[Blindmath] Math in your head

[Pranav Lal]

Hi all,

My biggest problem with geometry and math in your head came with startup
configuration. I was in middle-school and most things start with the word
triangle. If someone told me imagine a triangle, my question would be what kind
of triangle? How is it oriented that is, if it is an isosceles triangle, where
is the pointy end? If it is a right angle triangle, where is the right angle? Is
it on my right, at the bottom or on the top?

Everything goes downhill from there oh and the moment someone mentions a solid
around the y axis, I think of a cylinder wrapped around a vertical line and a
horizontal line below the entire construct. I do not think of a 2d
representation of that cylinder.
Pranav

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of Steve
Jacobson via Blindmath
Sent: Wednesday, December 16, 2015 7:33 AM
To: jheim at math.wisc.edu; 'Blind Math list for those interested in mathematics'
<blindmath at nfbnet.org>
Cc: Steve Jacobson <steve.jacobson at visi.com>
Subject: Re: [Blindmath] Math in your head

John,

You might find this of interest.  When we studied the revolution of a solid, a
concept where a two-dimensional shape was revolved on the Y-axis, the instructor
actually told me he thought I had an easier time with the concept because I was
able to imagine it while he found most of the students tried to picture it as a
three-dimensional drawing on a two-dimensional surface as they usually handled
three dimensions.  I truly do not know if I was at an advantage or not, but I
did seem to have an easier time with it than many others in the class.  I think
we have to understand graphs to get a start at being able to imagine what
something would look like, but where we can think beyond the paper, we'll have
an advantage.  The same is true of doing math in our heads.  The more we're able
to do, the quicker we'll be at solving equasions, etc.  However, I think it is a
very individual thing.  I would venture to say that when solving complex
equasions, most of us are going to run into that so-called brick wall and need a
way to write it out efficiently at some point.  

-----Original Message-----
From: Blindmath [mailto:blindmath-bounces at nfbnet.org] On Behalf Of John G Heim
via Blindmath
Sent: Tuesday, December 15, 2015 8:29 AM
To: Blind Math list for those interested in mathematics <blindmath at nfbnet.org>
Cc: John G Heim <jheim at math.wisc.edu>
Subject: Re: [Blindmath] Math in your head

A faculty member here at the UW sent me this link to an article from the web
site of the American Mathematical Society. It talks about blind mathematicians
relying more on memory and something like visualization than typical
mathematicians. IMO, relying on your memory is not a bad thing. I think of it as
a skill blind people develop similar to listening to synthesized speech at a
really high rate. As for visualization, when people ask me how I do geometry in
my head, I often call it feelization. It's not visual. But feelization is an
inadequate term because it's just made up and I always have to explain it.
English doesn't have a word for visualizing something without vision. Anyway,
here's that link:

http://www.ams.org/journals/notices/200210/comm-morin.pdf


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