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Accessibility Features and Information

“The power of the Web is in its universality. Access by everyone regardless of disability is an essential aspect.” -- Tim Berners-Lee, W3C Director, and inventor of the World Wide Web.

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A summary of the accessibility features offered on this website is given below. Owing to potential compatibility issues, accesskeys are no longer used on this site.

  1. The first link on each page is an invisible ‘Skip to main content’ link that enables screen readers to bypass the standard navigation bar at the top of the page.
  2. Sometimes a puzzle is restated at the beginning of the solution page. In this case, if the puzzle statement is longer than one sentence, an invisible ‘Skip restatement of puzzle’ link is provided.
  3. Links are written to make sense out of context. Many browsers and screen readers (such as JAWS® for Windows, IBM® Home Page Reader, Lynx, and Opera) can extract the list of links on a page and allow the user to browse the list, separately from the page.
  4. Many links have title attributes which describe the link in greater detail, unless the text of the link already fully describes the target.
  5. Adjacent links are separated in one of two ways: (a) structurally, as list elements, or (b) by interposing a non-blank character, such as a vertical bar. This helps screen readers to render the links distinctly.
  6. With one exception, two links with the same link text always point to the same address. The exception is that each hint, answer and solution uses the same link text. However, in this case, a link title (see above) is provided, allowing individual links to be distinguished.
  7. All links can be followed in any browser, even if scripting is turned off.
  8. There are no links that open new windows.
  9. There are no image maps.


  1. All data tables are simple. That is, the column headers for any given data cell are in the same column as the cell, and similarly for the row headers and rows. Column and row headers are always marked up as such, and always form the first column or row. This allows screen readers to render the table intelligently.
  2. Each data table has a caption and a summary. The summary is not displayed visually, but provides an extended description that can be read by a screen reader.
  3. The use of tables for layout purposes is minimized. Their main use is to horizontally align the ‘equals’ sign in successive rows of equations. All layout tables make sense when read line-by-line.


  1. All content images specify equivalent ALT text. Purely decorative graphics include null ALT attributes.
  2. Complex images, which include many mathematical equations, specify a LONGDESC document. This enables screen readers to give an extended text-only description to non-visual readers. This is a work-in-progress.
  3. There are no animated or flickering images.

Overall design

  1. All pages on this site validate as HTML 4.01 Strict. Logical markup reflects the document structure. For example, each puzzle page contains 10 puzzles, each of which is marked up as a header. Since many screen readers are able to jump from heading to heading, it is easy to jump to the next puzzle on a page.
  2. A single externally linked stylesheet is used to deliver a consistent visual layout.
  3. The combination of valid CSS (Cascading Style Sheets) and Strict HTML helps to maintain a separation between content and presentation, enabling the document to be more easily rendered by non-visual user agents.
  4. If your browser does not support stylesheets, or if they are switched off, the content of the page is still readable and usable.
  5. This site uses only relative font sizes, compatible with the user-specified ‘text size’ option in visual browsers.
  6. Although this site makes no use of PDF, it does link to PDF pages. All PDF links are clearly noted as such. For information on using PDF documents, visit Adobe's page on Acrobat accessibility.


I believe that all pages on this site, other than the one listed below, conform to level A of the W3C Web Content Accessibility Guidelines 1.0. To some extent, this is a judgment call. If you find a page that you think does not conform, please let me know. Most pages also conform to most individual level AA and AAA accessibility guidelines.

Pages not in conformance

The following page does not conform to level A of the W3C Web Content Accessibility Guidelines 1.0.

Mathematics and accessibility

Ensuring the accessibility of mathematics poses some special challenges. Clearly, diagrams and geometrical images must be carefully described, in order that people with impaired vision can understand them.

Less obviously, mathematical expressions, whether in text or graphical form, can be difficult to interpret non-visually. They may contain many terms, with complicated nested parentheses. They may contain specialized symbols, such as the integral sign, or matrices. Text is linear in nature, while mathematical equations are two dimensional. Ironically, despite its origins in the scientific community, HTML was not designed to mark up mathematical content, and the current generation of screen readers is not designed to render it.

One solution to this problem may be MathML. MathML is to mathematics what HTML/CSS is to text. It is an XML-based language that encodes the meaning of a mathematical expression, and contains enough presentational information for user agents to provide a useful rendering, whether that be visual or non-visual. Unfortunately, MathML is not yet widely supported, either by visual browsers or by screen readers. Hence this site does not currently use MathML. However, I am interested in exploring this avenue.

This leaves the question of how someone using a screen reader, or a refreshable Braille display, can interpret complex mathematical expressions. I can't really answer this question. In some cases, setting a screen reader to read an expression character-by-character may be sufficient. For more complicated expressions, I aim to provide an extended description, via the LONGDESC attribute. This is a work-in-progress.

I would appreciate any ideas on improving the accessibility of mathematics.

Further reading

  1. Web Accessibility Initiative (WAI)
  2. Web Accessibility In Mind
  3. MathEQ Expression Editor and MathSpeak - MathEQ is a MathML-based equation editor. MathSpeak then creates a textual representation of the equation that is read by screen readers such as JAWS and Window-Eyes, while MathML creates a standard visual representation of the mathematical expression for sighted users.

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Nick Hobson
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Last updated: June 11, 2005