Software development. Tech punditry. Retro gaming.
The Sierpiński triangle is what is known as a fractal – a geometric shape that shows structure at arbitrarily small scale, often with a similar appearance as the scale changes. The Sierpiński triangle is basically an equilateral triangle, subdivided recursively into smaller equilateral triangles, ad infinitum. It is named after the Polish mathematician Wacław Sierpiński, although the pattern …
In a previous article we took a look at menu bars in iPadOS and macOS 26. The new operating systems bring some big changes – of particular interest here is menu bars for the first time on the iPad. We outlined new features and differences between the two systems, and some of the issues apps may encounter when using menu …
The next version of iPadOS and macOS is version 26 – based on the year 2026, though due toward the end of 2025. The updates (including iOS and tvOS) bring many changes already discussed on other websites. Briefly discussed by others is the inclusion of menu bars in iPadOS for the first time, though there are also changes to …
At some point in high school students are taught about factorials. A fairly simple concept, the factorial of a non-negative whole number is written as n! and defined as the product (that means you multiply the numbers) of all the positive whole numbers less than or equal to that number. So 5! = 5 ⨉ 4 ⨉ 3 ⨉…
Thinking back to high school you may remember being taught about pi and using it in maths classes to calculate perimeters and areas of circles. You may remember being told a good approximation of pi is 3.14, or 22/7. But you may also recall that pi is irrational (meaning, in maths, that it cannot be expressed exactly as …