Interesting Esoterica

Dependency Graph of Propositions in Euclid’s Elements

Article by Thomson Nguyen
  • Published in 2007
  • Added on
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This is a dependency graph of propositions from the first book of Euclid’s Elements. We say that a proposition \(A\) depends on \(B\) iff proposition \(B\) is necessary in the proof of proposition \(A\). In the dependency graph below,this will be denoted by an arrow starting at \(A\) and pointing at \(B\). Figure 1 is a dependency graph of all propositions in the first book. Figure 2 is a dependency graph of all propositions that state a relation between two objects, while Figure 3 is a dependency graph of all propositions that state the existence of an unmarked straightedge and compass construction of something.The dependencies were gratefully extracted from Richard Fitzpatrick’s edition of Euclid’s Elements. The graph itself was written in DOT and converted to pslatex with dot2tex. The motivation for this graph was from Mariusz Wodzicki’s Spring 2007 History of Mathematics course at the University of California, Berkeley. Corrections and comments are always appreciated at thomson@ocf.berkeley.edu.

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BibTeX entry

@article{DependencyGraphOfPropositionsInEuclidsElements,
	title = {Dependency Graph of Propositions in Euclid’s Elements},
	abstract = {This is a dependency graph of propositions from the first book of Euclid’s Elements. We say that a proposition \(A\) depends on \(B\) iff proposition \(B\) is necessary in the proof of proposition \(A\). In the dependency graph below,this will be denoted by an arrow starting at \(A\) and pointing at \(B\). 

Figure 1 is a dependency graph of all propositions in the first book. Figure 2 is a dependency graph of all propositions that state a relation between two objects, while Figure 3 is a dependency graph of all propositions that state the existence of an unmarked straightedge and compass construction of something.The dependencies were gratefully extracted from Richard Fitzpatrick’s edition of Euclid’s Elements. The graph itself was written in DOT and converted to pslatex with dot2tex. The motivation for this graph was from Mariusz Wodzicki’s Spring 2007 History of Mathematics course at the University of California, Berkeley. Corrections and comments are always appreciated at thomson@ocf.berkeley.edu.},
	url = {https://www.ocf.berkeley.edu/{\~{}}thomson/euclid/euclid.pdf},
	year = 2007,
	author = {Thomson Nguyen},
	comment = {},
	urldate = {2021-04-14},
	collections = {history}
}