nycki

I'm currently trying to set up a homebrew cassette tape storage format, but trying to use existing tech where possible. I was excited to see that minimodem already exists for converting an audio stream to a byte stream, and is even available in termux for android, so I could decode cassettes with my phone! However, I'd like some sort of higher-level tool to encode and decode "packets" or "slices" so that I can add error correction. I'm sure this sort of thing must exist for amature radio purposes.

I could write a script that cuts a file into slices, with checksums and redundancy for each slice, and then pads them with null bytes so I can isolate each frame when decoding. What I want is to find out if that's already been done. I've heard of AX.25 packets but I can't find a tool that does that with stdio.

This article says that NASA uses 15 digits after the decimal point, which I'm counting as 16 in total, since that's how we count significant digits in scientific notation. If you round pi to 3, that's one significant digit, and if you round it to 1, that's zero digits.

I know that 22/7 is an extremely good approximation for pi, since it's written with 3 digits, but is accurate to almost 4 digits. Another good one is √10, which is accurate to a little over 2 digits.

I've heard that 'field engineers' used to use these approximations to save time when doing math by hand. But what field, exactly? Can anyone give examples of fields that use fewer than 16 digits? In the spirit of something like xkcd: Purity, could you rank different sciences by how many digits of pi they require?