What is common in all odd numbers
etymology Why are numbers that are divisible by 2 called "even" numbers?
The term "even" number has - this will surprise many - linguistically nothing at all to do with straight lines or that odd numbers were viewed as somehow "crooked".
Etymology: rathjo - rathjan - girat
The "straightness" of lines or numbers goes back to two completely different word stems. The “even” numbers can be traced back to the Gothic word “rathjo”, which simply meant “number”, and this then became a verb (ge) rathjan - to count. This resulted in “girat” in Old High German, which at first meant something like countable, equal.
Nobody really knows why the meaning of the word was later reduced to “straight” in the sense of “divisible into two equal halves”.
One possibility could be: The prefix ge in the Germanic languages (similar to co- or com in Latin) always means that something is connected with each other (best example: gem-lonely). Rathjan was "counting", ge-rathjan could then have got the analogous meaning "counting in pairs", from which girat "counting in pairs" has developed. But maybe it was completely different, I haven't found any reliable sources about it.
It becomes interesting if you go back further and ask: Where does this Gothic word “rathjo” come from? And one or the other may already suspect it: This is probably a borrowing from the Latin "ratio", meaning reason, calculation. The little punch line here is that in mathematics we have even numbers on the one hand, but also the group of rational numbers on the other. But etymologically they are actually identical, go back to the same word. And another word where the root of the word can still be found in German is the "rate".
"Straight" line has a different root: fast and slim
The “straight” line, on the other hand, comes from another word, namely “rado” - which means “fast” and “slim”, and our word “wheel” is also related to it. So you can say: The “straight” line is related to the “wheel”, while the “even” number is related to the rate. These are two completely different stems of the word, a "tea kettle" if you will.
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