Equations in Knol

An introduction to the Knol Equation Editor

What is ?
Using the Equation Editor in Knol
Examples
The definition of Euler's Number ()
Taylor Series
Schrödinger equation
Resources

HTML is the markup language that powers much of Internet and is used as the basis for all read words in Knol. You can insert an image into your knol and embed a Google Document or Google Spreadsheet, but expressing complex mathematical formulas can be a real challenge with standard HTML. Superscripts, subscripts, punctuation symbols and parenthesis can express a simple formula like: a² + b² = c², but to express large equations that involve multiple levels and symbols not found on a traditional keyboard, you need the power of a different markup language called: $\small{\LaTeX}$ .

What is $\large{\LaTeX}$ ?

$\small{\LaTeX}$ is a document preparation system for high-quality typesetting that is most often used for scientific publications on paper or PDF/PostScript format [1] but subsets of the $\small{\LaTeX}$ language can also be used to express mathematical formulas. $\small{\LaTeX}$ is based on the $\small{\TeX}$ typesetting system developed in the 1970's.

This markup language beautifully aligns, sizes and indents mathmatical symbols after they are expressed using a combination of standard letters, words and punctuation characters. The typical $\small{\LaTeX}$ equation is difficult to read until it is rendered by the typesetting engine that produces an image with the right size, layout and margins that you would expect to see in the equation if it were written in a book. For example, the $\small{\LaTeX}$ markup denoted by: F(x) = \int_a^x f(t)\, dt\, (the fundamental theorem of calculus) is rendered into the image:

$F(x) = \int_a^x f(t)\, dt\,$

Even though $\small{\LaTeX}$ can be used to format and markup entire documents, we only support the subset of the $\small{\LaTeX}$ language that is used to describe mathematical equations and expect that you'll use the standard knol editor to handle formatting for the rest of your document.

Using the Equation Editor in Knol

To add an equation like the fundamental theorem of calculus to your knols, simply place the cursor at the position that you would like the equation to be displayed and open the equation editor found in the [Insert] menu of the editing toolbar.

The opened equation editor with blank input

Once the equation editor is opened, you can begin to type the markup symbols needed to render your equation. If you are unfamiliar with $\small{\LaTeX}$ markup or need help remembering a symbol's format, we have a palette of commonly used symbols and equation templates that you can visually browse. Once you've found the symbol you're looking for, just click it to have that symbol inserted into your equation in-progress.

Browsing symbols using the palette

As you change your equation in the editor input dialog, you'll see a live preview of how your equation will be rendered. When you are finished editing the equation, simply click the "Insert equation" button to have that preview image inserted into your document.

Once you have inserted an equation, you can change it at any time by clicking on the equation and then the "Edit" link in the popup bubble. There is a also a link there to delete your equation, if needed.

The "Edit" and "Remove" links

Equation images are treated similarly to regular text in the Knol editor in the way that they can be copied, pasted, given a line of their own, fit next to regular text and even centered or right-aligned.

Examples

The definition of Euler's Number ( $e$ )

$e = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n$
e = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n

Taylor Series

$\sum_{n=0} ^ {\infty} \frac {f^{(n)}(a)}{n!} \, (x-a)^{n}$
\sum_{n=0} ^ {\infty} \frac {f^{(n)}(a)}{n!} \, (x-a)^{n}

Schrödinger equation

$i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = \hat H \Psi(\mathbf{r},\,t)$
i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},\,t) = \hat H \Psi(\mathbf{r},\,t)

$\large{\LaTeX}$ Resources

There are many references, tutorials and primers on the web that can help you get started with writing $\small{\LaTeX}$ equations. There are a few listed here, but feel free to suggest your favorites!