[BlindMath] The state of math equations across solutions

Sun Mar 17 19:21:42 UTC 2024

Hello Bert,

Sorry, I'm really not the best one to ask for help on this one. I hope someone else can help.

Your question is screen reader specific, and I guess has language and display settings that matter too. Please let people know which screen reader you're using most, and that you are successfully reding all content other than math with your braille display. That should help avoid unnecessary advice.

To explain my circumstances, I use 8 dot computer braille on my display so that I get one cell per ASCII character (OK, not all of them) because this suits my needs. I also have just one display and it sits on my desk at work even though I don't spend much time sitting at that desk.

So I end up very seldom reading math on my braille display. Most of the math content I deal with is created by me, and unless I suddenly turn into a mathematical statistician, the content is occasional and mostly inline. That makes it relatively smooth with audio.

Jonathan

-----Original Message-----
From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Bert Van Landeghem via BlindMath
Sent: Sunday, March 17, 2024 9:52 PM
To: Blind Math list for those interested in mathematics <blindmath at nfbnet.org>
Cc: Bert Van Landeghem <b.vanlandeghem at sheffield.ac.uk>
Subject: Re: [BlindMath] The state of math equations across solutions

Dear all,

This is a very interesting discussion.

Jonathan, can you remind me, when consuming HTML, how do you read the equations on your Braille display? How do you have JAWS configured? When I am reading maths on a webpage, it is spoken to me but not displayed on the Braille display. But I am also not using contracted US Braille.

Kind regards,
Bert

On Sat, 16 Mar 2024 at 21:34, Jonathan Godfrey via BlindMath < blindmath at nfbnet.org> wrote:

> Hello Jeff,
>
> I would ask a sighted person to use the practice of document creation
> that is most native to them. Authoring content in a non-native fashion
> will be more work than adding the extra steps necessary with familiar
> software's
>
> If they are not MS Word users, then there are relatively few
> alternatives that are in widespread use. By widespread, I mean users
> numbering in the tens of thousands.
>
> The largest non-MS users are most likely to be LaTeX users, but if
> they are in a statistics or data science group using R or Python as
> the primary analysis software, they may well be using a flavour of markdown.
>
> LaTeX authors who use a GUI to process their source files do not
> generally know how to send their source to an HTML outcome. Options
> include TeX4ht and latexml but this requires use of a command line
> unless they have configured the GUI to use the command lines in the
> background. I don't know of a GUI that embraces HTML output yet, but
> would love to learn of one. I configured TexnikCenter o do it (a long time ago).
>
> Anyone using markdown has to work harder to go to less accessible
> output documents than HTML. Conversion usually involves pandoc for
> these authors, whether that be explicit or hidden away and run in the
> background.  Any sighted author using RStudio for example has their
> work converted to HTML very easily because everything needed to do so is already installed.
> Conversion to pdf (undesirable for access) requires a full blown
> installation of a TeX processor. That might be tinyTeX but is more
> commonly TeXLive or miktex.
>
> HTH,
> Jonathan
>
>
> -----Original Message-----
> From: Jeff Bishop <jeff at jeffbishop.com>
> Sent: Sunday, March 17, 2024 10:19 AM
> To: Blind Math list for those interested in mathematics <
> blindmath at nfbnet.org>
> Cc: Jonathan Godfrey <A.J.Godfrey at massey.ac.nz>
> Subject: RE: [BlindMath] The state of math equations across solutions
>
> Jonathan,
>
> If you were to instruct a math professor or TA on producing MathML
> content without the use of Microsoft products and Math Type, what
> would you suggest here? Do you suggest any specific tools or would you
> suggest that they do it manually through the generation of the content in LaTeX?
>
> Sorry for such a basic question, just trying to catch up in this space
> from a few years while focusing on other areas of accessibility.
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Jonathan
> Godfrey via BlindMath
> Sent: Saturday, March 16, 2024 2:12 PM
> To: Blind Math list for those interested in mathematics <
> blindmath at nfbnet.org>
> Cc: Jonathan Godfrey <A.J.Godfrey at massey.ac.nz>
> Subject: Re: [BlindMath] The state of math equations across solutions
>
> Hello Justin,
>
> First up, thanks for the link.
> While I am well aware of MathType, and did have it installed on my
> computers when I was more frequently using MS products, it was good to
> check out the current situation via their website.
>
> Like so many accessibility assessments and claims, their site seems to
> think screen reader users are only consumers of their content and that
> somehow giving me read access is sufficient. <sigh> Unfortunately the
> soft bigotry of low expectations is all around us.
>
> I used to switch between LaTeX and the display format in order to
> create content using MathType. I assume this remains feasible. (?)
> Alt+\ from memory.
>
> From what I can tell, most of my MS-loving colleagues no longer
> require MathType for their general use. I suspect some of them might
> benefit from the handwriting conversion tool, but the reality is that
> most sighted authors don't need MathType to get on with their job
> courtesy of the in-built equation editor.
>
> I assume therefore (??) that in order to create accessibility through
> HTML with MathML, a person/team can use MathType to convert the math
> content created by non-MathType using authors. If this was the case,
> purchasing MathType in order to gain greater access might well be on
> the necessary tools list for people wanting to consume MS Word
> documents. Some folks might think shelling out the necessary $ for
> MathType is unacceptable; I saw it as a cost of disability and just
> got on with it until I realised I had not used it in over two years.
>
> I'd be happy to test pandoc conversion of content created within MS
> Word, both using MathType and just MS Word's native equation editor. I
> don't have any documents to do the testing on though because so much
> of my life is already entrenched in HTML, both as a consumer and a producer of content.
>
> Jonathan
>
>
>
>
>
> -----Original Message-----
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Romack,
> Justin via BlindMath
> Sent: Sunday, March 17, 2024 4:06 AM
> To: Blind Math list for those interested in mathematics <
> blindmath at nfbnet.org>
> Cc: Romack, Justin <justinr at disability.tamu.edu>; Jonathan Fine via
> BlindMath <blindmath at nfbnet.org>
> Subject: Re: [BlindMath] The state of math equations across solutions
>
> A point of clarification…
>
> My team uses Word with MathType (
> https://www/.
> wiris.com%2Fen%2Fmathtype%2Fmicrosoft-office%2F&data=05%7C02%7Ca.j.god
> frey%40massey.ac.nz%7C034388722d644bccb92d08dc465fc585%7C388728e1bbd04
> 37898dcf8682e644300%7C1%7C0%7C638462624400864206%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=m%2F%2FSIf%2FT6SVIm9zgIF7Uh8p0u3NY5SSWdJ084nMcOl0%3D&reserved=0) to build out accessible math content. MathType will export HTML/MathML from Word through its suite of tools. I am not aware of a workflow with Word alone to produce HTML with MathML.
>
> Thanks!
>
>
>
> - - - - - - - - - - - - - - - - - - - - - - - -
>
> Justin Romack  | Assistant Director
> Disability Resources | Texas A&M University
> 1224 TAMU | College Station, TX 77843-1224
>
> ph: 979.845.1637 | justinr at disability.tamu.edu<mailto:
> justinr at disability.tamu.edu> | disability.tamu.edu
> - - - - - - - - - - - - - - - - - - - - - - - - DIVISION OF STUDENT
> AFFAIRS | One Division. One Mission.
>
> From: BlindMath <blindmath-bounces at nfbnet.org> On Behalf Of Diego
> Vicioso via BlindMath
> Sent: Friday, March 15, 2024 9:31 PM
> To: Blind Math list for those interested in mathematics <
> blindmath at nfbnet.org>
> Cc: Diego Vicioso <viciosodiego at icloud.com>
> Subject: Re: [BlindMath] The state of math equations across solutions
>
> I don’t believe exporting from word will give you mathML. I tried it
> on the word version of Mac two years ago and it wasn’t possible,
> although I don’t quite remember if the math was formatted as planetext
> or if it appeared at all. Diego > ZjQcmQRYFpfptBannerStart This
> Message Is From an External Sender This message came from outside your organization.
> ZjQcmQRYFpfptBannerEnd
>
> I don’t believe exporting from word will give you mathML. I tried it
> on the word version of Mac two years ago and it wasn’t possible, although I
> don’t quite remember if the math was formatted as   planetext or if it
> appeared at all.
>
>
>
>
>
> Diego
>
>
>
> > On Mar 15, 2024, at 9:57 PM, Jonathan Godfrey via BlindMath <
> blindmath at nfbnet.org<mailto:blindmath at nfbnet.org>> wrote:
>
> >
>
> > Yes and no.
>
> >
>
> > HTML with MathML is a subset of HTML with MathJax, and the added
> > benefit
> of MathJax coupling the LaTeX source alongside is that even if some
> obscure LaTeX is used we have a chance to unpack it.
>
> >
>
> > The challenge is that an immediately useful conversion from LaTeX to
> HTML is not within reach of most LaTeX users. If they know enough to
> bring in add-on packages, and use the command line to process  their
> documents, then the ability to use MathJax is feasible. A GUI user of
> LaTeX may not see how readily they can convert to HTML with MathML or MathJax.
>
> >
>
> > There are (at least) two options for LaTeX to HTML. I've used TeX4ht
> > in the past and have a few legacy documents that are processed this
> > way. I went that way because it provide the math in MathJax. I must
> > admit though that I now create most content from markdown so the
> > pandoc processing gives me MathJax (and therefore MathML)
>
> >
>
> > The question of what the output content should be delivered in ought
> > to
> recognise the author's natural input methodology. Asking someone to
> deliver MS Word if they are primarily a LaTeX user is asking for
> resistance. The opposite is also true.
>
> >
>
> > There are nowhere nearly as many authors who start in markdown as
> > either
> LaTeX or MS Word, but we have the benefit of converting to either
> end-product.
>
> >
>
> > Someone else will need to tell us (including me) if the MS Word
> > ability
> to convert a docx file to HTML is sufficiently reliable. I haven't
> initiated a Word document in so long and I have no capability to
> create math content in MS Word anymore. I doubt this leads to HTML
> with MathJax, but if it does lead to HTML with MathML equations then
> that's going to be quite acceptable most of the time.
>
> >
>
> > Another issue I would raise for the conversation with respect to MS
> > Word
> is that the version of MS Word matters. There are plenty of legacy
> workflows that did not lead to accessible math content in the docx
> file let alone any other format. A legacy MS Word file may not
> successfully convert to what we see in a current docx file. This
> matters for copying and pasting content from legacy material as compared to creating content from scratch.
>
> >
>
> > Jonathan
>
> >
>
> >
>
> >
>
> >
>
> >
>
> >
>
> >
>
> >
>
> > -----Original Message-----
>
> > From: BlindMath
> > <blindmath-bounces at nfbnet.org<mailto:blindmath-bounces at nfbnet.org>>
> > On Behalf Of Diego Vicioso via BlindMath
>
> > Sent: Saturday, March 16, 2024 4:06 AM
>
> > To: Blind Math list for those interested in mathematics
> > <blindmath at nfbnet.org<mailto:blindmath at nfbnet.org>>
>
> > Cc: Diego Vicioso
> > <viciosodiego at icloud.com<mailto:viciosodiego at icloud.com>>
>
> > Subject: Re: [BlindMath] The state of math equations across
> > solutions
>
> >
>
> >
>
> > Hey Jeff, if you want the best support possible  for equations, HTML
> > with MathML is still the best option Diego
>
> >
>
> >> On Mar 15, 2024, at 10:52 AM, Jeff Bishop via BlindMath <
> blindmath at nfbnet.org<mailto:blindmath at nfbnet.org>> wrote:
>
> >>
>
> >> Hello Everyone,
>
> >>
>
> >> If you were to offer advice to a math professor on which solution
> >> to
> utilize for accessible math solutions, which would you choose? Would
> you stick to a HTML-based solution, use Microsoft Word's Equation
> Editor or another solution for the widest support for math equations
> with both JAWS and NVDA? I have been away from this space for a while
> so wanting to get opinions on this as it relates to the current state
> of accessibility and tooling that is in market now.
>
> >>
>
> >> Thanks for any advice ...
>
> >>
>
> >> Jeff
>
> >>
>
> >> _______________________________________________
>
> >> BlindMath mailing list
>
> >> BlindMath at nfbnet.org<mailto:BlindMath at nfbnet.org>
>
> >> https://url/
> >> defense.com%2Fv3%2F__http%3A%2F%2Fnfbne%2F__%3B!!KwNVnqRv!B9vhXTGCq
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> >> hR
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> >> 7C
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> >> Ij
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> >> wt
> >> OB85noxOCbmsP7qodsEXnrWHwhVE3OR4cs%3D&reserved=0<https://apc01.safe/
> >> links.protection.outlook.com/?url=https%3A%2F%2Fapc01.safeli%2F&dat
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> >> nks.protection.outlook.com/?url=https%3A%2F%2Fapc01.safeli%2F&data=
> >> 05
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> >> de
> >> %7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462207696091790%7C
> >> Un
> >> known%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1
> >> ha
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> >> /
> >> nks.protection.outlook.com/?url=https%3A%2F%2Furldefense.com%2Fv3%2
> >> F_
> >> _http%3A%2Fnfbne%2F__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4Gjp
> >> FL
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> >> 05
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> >> 82
> >> %7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388671440%7C
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> >> known%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1
> >> ha
> >> WwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=h7d7IXHyJ37xyJCrrNzpOAyySjqg%2
> >> Be
> >> Z6iEFFdfRqACk%3D&reserved=0>
>
> >> t.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=05%7C02%7Ca.j.
> >> g
>
> >> odfrey%40massey.ac.nz%7C48d2effd254843da0ef308dc45019dbb%7C388728e1
> >> bb
> >> d
>
> >> 0437898dcf8682e644300%7C1%7C0%7C638461120466252579%7CUnknown%7CTWFp
> >> bG
> >> Z
>
> >> sb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn
> >> 0%
> >> 3
>
> >> D%7C0%7C%7C%7C&sdata=1GP0RdELV0OfhX6008tEkoLNBvXlMhw%2FCOT3%2BSnyEQ
> >> 4%
> >> 3
>
> >> D&reserved=0 To unsubscribe, change your list options or get your
>
> >> account info for BlindMath:
>
> >> https://url/
> >> defense.com%2Fv3%2F__http%3A%2F%2Fnfbne%2F__%3B!!KwNVnqRv!B9vhXTGCq
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> >> fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2W
> >> hR
> >> rameraq4EURh%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c97
> >> 9d
> >> 8184a86053608dc45cac182%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%
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> >> safelinks.protection.outlook.com/?url=https%3A%2F%2Furldefense.com%
> >> 2F
> >> v3%2F__http%3A%2Fnfbne%2F__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRI
> >> kB
> >> 4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRrameraq4EURh%24
> >> &d
> >> ata=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc
> >> 45
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> >> jQ
> >> 2RRLeAACoiyu76sQN7Y%3D&reserved=0>
>
> >> t.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fviciosodiego%254
> >> 0i
> >> c
>
> >> loud.com&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C48d2effd254843
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> >> ef308dc45019dbb%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461
> >> 12
> >> 0
>
> >> 466263729%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luM
> >> zI
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>
> >> LCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=OpHfXPeaBLwP8Awnn
> >> 5J
> >> J
>
> >> wzUB5vpJSYPRKze8yZXo3A4%3D&reserved=0
>
> >> BlindMath Gems can be found at
>
> >> <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2F%2Fwww%2F__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE
> 6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramer
> ffvrpR9%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C034388722d644bc
> cb92d08dc465fc585%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C6384626
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> 0sLYlM2S7MUa6mhaXhzOm2Tn8%3D&reserved=0
> <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2Fwww%2F__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_C
> q4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerffv
> rpR9%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C034388722d644bccb9
> 2d08dc465fc585%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C6384626244
> 00885734%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiL
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> IvGers5yUzFQicPuP9JuqfRs%3D&reserved=0
> >.
>
> >> blindscience.org%2Fblindmath-gems-home&data=05%7C02%7Ca.j.godfrey%4
> >> 0m
> >> a
>
> >> ssey.ac.nz%7C48d2effd254843da0ef308dc45019dbb%7C388728e1bbd0437898d
> >> cf
> >> 8
>
> >> 682e644300%7C1%7C0%7C638461120466270307%7CUnknown%7CTWFpbGZsb3d8eyJ
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> >> j
>
> >> oiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C
> >> %7
> >> C
>
> >> %7C&sdata=6eybtShX6QDNwDSHYbCzylWoEEjOW0jH6OfrscFmMCc%3D&reserved=0
> >> >
>
> >
>
> > _______________________________________________
>
> > BlindMath mailing list
>
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>
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> > efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fb
> > li
> > ndmath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLN
> > e9
> > 9F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerYZWM-44%24&data=05%7
> > C0
> > 2%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%7C
> > 38
> > 8728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388695423%7CUnknow
> > n%
> > 7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLC
> > JX
> > VCI6Mn0%3D%7C0%7C%7C%7C&sdata=S7heT6n7OiQIP81EwFODOeN%2FwU9YA7x%2FcC
> > 8k
> > 07%2BN2t0%3D&reserved=0<https://apc01.safelinks.protection.outlook.c/
> > om/
> > /
> > /
> > /?url=https%3A%2F%2Furldefense.com%2Fv3%2F__http%3A%2Fnfbnet.org%2Fm
> > ai
> > lman%2Flistinfo%2Fblindmath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fna
> > E6
> > _Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRrame
> > rY
> > ZWM-44%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a
> > 86
> > 053608dc45cac182%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461
> > 98
> > 4388700455%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luM
> > zI
> > iLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=Dqng0hbQ11OhIsZaG
> > m% 2FznwU4BX9uFayFWpZmW819LQ0%3D&reserved=0>
>
> > To unsubscribe, change your list options or get your account info
> > for
> BlindMath:
>
> > https://urld/
> > efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fbl
> > in
> > dmath_nfbnet.org%2Fa.j.godfrey*40massey.ac.nz__%3BJQ!!KwNVnqRv!B9vhX
> > TG
> > Cqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWe
> > D2
> > WhRramerdZu_QA7%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c
> > 97
> > 9d8184a86053608dc45cac182%7C388728e1bbd0437898dcf8682e644300%7C1%7C0
> > %7
> > C638461984388705252%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQ
> > Ij
> > oiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=AjHxN%2B
> > 9m
> > Y9mnyKBuYpkPhb4WgcGrEEDpiZ9yYCCouqM%3D&reserved=0<https://apc01.safe/
> > links.protection.outlook.com/?url=https%3A%2F%2Fapc01.safeli%2F&data
> > =05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C034388722d644bccb92d08dc465f
> > c585%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462624400894103
> > %7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI
> > 6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=wDCcBVb%2BPzg%2BK86HHRuXt
> > C2wGRs1FOqjMVWigw1l1N4%3D&reserved=0
> > nks.protection.outlook.com/?url=https%3A%2F%2Fapc01.safeli%2F&data=0
> > 5%
> > 7C02%7CA.J.Godfrey%40massey.ac.nz%7Cb1f6b68c4dd445ab8e4608dc45febfde
> > %7
> > C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462207696108842%7CUnk
> > no
> > wn%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWw
> > iL
> > CJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=MBvstOWC74g%2For6YGJMhlKr13Hbyw1RSC
> > TX
> > vfv082po%3D&reserved=0
> > /
> > nks.protection.outlook.com/?url=https%3A%2F%2Furldefense.com%2Fv3%2F
> > __
> > http%3A%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fa.j.
> > godfrey*40massey.ac.nz__%3BJQ!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB
> > 4G
> > jpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerdZu_QA7%24&da
> > ta
> > =05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45ca
> > c1
> > 82%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388710080%7
> > CU
> > nknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1
> > ha
> > WwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=%2B1NUYPhiRmo2lpxS4ukTw1iBKKIeT
> > y%
> > 2BAKx%2B9HexI4Ds%3D&reserved=0>
>
> > BlindMath Gems can be found at
> > <https://url/
> > defense.com%2Fv3%2F__http%3A%2F%2Fwww.blindscience.org%2Fblindmath-g
> > em
> > s-home__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5n
> > Iv
> > 7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerX88TPNp%24&data=05%7C02%7Ca.j.g
> > od
> > frey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%7C388728e1bbd
> > 04
> > 37898dcf8682e644300%7C1%7C0%7C638461984388714909%7CUnknown%7CTWFpbGZ
> > sb
> > 3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3
> > D%
> > 7C0%7C%7C%7C&sdata=9qmGs4xSMG1o%2B%2BrXnnH6Sa%2BYMMnoJ%2FOppDOWHtZ%2
> > Fq
> > z4%3D&reserved=0<http://h/
> > ttps%3A%2F%2Furldefense.com%2Fv3%2F__http%3A%2Fwww.blindscience.org%
> > 2F
> > blindmath-gems-home__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpF
> > LN
> > e99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerX88TPNp%24&data=05
> > %7
> > C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%
> > 7C
> > 388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388719386%7CUnkn
> > ow
> > n%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwi
> > LC
> > JXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=fGrWpTgLnYudheez5cb%2B4DUBC0BVZzE%2B
> > qt
> > 7v5cQzcdw%3D&reserved=0>>
>
> > _______________________________________________
>
> > BlindMath mailing list
>
> > BlindMath at nfbnet.org<mailto:BlindMath at nfbnet.org>
>
> > https://urld/
> > efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fb
> > li
> > ndmath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLN
> > e9
> > 9F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerYZWM-44%24&data=05%7
> > C0
> > 2%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%7C
> > 38
> > 8728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388723819%7CUnknow
> > n%
> > 7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLC
> > JX
> > VCI6Mn0%3D%7C0%7C%7C%7C&sdata=xy7MIJCqSeRCSLNnGv42awimqZb5IxIAJ3XLQB
> > AF
> > ja4%3D&reserved=0<https://apc01.safelinks.protection.outlook.com/?ur
> > l=
> > https%3A%2F%2Furldefense.com%2Fv3%2F__http%3A%2Fnfbnet.org%2Fmailman
> > %2
> > Flistinfo%2Fblindmath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4
> > JQ
> > 9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerYZWM-
> > 44
> > %24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a860536
> > 08
> > dc45cac182%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388
> > 72
> > 8668%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJ
> > BT
> > iI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=J%2Fa3pNjdoE0UoOxkjBrer
> > u% 2BJxxFfopaCfAfBdxQGN%2Fw%3D&reserved=0>
>
> > To unsubscribe, change your list options or get your account info
> > for
> BlindMath:
>
> > https://urld/
> > efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fbl
> > in
> > dmath_nfbnet.org%2Fviciosodiego*40icloud.com__%3BJQ!!KwNVnqRv!B9vhXT
> > GC
> > qe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD
> > 2W
> > hRramereY2vI27%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c9
> > 79
> > d8184a86053608dc45cac182%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%
> > 7C
> > 638461984388733550%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQI
> > jo
> > iV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=9i073fXDl
> > ZO
> > cRyOhKS10pCsGSrx7daoCHNw9xq4OMt8%3D&reserved=0<https://apc01.safelin/
> > ks.protection.outlook.com/?url=https%3A%2F%2Fapc01.safelinks%2F&data
> > =05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C034388722d644bccb92d08dc465f
> > c585%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462624400901037
> > %7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI
> > 6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=5jvtCLg0DZq1qQ74AwzyftYt3
> > EBgy06WNoZRiYY9nR8%3D&reserved=0
> > .protection.outlook.com/?url=https%3A%2F%2Fapc01.safelinks%2F&data=0
> > 5%
> > 7C02%7CA.J.Godfrey%40massey.ac.nz%7Cb1f6b68c4dd445ab8e4608dc45febfde
> > %7
> > C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462207696115610%7CUnk
> > no
> > wn%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWw
> > iL
> > CJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=15km3HDF4zZhnfuV6S6FCp8Cug7fM52Jh6y
> > DN
> > 0jEh%2B8%3D&reserved=0
> > /
> > .protection.outlook.com/?url=https%3A%2F%2Furldefense.com%2Fv3%2F__h
> > tt
> > p%3A%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fvicio
> > so
> > diego*40icloud.com__%3BJQ!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4Gjp
> > FL
> > Ne99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramereY2vI27%24&data=0
> > 5%
> > 7C02%7Ca.j.godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182
> > %7
> > C388728e1bbd0437898dcf8682e644300%7C1%7C0%7C638461984388738540%7CUnk
> > no
> > wn%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWw
> > iL
> > CJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=3qKx82UTJ89D5mNG9jPQs7eE3v0mmuZQ23h
> > r4
> > 5WaWGc%3D&reserved=0>
>
> > BlindMath Gems can be found at
> > <https://url/
> > defense.com%2Fv3%2F__http%3A%2F%2Fwww.blindscience.org%2Fblindmath-g
> > em
> > s-home__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5n
> > Iv
> > 7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerX88TPNp%24&data=05%7C02%7Ca.j.g
> > od
> > frey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%7C388728e1bbd
> > 04
> > 37898dcf8682e644300%7C1%7C0%7C638461984388744214%7CUnknown%7CTWFpbGZ
> > sb
> > 3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3
> > D%
> > 7C0%7C%7C%7C&sdata=yUE7tzrufgjrLFHXq3Joezhwz1LDxeK51UKS3lkISj4%3D&re
> > se
> > rved=0<https://apc01.safelinks.protection.outlook.com/?url=https%3A%25
> > 2F
> > %2Furldefense.com%2Fv3%2F__http%3A%2Fwww.blindscience.org%2Fblindmat
> > h-
> > gems-home__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QG
> > j5
> > nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerX88TPNp%24&data=05%7C02%7Ca.j.
> > godfrey%40massey.ac.nz%7Ca541c979d8184a86053608dc45cac182%7C388728e1
> > bb
> > d0437898dcf8682e644300%7C1%7C0%7C638461984388749476%7CUnknown%7CTWFp
> > bG
> > Zsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn
> > 0%
> > 3D%7C0%7C%7C%7C&sdata=gYIgwoYHyfwNpTD6HfRs16IrIekLzGPq5XT1mcF6S24%3D
> > &r
> > eserved=0>>
>
>
>
> _______________________________________________
>
> BlindMath mailing list
>
> BlindMath at nfbnet.org<mailto:BlindMath at nfbnet.org>
>
>
> https://urld/
> efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fbli
> ndmath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe9
> 9F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerYZWM-44%24&data=05%7C0
> 2%7Ca.j.godfrey%40massey.ac.nz%7C034388722d644bccb92d08dc465fc585%7C38
> 8728e1bbd0437898dcf8682e644300%7C1%7C0%7C638462624400908092%7CUnknown%
> 7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJX
> VCI6Mn0%3D%7C0%7C%7C%7C&sdata=9BchyK42X%2FrJYCpVN2xC%2BG7U7s4%2BKZ%2FE
> Z2CKFAvazM8%3D&reserved=0
> <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindm
> ath_nfbnet.org__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F2
> 9QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerYZWM-44%24&data=05%7C02%7
> Ca.j.godfrey%40massey.ac.nz%7C034388722d644bccb92d08dc465fc585%7C38872
> 8e1bbd0437898dcf8682e644300%7C1%7C0%7C638462624400912536%7CUnknown%7CT
> WFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI
> 6Mn0%3D%7C0%7C%7C%7C&sdata=YCXywyTuLqq%2BUusHSbZ8dZKR%2B8IgI2JwQD1jt9G
> 1grI%3D&reserved=0
> >
>
> To unsubscribe, change your list options or get your account info for
> BlindMath:
>
>
> https://urld/
> efense.com%2Fv3%2F__http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblin
> dmath_nfbnet.org%2Fjustinr*40disability.tamu.edu__%3BJQ!!KwNVnqRv!B9vh
> XTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZW
> eD2WhRrameraNyu_cz%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C0343
> 88722d644bccb92d08dc465fc585%7C388728e1bbd0437898dcf8682e644300%7C1%7C
> 0%7C638462624400917046%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJ
> QIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=utREZzc
> sx9XxBsU4ZJUtcdwQW%2F5FatJ651ZzBmSjwhw%3D&reserved=0
> <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindma
> th_nfbnet.org%2Fjustinr*40disability.tamu.edu__%3BJQ!!KwNVnqRv!B9vhXTG
> Cqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7JQLFtCGdXVLqJ-5HHi2AB85ZWeD2
> WhRrameraNyu_cz%24&data=05%7C02%7Ca.j.godfrey%40massey.ac.nz%7C0343887
> 22d644bccb92d08dc465fc585%7C388728e1bbd0437898dcf8682e644300%7C1%7C0%7
> C638462624400921841%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIj
> oiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C0%7C%7C%7C&sdata=ShDCGHLh9I
> R3xIHc6F796vWsEpTjYCmWVdfPu9hp2%2Fg%3D&reserved=0
> >
>
> BlindMath Gems can be found at <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems
> -home__%3B!!KwNVnqRv!B9vhXTGCqe1fnaE6_Cq4JQ9cRIkB4GjpFLNe99F29QGj5nIv7
> JQLFtCGdXVLqJ-5HHi2AB85ZWeD2WhRramerX88TPNp%24&data=05%7C02%7Ca.j.godf
> rey%40massey.ac.nz%7C034388722d644bccb92d08dc465fc585%7C388728e1bbd043
> 7898dcf8682e644300%7C1%7C0%7C638462624400926611%7CUnknown%7CTWFpbGZsb3
> d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7
> C0%7C%7C%7C&sdata=gEOSCPLsHMagdHwnEnXr60kjWBNvhcqzPonTwLGQ06g%3D&reser
> ved=0
> <
> https://urld/
> efense.com%2Fv3%2F__http%3A%2Fwww.blindscience.org%2Fblindmath-gems-ho
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