Here’s a visualisation that goes along with Euclid’s elements
A plot of which theorems are used in the proof of each theorem in Euclid’s elements, ordered by the book e.g. the black dots at the bottom say proofs in the book 13 mostly used theorems from all the books bar 7,8,9 and 12.
This was one of many from an article on “The Empirical MetaMathematics of Euclid and Beyond”. It is a long essay on the overarching structure of Euclid’s elements and verifies some claims made about Euclid’s Elements e.g. the proofs were ordered in nearly the most parsimonious way possible. It also finds the most difficult theorems in each book, the greatest possible reductions in proof length, and hints that the network of theorem dependancy has a local 2-d structure. Highly recommend the article.
Here’s a visualisation that goes along with Euclid’s elements
This was one of many from an article on “The Empirical MetaMathematics of Euclid and Beyond”. It is a long essay on the overarching structure of Euclid’s elements and verifies some claims made about Euclid’s Elements e.g. the proofs were ordered in nearly the most parsimonious way possible. It also finds the most difficult theorems in each book, the greatest possible reductions in proof length, and hints that the network of theorem dependancy has a local 2-d structure. Highly recommend the article.