3
$\begingroup$

When saying graph in mathematics, it can be either a graph of a function, or a graph in graph theory. However mathematically they have nothing in common. How did they get the same name?

I know graph theory has been invented by Euler (the seven bridges of Königsbergen, 1736), but I haven't been able to find the history of graphing a function. My guess is that Leibniz had done that as well while discovering functions.

Of course, they both have something related to graphical things, but you might as well say that about geometry, topology and often also combinatorics, so that isn't really a statistifactory argument.

How did 'graphing' a function and 'graph' theory get the same name? Was it a confusion, or did they have a common ancestor?

Improve this question
$\endgroup$
5
  • $\begingroup$ If you look on the Wikipedia pages for "graph of a function" and "graph theory" and compare the tables of links to the same pages in other languages then you'll see that in most (but not all) languages besides English the term graph for a function's graph and for the combinatorial object are not the same. $\endgroup$
    – KCd
    Jul 10, 2015 at 19:04
  • $\begingroup$ @KCd I'm not sure if I'd agree with that. Dutch ('grafiek' vs. 'graaf'), French ('graphe' vs. 'graphe d'une function'), and German ('Graph' vs. 'Funktionsgraph'). Chinese (函数图形 vs.图, where 函数 means function), which is You see, the words have just the word for function added. $\endgroup$
    – wythagoras
    Jul 10, 2015 at 19:12
  • $\begingroup$ I was not counting the examples with the word function in them. Though why do you single out Dutch as an example of that? I do not know Dutch, but grafiek and graaf do not involve the word for function (functie). $\endgroup$
    – KCd
    Jul 10, 2015 at 19:46
  • 1
    $\begingroup$ For history of function graphs see hsm.stackexchange.com/questions/2378/… and dam.brown.edu/people/mumford/beyond/coursenotes/2006PartIb.pdf $\endgroup$
    – Conifold
    Jul 11, 2015 at 0:58
  • $\begingroup$ @KCd No, that was just an example of the similarity between them. $\endgroup$
    – wythagoras
    Jul 18, 2015 at 19:19

1 Answer 1

Reset to default
7
$\begingroup$

All these words come from the same Greek root, "graphein" means to write in Greek. Later the meaning extended to include drawing. Also graphite, graphology, graphics (drawing), graphoman etc. Also photography, biography, histogram, cardiogram, grammar and telegraph have the same root. Graphs of functions and graphs in combinatorics are something that we draw, pictures.

Improve this answer
$\endgroup$
4
  • $\begingroup$ γράφω (“to scratch, to scrape, to graze”) and γραμματικὴ (art) are different roots. $\endgroup$
    – Conifold
    Jul 11, 2015 at 0:53
  • 4
    $\begingroup$ @Conifold. On the contrary: γράφω and γράμμα (<*graph-ma) are from the same root. $\endgroup$
    – fdb
    Jul 11, 2015 at 12:17
  • $\begingroup$ @fdb Interesting, so φω and μα are suffixes. What is the original meaning of γρά? $\endgroup$
    – Conifold
    Jul 13, 2015 at 18:40
  • 1
    $\begingroup$ @Conifold. No, the underlying Indo-European root is *gerbh-, zero-grade *grbh-, ‘to scratch’. In Greek the latter develops regularly to graph-, whence the verb (present) graph-ō, (aorist) e-grap-s-a, etc. -mat- is a common formative for neuter nouns, so graph+mat- > (nominative) gramma, (genitive) grammat-os, adjective grammat-ik-os, etc. $\endgroup$
    – fdb
    Jul 13, 2015 at 19:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.