ยง Bondi k-calculus
An alternative formalism to derive special relativity geometrically,
resting purely on hypotehses about the way light travels.
However, I've not been able to prove the correctness of the assumptions made,
by using coordinate geometry. I suspect this is because I will need to use
hyperbolic geometry for the "side lengths" to work out.
Indeed, I found another source, called as The k-calculus fiddle
which attempts to discredit k-calculus. The author of the above blog writes at
the end:
In asking Ray D'Inverno's permission to use his book as the example of k-calculus, he was kind enough to point out that the arguments I have given are invalid. Chapter 2 of his book should be read through to the end and then reread in the light of the fact that the geometry of space and time is Minkowskian. Euclidean geometry should not be used in interpreting the diagrams because their geometry is Minkowskian.
which seems to imply that we need to use hyperbolic geometry for this.