If you're programming a game where a boat moves through water, you might be tempted (as I would) to change the V-shape angle of the waves behind the boat based on how fast the boat was moving!

What if I told you that that V-shaped angle is always 19.47°, regardless of how fast the boat is travelling? 😱

This pattern even holds true for a duck traversing a pond. 🦆

The envelope of these waves stands at a fixed angle, and the wake has a characteristic feathered pattern.

This wake pattern was first explained mathematically by Lord Kelvin (William Thompson) and are known today as the Kelvin wake pattern.
Lord Kelvin described this pattern based on his observations and a rough interpretation of the physics involved. But nowadays we are studying other elements that come into play and can cause small differences based on the object's speed.

Physicists have used satellite images and mathematical modelling to study narrower wakes associated with fast-moving boats. You can read about this discussion here:

Why do we call it the "Square Root"?

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We have been using the popular square root symbol since childhood, yet most of us don't stop to think where it came from.

Let's fix that... 🧵 https://t.co/DkMqpcRSrztwitter.com/i/web/status/1…
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.

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.

I remember reading about determinants in high school. The name was scary and not much context was given. 😦

For a long time, a determinant was just a value I had to blindly compute using a formula.

Here's what I would like to know about determinants when I first started... 🧵 twitter.com/i/web/status/1… The word "determinant" appears when we are learning about matrices.

And since we want to build some *intuition*, let's look at a simple 2x2 matrix first.

We learn that the determinant of a 2x2 matrix is:

| a b |
| c d | = a*d - b*c

But where does that come from?

You know I always add some #math spice into my #gamedev courses, and that usually means touching some cool linear algebra.

But something most students still struggle with is the *intuition* behind the #Determinant of a matrix.

Let's quickly look at it together...🙂

[1/18] 🧵 Since we are really interested in building some *intuition*, let's look at the determinant of a 2x2 matrix first.

When we were in high school, we learned that the determinant of a 2x2 matrix is given by:

| a b |
| c d | = a*d - b-c

But, where does that come from?

[2/18]

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]

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]