Volume of a sphere
We want to calculate the volume 
of a sphere 
with radius 
.
Approximating the sphere with thin cylinders of heights
, for 
, and
approaching the limit, we get 
. Substituting 
and
, gives 
.
Utility for writing LaTeX equations within HTML
| Overview | Download | Documentation |
Gladtex is a utility that enables LaTeX equations within HTML code. You write HTML code as usual, but in addition you can include equations within the special tags <EQ>..</EQ>, as if within $$..$$ in LaTeX. For example, your source might look as follows:
|
<H3>Volume of a sphere</H3> <P> We want to calculate the volume <EQ>V</EQ> of a sphere <EQ>S^2 \subset \mathbb{R}^3</EQ> with radius <EQ>r</EQ>. </P> <P> Approximating the sphere with thin cylinders of heights <EQ>2\sqrt{r^2-t^2}</EQ>, for <EQ>t \in [0,r]</EQ>, and approaching the limit, we get <EQ>V = \int_0^r 2\pi t 2\sqrt{r^2-t^2}dt</EQ>. Substituting <EQ>u = r^2 - t^2</EQ> and <EQ>\frac{du}{dt} = -2t dt</EQ>, gives <EQ>V = -2\pi\int_{r^2}^0 \sqrt{u}du</EQ> <EQ>=2\pi\frac{2}{3}(r^2)^{3/2}</EQ> <EQ>=\frac{4}{3}\pi r^3</EQ>. </P> |
Then you run gladTeX, which outputs an HTML-file with the equations replaced by images. The result looks like this:
Volume of a sphere
We want to calculate the volume
Approximating the sphere with thin cylinders of heights
|
Features:
Gladtex is mainly tested on Linux-i386, but should compile and run on a wide range of unices. There is also a version that runs on Windows; see the download page.
Martin G. Gulbrandsen
http://folk.uio.no/martingu
