The Italians (around 1100~1200 A.D.) started to trade with the north of Africa. And back then, the north of Africa which was strongly touched by the Islamic empire.
The vast Islamic empire came from the Middle East and expanded to Asia, India, and also Europe.
One famous Italian tradesman was Leonardo Bonacci (Fibonacci).
Fibonacci used to trade between Pisa and what we know today as Algeria.
As he traded with the Islamic people, he acquired a large understanding of their math.
In 1202 he wrote "Liber Abaci."
Fibonacci thought it was important to demonstrate this Islamic math to the Europeans.
Liber Abaci was one of the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals".
By addressing applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system & these glyphs.
In this book, we can find one of the first mentions of something called "Radix Quadratum."
Some early notations used acronyms like "Rad" or just "R".
For example, to express that the square root of 9 is 3, we found manuscripts stating that:
"Rad9a3"
In 1525, Christoph Rudolff used the symbol "√" to represent the square root.
The symbol √ was *probably* inspired by the letter "r" from previous manuscripts.
The complete symbol - with the upper part (√‾‾) to enclose the entire radicand - would only appear in 1637.
And in 1637, René Descartes wrote "La Géométrie", which was the first to propose the idea of uniting algebra & geometry into a single subject (inventing an algebraic/analytic geometry).
It was the first time we saw the symbol that most of us recognize today as "Square Root".
And just to conclude out thread...
The Radix (the root) is what the Islamic called the sides of a square.
If you think about it, with a single side, one knows how to generate the entire square.
That's why the side is, indeed, the root of the shape. 🙂
Boom! ❤️
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Lately, I've been studying the early days of 3D polygons on home consoles for a new course.
We often think 3D on the #PS1 or #Saturn, but there was a bracket of time where special chips were added to both #SNES & #Genesis to help them render fast polygons.
Here's a review...🧵
It's probably not news to anyone here that retro consoles added special power to games by adding special chips *inside* the game cartridges!
Therefore, newer and fancier games were more expensive because manufacturing the cartridge with extra chips cost more for the developers.
If you took our course on #NES programming, you know that this was also true for 3rd gen. consoles.
For example, the NES console is always the same (CPU speed, RAM size, etc.), but NES games got better with time by adding these special chips *per* cartridge!
Since we discussed isometric games in a previous post, let's briefly mention one of the big #devs of this style: Chis Sawyer.
Most retro gamers think Chris' first isometric game was Transport Tycoon, but his journey started 10 years before.
So, let's dive in!
[1/15] 🧵...
In 1984, Chris programmed QOGO.
QOGO was a clone of the popular arcade game #QBert that ran on the Memotech computer.
QBert is one of the most popular arcade games to carry the isometric look. If you are a retro gamer, you probably played (or at least heard of) QBert.
[2/15]
Now, we mortals usually coded for these machines using some sort of BASIC. But we have to remember that BASIC is an interpreted language, meaning every high-level BASIC command needs to be translated to low-level machine code.
This is one of my favorite folklore stories about computer #bugs!
...
In the 1980s, Jake Poznanski had a programming mentor, Sergei, who was writing software for an SM-1800, a Soviet clone of the PDP-11.
[1/10] 🧵
The computer was just installed at a railroad station near Sverdlovsk, a major USSR shipping center at the time. The new system was designed to route trains and cargo to their intended destinations, but there was a nasty bug that was causing random failures and crashes.
[2/10]
The crashes would always occur once everyone had gone home for the night, but despite extensive investigation, the computer always performed flawlessly during manual and automatic testing procedures the next day.