# Theorem Network from Euclid's Elements

Graph of interdependence of theorems from Euclid's Elements

## Details

The nodes correspond to theorems, common notions and postulates.
Each node is a connected to nodes corresponding to the theorems etc. referenced in its proof.
A version of this network originally appeared in A New Kind of Science (Wolfram, 2002) on page 1176.

## Examples

### Basic Examples

Retrieve the basic network:

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Make a layered graph plot:

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Find axioms and theorems referenced by Book 1, Theorem 5:

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### Analysis

Count the total number of theorems + axioms:

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Find the axioms:

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Find the distribution of numbers of theorems referenced:

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Find the 5 most referenced theorems:

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Find the total number of theorems + axioms that ultimately contribute to the proof of each theorem:

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Create a key of axiom + theorem number:

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Make a map of what theorem references which others:

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Wolfram Research, "Theorem Network from Euclid's Elements" from the Wolfram Data Repository (2020) https://doi.org/10.24097/wolfram.61787.data