Spiel Mal Mathe

collatz-collection

A collection of games and interactive statistics about the Collatz conjecture.

Our topic: The Collatz conjecture

1. Procedure

Start with a number n ∊ ℕ

• If n is even → n becomes n / 2.
• If n is odd → n becomes 3n + 1.
• Repeat

2. Examples

8 → 4 → 2 → 1 → 4 → ...

5 → 16 → 8 → 4 → 2 → 1 → 4 → ...

3. Conclusion

Any number sequence of a starting number n ∊ ℕ (Collatz sequence) ends in the following scheme 4 → 2 → 1 → 4 → ...

4. Problem

1.3 has not been proven.

5. Collatz-Steps

The length of the Collatz sequence is the number of steps required to get to the value 1.

mathe-musik

A presentation on how Maths relates to Music.

Technical information

These sites are built using completely static HTML, CSS and JS, as well as some C++ that is compiled to WebAssembly for performance. We don't use warehouses of Node packages, instead we use KaTeX for math rendering, Chart.js for plotting charts, and reveal.js for presentations. The build, of course, requires more dependencies.

Dependencies

For a full rebuild of collatz-collection you will need the following software:

• A POSIX system (sh, mkdir, rm, time, ...)
• make
• inkscape
• imagemagick
• graphviz
• qrencode
• clang++
• lld (for wasm-ld)
• python3
• npx (for babel and html-minify)
• deno (do not install it via snap as Deno.run wouldn't work properly)
• graphviz (for dot)
• Optionally wasmer for testing

and the following fonts:

• Inter
• Manjari

On a Debian-based system, run these commands:

apt install -y make python3 curl inkscape imagemagick graphviz qrencode clang lld-12 nodejs npm fonts-inter

curl -Lo /usr/share/fonts/truetype/Manjari.ttf 'https://github.com/google/fonts/raw/main/ofl/manjari/Manjari-Regular.ttf'

Even though installing deno without the 'install.sh' is recommended, running this command is fast and easy and gets you deno installed.

curl -fsSL https://deno.land/x/install/install.sh | export DENO_INSTALL=/usr/local sh

Building

1. Delete the previous build: make clean
2. Build: make -j$(nproc) all
3. Optionally test and benchmark: make test benchmark