[BlindMath] Learning High School Math

Mon Jul 26 18:53:59 UTC 2021

> Even if there are some math extensions they are not standard and thus not included in the language.

hmm, what is then the role of the dollar signs? I’d be really interested in that.

Markdown vs. LaTeX is an ongoing topic, with both having their advantages and disadvantages. And while LaTeX may be still significantly present in academic papers, notebooks as an example are dominated by Markdown (Jupyter lab, Sage notebook etc.)

To understand the “real” difference between these two languages, we have to take a brief look to the history.

LaTeX is a system dating back to 1984. In those times, computer graphics was still quite a miracle, very far from what we have today. Heh, people were happy if they got things printed on the screen in the first place, there was hardly a room for anything beyond.

And LaTeX reflects this state quite well. While it undoubtebly brought many ways to ease the formatting (that’s why it became so popular after all), its approach is still quite “mechanic” (if you want to do something “special”, you literally have to instruct LaTeX how to do it, it doesn’t really care what things are, just how should they look) like.

HTML (one of the most used markup languages), while not much younger, has came through a very interesting development in times, when graphical interface was already a normal thing and programmers could take technologies to a new level.

It takes a different approach than LaTeX. Instead of specifying how exactly should things look like, you rather specify what they are (heading, link, table etc.), and on another place (CSS) you can define the design of individual types.

This is a revolutionary idea for few reasons:

-

In the main document, you can focus completely on the content, which will be very readable and easy to modify (no graphical mess involved).

-

All elements are of a known type, what means they don’t need to be pre-printed into a static image. Instead, a browser or a printer can evaluate the available space and display things nicely on displays or papers of all sizes and shapes.

-

Because the elements of the document are known to the interpreter (a browser for example), it’s easy to add a dynamic functionality and interactive elements to papers or books.

-

And finally, the elements are not just known to the browser, but also to screenreaders, so they are typically very accessible for blind people.

Markdown is also a markup language, just with a simpler syntax. It has been originally developed as a blogging format, what’s probably one of the reasons why adapting it for scientific papers may not be that straight-forward.

As an example, you can’t write the text in columns, Markdown was not designed to do this.

But on the other hand, the term Markdown itself is these times quite unspecific, as its broad adoption produced various flavors like Pandoc Markdown, GitHub Markdown, may be Stack overflow markdown? (I’m not sure if they have their own flavor or not).

And surely there are flavors for science as well like RMarkdown.

And if one still can’t find a suitable option, there’s always the possibility to simply call out from the script to HTML / CSS or even JavaScript to create the design of one’s dreams.

It mostly doesn’t matter how wild they are, anything will be more readable than LaTeX. :D

So, this is the primary comparison of these two languages, design oriented vs. content oriented.

There is also of course the group of people, who will push LaTeX just because it is “the standard”, and “the only way to do it”. I hope that approach doesn’t need a comment here. In 9th century, the church was actively enforcing the idea, that there are just three languages worth of praising God (Hebrev, Greek and Latin).

St. Cyril and Methodius disproved the non-sense quite well, but yeah, some people will never learn, even thousand years later.

I’m not trying to say that LaTeX is bad, just as I’m not saying latin or Greek is bad. I’m rather suggesting that every tool has its advantages and disadvantages, which should be the ones taken into consideration, instead of conventions and prejudices.

But having that said, may be even more important question, related to the actual topic is, does all of this really matter?

I mean, we are talking about a high-school student here, communicating with her teachers. She’s not going to write scientific papers and she’s not going to hold a scientific presentation or class.

Thus, the purpose is not to make things nice, but fast and accurate.

And in that case, even Markdown is a drag. The teachers aren’t (or at least shouldn’t be) stupid, they can read formats like AsciiMath right away and don’t need any sophisticated formatting, which would just slow things down.

The girl will eventually learn Markdown, HTML, CSS and even LaTeX when they’ll be needed, but that has time (it’s not even clear if she will study math or a related topic).

So I wouldn’t personally make such drama out of it (even though it seems bit contrary with the rest of this message. :D )

Best regards

Rastislav

Dňa 26. 7. 2021 o 16:42 Kevin Fjelsted via BlindMath napísal(a):

> If the goal is writing math equations Markdown is not really set up very well for that. Even if there are some math extensions they are not standard and thus not included in the language.
>
> If the goal for reading equations is Braille then Latex-Access is the best solution however it take a bit of work to set it up correctly.
> http://latex-access.sourceforge.net
> If the goal is to create math equations that can be printed out in the best format for sighted reading such as to hand in to a teacher than Latex is absolutely the best approach.
>
>> On Jul 26, 2021, at 7:26 AM, Traci W via BlindMath
>> [<blindmath at nfbnet.org>](mailto:blindmath at nfbnet.org)
>> wrote:
>>
>> I was doing some YouTube searching this am. And found this video. There is
>> a comment about markdown working better than Latex for screenreaders. Any
>> input?
>> https://youtu.be/bqHNpNLa7ew
>> Traci
>>
>> On Sun, Jul 25, 2021 at 10:43 PM Traci W
>> [<traci.mwd at gmail.com>](mailto:traci.mwd at gmail.com)
>> wrote:
>>
>>> Ok. We use 365 so I will try to tell it to install the 33 bit version!
>>>
>>> Thanks for the Notepad info too. My kids used Notepad++ at a Cyber camp
>>> and liked it!
>>>
>>> Traci
>>>
>>> On Sun, Jul 25, 2021 at 10:32 PM Shail M
>>> [<momdadofarushi at hotmail.com>](mailto:momdadofarushi at hotmail.com)
>>> wrote:
>>>
>>>> Hi Traci,
>>>>
>>>> You can uninstall the Word from your machine and then reinstall the
>>>> 32-bit version of Word as 32 bit applications are supported on 64-bit
>>>> machine/Windows OS. Installation process will be same, it just using a
>>>> different installer:
>>>>
>>>> Note: Make sure that the product key is handy before uninstalling the
>>>> Word from the machine.
>>>>
>>>> Download and install or reinstall Microsoft 365 or Office 2019 on a PC or
>>>> Mac - Office Support
>>>> [<https://support.microsoft.com/en-us/office/download-and-install-or-reinstall-microsoft-365-or-office-2019-on-a-pc-or-mac-4414eaaf-0478-48be-9c42-23adc4716658#installsteps=pc_step-by-step>](https://support.microsoft.com/en-us/office/download-and-install-or-reinstall-microsoft-365-or-office-2019-on-a-pc-or-mac-4414eaaf-0478-48be-9c42-23adc4716658#installsteps=pc_step-by-step)
>>>> Excerpt:
>>>>
>>>> The 64-bit version is installed by default unless Office detects you
>>>> already have a 32-bit version of Office (or a stand-alone Office app such
>>>> as Project or Visio) installed. In this case, the 32-bit version of Office
>>>> will be installed instead.
>>>>
>>>> To change from a 32-bit version to a 64-bit version
>>>> [<https://support.microsoft.com/en-us/office/choose-between-the-64-bit-or-32-bit-version-of-office-2dee7807-8f95-4d0c-b5fe-6c6f49b8d261?wt.mc_id=scl_installoffice_home>](https://support.microsoft.com/en-us/office/choose-between-the-64-bit-or-32-bit-version-of-office-2dee7807-8f95-4d0c-b5fe-6c6f49b8d261?wt.mc_id=scl_installoffice_home)
>>>> or
>>>> vice versa, you need to uninstall
>>>> [<https://support.microsoft.com/en-us/office/uninstall-office-from-a-pc-9dd49b83-264a-477a-8fcc-2fdf5dbf61d8>](https://support.microsoft.com/en-us/office/uninstall-office-from-a-pc-9dd49b83-264a-477a-8fcc-2fdf5dbf61d8)
>>>> Office
>>>> first (including any stand-alone Office apps you have such as Project of
>>>> Visio). Once the uninstall is complete, sign in again to
>>>> www.office.com
>>>> and
>>>> select *Other install options*, choose the language and version you want
>>>> (64 or 32-bit), and then select *Install*. (See Install Visio
>>>> [<https://support.microsoft.com/en-us/office/install-visio-or-access-visio-for-the-web-f98f21e3-aa02-4827-9167-ddab5b025710>](https://support.microsoft.com/en-us/office/install-visio-or-access-visio-for-the-web-f98f21e3-aa02-4827-9167-ddab5b025710)
>>>> or Install Project
>>>> [<https://support.microsoft.com/en-us/office/install-project-7059249b-d9fe-4d61-ab96-5c5bf435f281>](https://support.microsoft.com/en-us/office/install-project-7059249b-d9fe-4d61-ab96-5c5bf435f281)
>>>> if
>>>> you need to reinstall those stand-alone apps.)
>>>>
>>>> Regarding running Latex on Notepad, you can use the steps detailed at LaTeX
>>>> on Windows with MiKTeX and Notepad++ – Nimal's Weblog
>>>> [<https://nimal.info/blog/2010/latex-on-windows-with-miktex-and-notepad/>](https://nimal.info/blog/2010/latex-on-windows-with-miktex-and-notepad/)
>>>> .
>>>>
>>>> Thanks
>>>>
>>>> Shail
>>>>
>>>> *From:* Traci W
>>>> [<traci.mwd at gmail.com>](mailto:traci.mwd at gmail.com)
>>>> *Sent:* Sunday, July 25, 2021 7:18 PM
>>>> *To:* Blind Math list for those interested in mathematics <
>>>> blindmath at nfbnet.org
>>>>>
>>>> *Cc:* Rastislav Kish
>>>> [<rastislav.kish at protonmail.com>](mailto:rastislav.kish at protonmail.com)
>>>> ; Shail M <
>>>> momdadofarushi at hotmail.com
>>>>>; Louis Maher
>>>> [<ljmaher03 at outlook.com>](mailto:ljmaher03 at outlook.com)
>>>> *Subject:* Re: [BlindMath] Learning High School Math
>>>>
>>>> We did play with it on our old laptops and were successful with Word,
>>>> NVDA and Mathplayer and MathType installed....
>>>>
>>>> But we now have 64 bit computers and are back to square one.  My next
>>>> look is at the Accessible Equation Editor Project.  But I am also
>>>> looking at Notepad++ with LaTex.
>>>>
>>>> Traci
>>>>
>>>> On Sun, Jul 25, 2021 at 9:56 PM Shail M via BlindMath <
>>>> blindmath at nfbnet.org
>>>>> wrote:
>>>>
>>>> Just to mention, MathPlayer plugin is visible in Word, only if the 32-bit
>>>> Word is installed.
>>>>
>>>> The NVDA documentation states the below but when tried on OpenStax and
>>>> few other pages with Math content, it didn't worked as claimed.
>>>>
>>>> 7. Reading Mathematical Content
>>>>
>>>> Using MathPlayer 4 from Design Science, NVDA can read and interactively
>>>> navigate supported mathematical content. This requires that MathPlayer 4 is
>>>> installed on the computer. MathPlayer is available as a free download from:
>>>> https://www.dessci.com/en/products/mathplayer/
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dessci.com%2Fen%2Fproducts%2Fmathplayer%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=US8oB9Xbr%2BeaG1zMTrXZRffjiJVxpXw7O05fR9whit4%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dessci.com%2Fen%2Fproducts%2Fmathplayer%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=US8oB9Xbr%2BeaG1zMTrXZRffjiJVxpXw7O05fR9whit4%3D&reserved=0)
>>>> NVDA supports the following types of mathematical content:
>>>>
>>>>    MathML in Mozilla Firefox, Microsoft Internet Explorer and Google
>>>> Chrome.
>>>>    Design Science MathType in Microsoft Word and PowerPoint. MathType
>>>> needs to be installed in order for this to work. The trial version is
>>>> sufficient. It can be downloaded from
>>>> https://www.dessci.com/en/products/mathtype/
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dessci.com%2Fen%2Fproducts%2Fmathtype%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=VkZEtfh5PjOINnA59hkBVqXzafN4rq3otWfYjyxrIo4%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.dessci.com%2Fen%2Fproducts%2Fmathtype%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=VkZEtfh5PjOINnA59hkBVqXzafN4rq3otWfYjyxrIo4%3D&reserved=0)
>>>> MathML in Adobe Reader. Note that this is not an official standard
>>>> yet, so there is currently no publicly available software that can produce
>>>> this content.
>>>>    Math in Kindle for PC for books with accessible math.
>>>>
>>>> When reading a document, NVDA will speak any supported mathematical
>>>> content where it occurs. If you are using a braille display, it will also
>>>> be displayed in braille.
>>>>
>>>> Thanks
>>>> Shail
>>>>
>>>> -----Original Message-----
>>>> From: BlindMath
>>>> [<blindmath-bounces at nfbnet.org>](mailto:blindmath-bounces at nfbnet.org)
>>>> On Behalf Of Louis Maher
>>>> via BlindMath
>>>> Sent: Sunday, July 25, 2021 6:29 PM
>>>> To: Rastislav Kish
>>>> [<rastislav.kish at protonmail.com>](mailto:rastislav.kish at protonmail.com)
>>>> ; Blind Math list for
>>>> those interested in mathematics
>>>> [<blindmath at nfbnet.org>](mailto:blindmath at nfbnet.org)
>>>> Cc: Louis Maher
>>>> [<ljmaher03 at outlook.com>](mailto:ljmaher03 at outlook.com)
>>>> Subject: Re: [BlindMath] Learning High School Math
>>>>
>>>> Hello,
>>>>
>>>> MathPlayer's manual and download site is at
>>>> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.wiris.com%2Fen%2Fmathplayer%2Fstart&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339694906%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=fHFXNEbxxsptKG8WEAI36otlYAeADemN0PO9wyII3rg%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.wiris.com%2Fen%2Fmathplayer%2Fstart&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=CKffYQnxO9XxwRaXQnqD0MccsvSr%2FhvlG1ElXm5oiIM%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdocs.wiris.com%2Fen%2Fmathplayer%2Fstart&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048259514%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=CKffYQnxO9XxwRaXQnqD0MccsvSr%2FhvlG1ElXm5oiIM%3D&reserved=0)
>>>> Regards
>>>> Louis Maher
>>>> Phone: 713-444-7838
>>>> E-mail:
>>>> ljmaher03 at outlook.com
>>>> -----Original Message-----
>>>> From: BlindMath
>>>> [<blindmath-bounces at nfbnet.org>](mailto:blindmath-bounces at nfbnet.org)
>>>> On Behalf Of Rastislav
>>>> Kish via BlindMath
>>>> Sent: Sunday, July 25, 2021 6:25 PM
>>>> To:
>>>> blindmath at nfbnet.org
>>>> Cc: Rastislav Kish
>>>> [<rastislav.kish at protonmail.com>](mailto:rastislav.kish at protonmail.com)
>>>> Subject: Re: [BlindMath] Learning High School Math
>>>>
>>>> Hey there,
>>>>
>>>> one question, does MathPlayer still exist? Or what happened to it?
>>>>
>>>> It has crossed my mind as well in the discussion as it was the only
>>>> choice of accessing math in Jaws 16-? Or 15- I'm not sure now.
>>>>
>>>> But search results from Google simply redirect me to MathType, which
>>>> doesn't seem to have included the MathPlayer functionality as far as I've
>>>> tested.
>>>>
>>>> Does anyone know what happened?
>>>>
>>>> Best regards
>>>>
>>>> Rastislav
>>>>
>>>> Dňa 25. 7. 2021 o 5:56 Shail M via BlindMath napísal(a):
>>>>
>>>>> Hi @Susan,
>>>>>
>>>>> Hope, you are doing well. Thanks much for providing the references to
>>>>
>>>> the Math books.
>>>>
>>>>> Though Math equation speak is normally error prone by NVDA as well as
>>>>
>>>> JAWS. I lately learned that Math Player + Firefox + NVDA is the best among
>>>> all options. I am trying it out.
>>>>
>>>>> Canute is really promising and something that might be affordable
>>>>
>>>> compared to other notetakers. I really hope, this becomes the game changer
>>>> and people with VI can read more content with scrolling for every line.
>>>>
>>>>> Thanks
>>>>> Shail
>>>>>
>>>>> -----Original Message-----
>>>>> From: BlindMath
>>>>> [<blindmath-bounces at nfbnet.org>](mailto:blindmath-bounces at nfbnet.org)
>>>>> On Behalf Of Susan
>>>>> Jolly via BlindMath
>>>>> Sent: Wednesday, July 21, 2021 4:20 PM
>>>>> To:
>>>>> blindmath at nfbnet.org
>>>>> Cc: Susan Jolly
>>>>> [<easjolly at ix.netcom.com>](mailto:easjolly at ix.netcom.com)
>>>>> Subject: [BlindMath] Learning High School Math
>>>>>
>>>>> Hi Shail,
>>>>>
>>>>> Thank you for reading my article and your nice words about it.
>>>>>
>>>>> You mentioned an algebra book on OpenStax that seems like it would be
>>>>
>>>> difficult to convert to braille.  I agree.  It may be that the UTMOST
>>>> project I mentioned previously is planning to provide some algebra books in
>>>> braille.  You might want to contact them if the next two suggestions aren't
>>>> helpful.
>>>>
>>>>> Here are two sources for braille books including algebra books which
>>>>
>>>> are available free to eligible persons.  A TVI should know what is required
>>>> to request a book from either source.
>>>>
>>>>> The APH Louis database attempts to keep a record of every available
>>>>
>>>> book transcribed to braille for educational purposes.
>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Flouis
>>>>> .aph.org
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Faph.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048269472%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=PzNYLE9Rfs1e%2BKMrRfd1B%2BVoK%2B3Wq3jTUKNNdagZ0pE%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Faph.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048269472%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=PzNYLE9Rfs1e%2BKMrRfd1B%2BVoK%2B3Wq3jTUKNNdagZ0pE%3D&reserved=0)
>>>> %2Fcatalog%2FCategoryInfo.aspx%3Fcid%3D152&data=04%7C01%7C
>>>>
>>>>> %7C1d76b48b27f942e7f30608d94fc39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa
>>>>> %7C1%7C0%7C637628523756687304%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAw
>>>>> MDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=5T
>>>>> i62emReazsXfmCD9dd0MTFoQ9imxvAF%2FXJ1I%2FKYPo%3D&reserved=0
>>>>>
>>>>> BookShare has a huge number of books in various accessible formats
>>>>
>>>> including algebra books in braille.
>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.b
>>>>> ookshare.org
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fookshare.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048269472%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=pJekxmjTfplzqNAWHcDKahMMYi4I%2Fzh70aK3D%2FkST2Q%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fookshare.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048269472%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=pJekxmjTfplzqNAWHcDKahMMYi4I%2Fzh70aK3D%2FkST2Q%3D&reserved=0)
>>>> %2Fcms%2F&data=04%7C01%7C%7C1d76b48b27f942e7f30608d94f
>>>>
>>>>> c39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628523756687304
>>>>> %7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6I
>>>>> k1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=%2BLkurfcvRm%2BlSIX9QKY7K7N5HTW
>>>>> DQRoemdL6PZi3jjk%3D&reserved=0
>>>>>
>>>>> You also mentioned the difficulty of working with a complex formula in
>>>>
>>>> either LaTeX or Nemeth.  There's actually been a lot of research in the
>>>> area of how to explore complex formulas non-visually.  To take your example
>>>> one possibility would reveal the outermost view as an expresson raised to a
>>>> fractional power. The first  inner view is that the expression is a simple
>>>> fraction.  Next one could explore the numerator and denominator and then
>>>> their individual factors.
>>>>
>>>>> It is my understanding that both MathJax and NVDA provide for such
>>>>
>>>> exploration via tabbing.  I don't know the details of how to do this but
>>>> perhaps someone else on the list can help.
>>>>
>>>>> As for manipulating the formula in braille it might be helpful to have
>>>>
>>>> an embossed braille copy.  Some people prefer to do braille math on a
>>>> Perkins so as to read several lines at once.  The Canute 360 braille
>>>> e-reader which has nine 40-cell lines  is just back in production so that
>>>> will be another option hopefully available soon.
>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.br
>>>>> istolbraille.co.uk
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fistolbraille.co.uk%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048279429%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=pbWGik%2F8XAfLTsz36347J1fQIPp%2FX2GdLfUY6KX9KcI%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fistolbraille.co.uk%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048279429%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=pbWGik%2F8XAfLTsz36347J1fQIPp%2FX2GdLfUY6KX9KcI%3D&reserved=0)
>>>> %2F&data=04%7C01%7C%7C1d76b48b27f942e7f30608d94f
>>>>
>>>>> c39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628523756687304
>>>>> %7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6I
>>>>> k1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=5H7%2FGtweNYH4IMqBYCVqVYU9i4Rm7
>>>>> 1wQPUEs6EVrL%2Bs%3D&reserved=0
>>>>>
>>>>> Best wishes,
>>>>> Susan J.
>>>>>
>>>>> _______________________________________________
>>>>> BlindMath mailing list
>>>>> BlindMath at nfbnet.org
>>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet
>>>>> .org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7
>>>>> C1d76b48b27f942e7f30608d94fc39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7
>>>>> C1%7C0%7C637628523756687304%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMD
>>>>> AiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=ugTs
>>>>> 088apvstjCoCEsbnpT%2FCWaWApdY4G4e48uRYZ0w%3D&reserved=0
>>>>> To unsubscribe, change your list options or get your account info for
>>>>
>>>> BlindMath:
>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet
>>>>> .org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fmomdadofarushi%2540h
>>>>> otmail.com
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fotmail.com%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048279429%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=b%2FcMWcKK6u5Gxcoku8wp0rqLhawvYAYImyHTP1PnlGU%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fotmail.com%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048279429%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=b%2FcMWcKK6u5Gxcoku8wp0rqLhawvYAYImyHTP1PnlGU%3D&reserved=0)
>>>> &data=04%7C01%7C%7C1d76b48b27f942e7f30608d94fc39863%7C84
>>>>
>>>>> df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628523756687304%7CUnknown%
>>>>> 7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJX
>>>>> VCI6Mn0%3D%7C1000&sdata=Ya0KSeXqE3Kgkse9cKDD8f%2BIGaRHlEhUINaWZ7%2
>>>>> BSODc%3D&reserved=0 BlindMath Gems can be found at
>>>>> <
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.b
>>>>> lindscience.org
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flindscience.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=1Jh61gffrf7KFNU0l93g5sf%2FaFHsdeDfXgts91qzTIY%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flindscience.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=1Jh61gffrf7KFNU0l93g5sf%2FaFHsdeDfXgts91qzTIY%3D&reserved=0)
>>>> %2Fblindmath-gems-home&data=04%7C01%7C%7C1d76b48b27
>>>>
>>>>> f942e7f30608d94fc39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63
>>>>> 7628523756687304%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV
>>>>> 2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=kGlEZiud2zM5FwZ
>>>>> yJJPREiTNmjY%2BEBzMvagaAAKu0S8%3D&reserved=0>
>>>>>
>>>>> _______________________________________________
>>>>> BlindMath mailing list
>>>>> BlindMath at nfbnet.org
>>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet
>>>>> .org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7
>>>>> C1d76b48b27f942e7f30608d94fc39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7
>>>>> C1%7C0%7C637628523756687304%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMD
>>>>> AiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=ugTs
>>>>> 088apvstjCoCEsbnpT%2FCWaWApdY4G4e48uRYZ0w%3D&reserved=0
>>>>> To unsubscribe, change your list options or get your account info for
>>>>
>>>> BlindMath:
>>>>
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet
>>>>> .org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Frastislav.kish%2540p
>>>>> rotonmail.com
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Frotonmail.com%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=4mBS%2FohZKT%2B%2BP%2FJeVrwPv7KGiJm0s%2FcBHMElqfhZLzk%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Frotonmail.com%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=4mBS%2FohZKT%2B%2BP%2FJeVrwPv7KGiJm0s%2FcBHMElqfhZLzk%3D&reserved=0)
>>>> &data=04%7C01%7C%7C1d76b48b27f942e7f30608d94fc39863%7
>>>>
>>>>> C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628523756687304%7CUnkno
>>>>> wn%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiL
>>>>> CJXVCI6Mn0%3D%7C1000&sdata=5V6pEPsNaIcW87GidCpHxcD0aGPWTJwYm74Vd3d
>>>>> kF7M%3D&reserved=0 BlindMath Gems can be found at
>>>>> <
>>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.b
>>>>> lindscience.org
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flindscience.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=1Jh61gffrf7KFNU0l93g5sf%2FaFHsdeDfXgts91qzTIY%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flindscience.org%2F&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048289392%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=1Jh61gffrf7KFNU0l93g5sf%2FaFHsdeDfXgts91qzTIY%3D&reserved=0)
>>>> %2Fblindmath-gems-home&data=04%7C01%7C%7C1d76b48b27
>>>>
>>>>> f942e7f30608d94fc39863%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C63
>>>>> 7628523756697260%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV
>>>>> 2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=3516N6MqX6DgikJ
>>>>> gK7EGXfD0%2B0zShXyqL%2FTpJTNAskQ%3D&reserved=0>
>>>>
>>>> _______________________________________________
>>>> BlindMath mailing list
>>>> BlindMath at nfbnet.org
>>>>
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339694906%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=gNluHtOX5EoQR9L01aVm3HYoticNZ5xWq1QN8KyH%2Bxc%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048299342%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=CN0Y%2F3HdhCxEly9pEuWHISQGELeF7p20ZiRGBSBw11k%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048299342%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=CN0Y%2F3HdhCxEly9pEuWHISQGELeF7p20ZiRGBSBw11k%3D&reserved=0)
>>>> To unsubscribe, change your list options or get your account info for
>>>> BlindMath:
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fljmaher03%2540outlook.com&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339704864%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=fGIHE%2BOUcpmzYiXusCXyTYMsPVOI%2Fn47RuCzE%2BlRghE%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fljmaher03%2540outlook.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048299342%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=qoTZH7nICpL66jZdDQrXxjvt%2FgOwuasRoinwnTc1wRQ%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fljmaher03%2540outlook.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048299342%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=qoTZH7nICpL66jZdDQrXxjvt%2FgOwuasRoinwnTc1wRQ%3D&reserved=0)
>>>> BlindMath Gems can be found at <
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339704864%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=7CPmFhO9NZQsRYFhOljHYYzBn4A%2FsVGVlE37LluK%2Fr4%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048309295%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=DbrbZtMvFP%2B63vkDNFeJYshpQVWyMpAWzzEtiW5hmPc%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048309295%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=DbrbZtMvFP%2B63vkDNFeJYshpQVWyMpAWzzEtiW5hmPc%3D&reserved=0)
>>>>
>>>>>
>>>>
>>>> _______________________________________________
>>>> BlindMath mailing list
>>>> BlindMath at nfbnet.org
>>>>
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339704864%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=6U9rPd5Tr4tm8%2FpY%2BcGW%2BbNIE348ZFbzhZHQpydVaJA%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048309295%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=fh70HescVpUod0jijXTAGT68%2B4RkwwkPin%2Bb5NsjACQ%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048309295%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=fh70HescVpUod0jijXTAGT68%2B4RkwwkPin%2Bb5NsjACQ%3D&reserved=0)
>>>> To unsubscribe, change your list options or get your account info for
>>>> BlindMath:
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fmomdadofarushi%2540hotmail.com&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339704864%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=30u%2BG2kjXzKx1PnL%2FvOqdFkXV6XhLJXQoyZSxvmR5EM%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fmomdadofarushi%2540hotmail.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048319253%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=D9ML2zw7k%2FLeKCDasvuuv0p28GCAmE%2BnnXr036M1fKw%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Fmomdadofarushi%2540hotmail.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048319253%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=D9ML2zw7k%2FLeKCDasvuuv0p28GCAmE%2BnnXr036M1fKw%3D&reserved=0)
>>>> BlindMath Gems can be found at <
>>>> https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7C5611d6663714436dada908d94fd4f5eb%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628598339704864%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=7CPmFhO9NZQsRYFhOljHYYzBn4A%2FsVGVlE37LluK%2Fr4%3D&reserved=0
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048319253%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=GcSJ048MkN%2B0BzSF2S%2B4SYtE51bg7mzATT%2FBnS%2BzdvI%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048319253%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=GcSJ048MkN%2B0BzSF2S%2B4SYtE51bg7mzATT%2FBnS%2BzdvI%3D&reserved=0)
>>>>
>>>>>
>>>>
>>>> _______________________________________________
>>>> BlindMath mailing list
>>>> BlindMath at nfbnet.org
>>>>
>>>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048329208%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=J%2BycjHo5H5SSlE8P9K4umpK62gHaD1RcgwDBnE4KJm8%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Flistinfo%2Fblindmath_nfbnet.org&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048329208%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=J%2BycjHo5H5SSlE8P9K4umpK62gHaD1RcgwDBnE4KJm8%3D&reserved=0)
>>>> To unsubscribe, change your list options or get your account info for
>>>> BlindMath:
>>>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/traci.mwd%40gmail.com
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Ftraci.mwd%2540gmail.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048329208%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=jIEbD9zouWq0gDP0Vqgcj4xCAJoFNz8JZ0YfzKjSkQ4%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fnfbnet.org%2Fmailman%2Foptions%2Fblindmath_nfbnet.org%2Ftraci.mwd%2540gmail.com&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048329208%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=jIEbD9zouWq0gDP0Vqgcj4xCAJoFNz8JZ0YfzKjSkQ4%3D&reserved=0)
>>>> BlindMath Gems can be found at <
>>>> http://www.blindscience.org/blindmath-gems-home
>>>>
>>>> [<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048339158%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=Uw4aW%2FsRVd6wRsMkwIVRZocILveaespkvnxyky8JF9M%3D&reserved=0>](https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.blindscience.org%2Fblindmath-gems-home&data=04%7C01%7C%7Cd0997de5e12b4e9e91ed08d94fdba378%7C84df9e7fe9f640afb435aaaaaaaaaaaa%7C1%7C0%7C637628627048339158%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=Uw4aW%2FsRVd6wRsMkwIVRZocILveaespkvnxyky8JF9M%3D&reserved=0)
>>>>
>>>>>
>>>>
>>>> --
>>>
>>> Traci Wilkerson
>>> Cell – 919-971-6526
>>>
>>> --
>>
>> Traci Wilkerson
>> Cell – 919-971-6526
>> _______________________________________________
>> BlindMath mailing list
>> BlindMath at nfbnet.org
>>
>> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
>> To unsubscribe, change your list options or get your account info for BlindMath:
>> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/kfjelsted%40gmail.com
>> BlindMath Gems can be found at
>> [<http://www.blindscience.org/blindmath-gems-home>](http://www.blindscience.org/blindmath-gems-home)
>
> _______________________________________________
> BlindMath mailing list
> BlindMath at nfbnet.org
>
> http://nfbnet.org/mailman/listinfo/blindmath_nfbnet.org
> To unsubscribe, change your list options or get your account info for BlindMath:
> http://nfbnet.org/mailman/options/blindmath_nfbnet.org/rastislav.kish%40protonmail.com
> BlindMath Gems can be found at
> [<http://www.blindscience.org/blindmath-gems-home>](http://www.blindscience.org/blindmath-gems-home)