Mathemagics

Article by Pierre Cartier

In collections: Notation and conventions, The act of doing maths

My thesis is:there is another way of doing mathematics, equally successful, and the two methods should supplement each other and not fight.

URL: http://ftp.gwdg.de/pub/misc/EMIS/journals/SLC/wpapers/s44cartier1.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Mathemagics

The innovation here seems to be in the emphasis placed on the properties of the sum of the roots and the product of the roots.

And now, substituting into the formula for \(r\) and \(s\), we get \(r, s = -\frac{b}{2} \pm \sqrt{\frac{b^2}{4} - c}\).

But this is just the same as \(\frac{-b \pm \sqrt{b^2 - 4c}}{2}\), which is exactly what we would expect from the standard formula, given that \(a=1\)! The general derivation, for \(a \neq 1\), takes a few more steps, but is fairly straightforward.

Now, the only way we can have \(r+s = -b\) is if \(r = -\frac{b}{2} + z\) and \(s = -\frac{b}{2} - z\), for some \(z\).

Since \(rs = c\), this means that \(c = \frac{b^2}{4} - z^2\).

Rearranging, we get \(z = \pm \sqrt{\frac{b^2}{4} - c}\).

The trick is as follows: Assume, first of all, that \(a=1\), and let \(r\) and \(s\) be the (unknown) roots. Then we can write \(x^2 + bx + c = (x - r)(x - s)\).

Expanding the right-hand side, we get \(x^2 + bx + c = x^2 - (r+s)x + rs\).

So we have \(r + s = -b\), and \(rs = c\).

I've just discovered something incredible: Jim Fowler has compiled TikZ to WebAssembly! That means you can render TikZ diagrams in web pages, **on the fly**!!

I've made a demo page with an editor, so you can see it and believe it: https://tikzjax-demo.glitch.me

Earliest Uses of Various Mathematical Symbols

Web page by Jeff Miller

In collections: History, Notation and conventions

These pages show the names of the individuals who first used various common mathematical symbols, and the dates the symbols first appeared. The most important written source is the definitive A History of Mathematical Notations by...

URL: http://jeff560.tripod.com/mathsym.html

Entry: http://read.somethingorotherwhatever.com/entry/EarliestUsesofVariousMathematicalSymbols

What are your favorite tiny tools when working with data?

Here are three examples:

→ http://ucbvislab.github.io/d3-deconstructor/ to get the data out of d3 visualizations

→ https://shancarter.github.io/mr-data-converter/ convert CSV to JSON

→ https://countries.zeto.io input country name, output country codes (by @zeto@twitter.com)

This is fun! #LaTeX typing game! My PB so far is 36, what's yours?

Yesterday, I played a game of Dialect with @skalyan and two other people in the Guild in Canberra. We narrated the story and language of the bots in charge of maintaining and preserving Waste-/Land, a nature reserve/hazard waste dump planet long forgotten by humanity. The game worked really well (I think it deserves its ENnie nomination), apart from the fact that we were not good at streamlined Conversation framing and resolution, but that can be improved by re-reading the rules.

Leiden wall formulas: http://muurformules.nl/

The last time I was in Leiden they were decorating the exterior walls of all their buildings with poems of many different languages. Now they've moved on to the language of mathematics.

“Rudolph the Red-Nosed Reindeer” in Anglo-Saxon meter https://t.co/LoqOnmXkul #linguistics

- Favourite Unicode math font
- Libertinus

- Currently studying
- Category theory; group theory

Joined Jul 2018