Appendix 4 The HTML with embedded picture of math notation

The most obvious problems with HTML for mathematical communication are of two types.

Display Problems. Consider the equation . This equation is sized to match the surrounding line in 14pt type on the system where it was authored. Of course, on other systems, or for other font sizes, the equation is too small or too large. A second point to observe is that the equation image was generated against a white background. Thus, if a reader or browser resets the page background to another color, the anti-aliasing in the image results in white `halos'. Next, consider the equation shown with the equation's horizontal alignment axis above the tops of the lower-case letters in surrounding text.

This equation has a descender which places the baseline for the equation at a point about a third of the way from the bottom of the image. One can pad the image like this: , so that the centerline of the image and the baseline of the equation coincide, but this causes problems with the inter-line spacing, which also makes the equation difficult to read. Moreover, center alignment of images is handled in slightly different ways by different browsers, making it impossible to guarantee proper alignment for different clients.

Image-based equations are generally harder to see, read and comprehend than the surrounding text in the browser window. Moreover, these problems become worse when the document is printed. The resolution of the equations will be around 70 dots per inch, while the surrounding text will typically be 300 or more dots per inch. The disparity in quality is judged to be unacceptable by most people.

Encoding Problems. Consider trying to search this page for part of an equation, for example, the `=10' from the first equation above. In a similar vein, consider trying to cut and paste an equation into another application; even more demanding is to cut and paste a subexpression. Using image-based methods, neither of these common needs can be adequately addressed. Although the use of the alt in the document source can help, it is clear that highly interactive Web documents must provide a more sophisticated interface between browsers and mathematical notation. Another problem with encoding mathematics as images is that it requires more bandwidth. By using markup-based encoding, more of the rendering process is moved to the client machine. Markup describing an equation is typically smaller and more compressible than an image of the equation.