Bondi k-calculus

Bondi k-calculus is a method of teaching special relativity popularised by Sir Hermann Bondi, that has been used in university-level physics classes (e.g. at the University of Oxford^[1]), and in some relativity textbooks.^{[2]: 58–65 [3]}

The usefulness of the k-calculus is its simplicity. Many introductions to relativity begin with the concept of velocity and a derivation of the Lorentz transformation. Other concepts such as time dilation, length contraction, the relativity of simultaneity, the resolution of the twins paradox and the relativistic Doppler effect are then derived from the Lorentz transformation, all as functions of velocity.

Bondi, in his book Relativity and Common Sense,^[4] first published in 1964 and based on articles published in The Illustrated London News in 1962, reverses the order of presentation. He begins with what he calls "a fundamental ratio" denoted by the letter ${\displaystyle k}$ (which turns out to be the radial Doppler factor).^[3]: 40 From this he explains the twins paradox, and the relativity of simultaneity, time dilation, and length contraction, all in terms of ${\displaystyle k}$. It is not until later in the exposition that he provides a link between velocity and the fundamental ratio ${\displaystyle k}$. The Lorentz transformation appears towards the end of the book.