Words, pictures & a little mathematics

A notebook begins with a blank page. This one begins with a small demonstration: a few paragraphs, an illustration, and an equation or two. Consider it a type specimen rather than an essay.

A little room for words

The web can still be a place for a page, a picture, and an idea worth spending time with. No hurry to finish. No need to fit everything into a feed.

A page can be small without having to feel unfinished.

There is room here for a point of emphasis, a passing thought, and a path back to the index. Footnotes can live quietly at the bottom of the page.¹

A picture in the margins

An ink study of an elliptical orbit, with a small sun at one focus.

Figure 1. An original line drawing, made for this notebook.

An image can sit alongside an idea without becoming its entire argument. This drawing is a vector image, so the lines stay crisp at any size; ordinary photographs and screenshots work here too.

A little mathematics

Some ideas are easier to write in symbols. An ellipse with semi-axes $a$ and $b$ satisfies

\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.

Its eccentricity is $e = \sqrt{1 - b^2/a^2}$ . When $a=b$ , the ellipse becomes a circle, and $e=0$ .

Longer expressions can take their own space:

\begin{aligned} \int_{-\infty}^{\infty} e^{-x^2}\,dx &= \sqrt{\pi}, \\ \sum_{n=0}^{\infty}\frac{x^n}{n!} &= e^x. \end{aligned}

And the occasional piece of code

from math import pi

def ellipse_area(a, b):
    return pi * a * b

That is enough for a first page. The rest of the notebook is still to be written.

A footnote is a useful place for a small detour. ↩