go off on a tangent.

[kjc0123]

Why does the phrase of "go off on a tangent" become to mean "to suddenly start doing, discussing, or thinking about something completely different"?

[Quizmonster]

In mathematics, a tangent is a line that touches a curve or circle. For example, if you place an orange on a table, the table's surface is "at a tangent" to the orange's surface. So, in speech, someone who starts a completely new topic of discussion is also said to have 'gone off on (ot at) a tangent'.

[Quizmonster]

The words in brackets above should read: 'or at', Kjc.

[New Forester]

It particularly refers to where an object is moving in a curve, and then stops being restrained and so continues in a straight line.  Imagine being on the ice with a weight on a string.  Then slide the weight around you faster and faster, and finally let go.  The weight will draw a circle on the ice, then as you let go it will continue in a straight line.  The line touches the edge of the circle -- a tangent.

 

[Merlin]

Further: If a conversation is "going round in circles" or people are "talking in circles", then the participants keep repeating themselves and discussing the same details and arguments over and over again.

I was in a meeting with company directors when the managing director castigated (there's a good word) someone for going off at a tangent. He immediately replied "Well, if we don't go off at a tangent, we'll just keep talking in circles - and that will get us nowhere!".

[mje1066]

More simply, a tangent is a line drawn at right angles to a given line. From this the metaphorical meaning is clear.

[jocook17]

simply put, it means having a very loose connection to the original subject. It must have some vague connection otherwise that would just be changing the subject. It is usually irrelevant but mildy interesting.

i.e, a discussion on how to grow oranges, and then someone begins to talk about their grandmother - seemingly unnconected but the speaker is reminded - because of the oranges - of when, as a child his gran  used to make orange jam and in telling about the jam, they mention the strawberry jam she made too which leads on to the homemade bread, then the really nice bread you can buy at the bakers down the road, how the baker got divorced etc etc - oranges and divorce in one conversation