s  school to support his learning in a High School Geometry class.  He has access to an IPAD, Surface Pro, BrailleNote touch plus , and graphing calculator. Unfortunately, no one seems to know how to use these or other tools to make graphs, charts, angles, and other geometry activities meaningfully accessible to him. I appreciate your help.
>
> Sonya
> Sent from my iPhone
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-- 
John .G. Heim
jheim at math.wisc.edu