What is the definition of Curve

I recently joined an Investment Bank and I see lot of mentions of a term called Curve. Typically, a text book does not put such an emphasis on this term.

So my question, what is the definition of Curve in IB world? Is it basically, a group of risk factors like say discount factor at time 1/2/3/... year

Appreciate if someone share any detailed explanation

• There are many curves, the most important is this one ustreasuryyieldcurve.com (and it is in every textbook) Sep 5 at 5:30
• You can read the methodology for Euro area yield curves here. The idea of Interest rate swap curves is outlined in this answer. As @nbbo2 mentioned, any textbook should discuss curves though. Sep 5 at 6:16

In my books, mainly about IRS trading, I actually go into quite of lot of detail about curves. But it suffices to say that a Curve in finance represents datetime indexed values. for example a set of (date, discount factor) pairs: $$\{(d_1, v_1), .., (d_n, v_n)\}$$. Ideally one requires a pair of (date, values) for every possible date. Practically curves tend to employ interpolation to fill in gaps when the curve is parametrized by a smaller set of pairs.
As with many things in finance there tends to be some overlap with different people's use of the word Curve. As an analogy I am European, if someone says the temperature is going to be 90 degrees tomorrow that is meaningless to me. I will always convert that value (which is Fahrenheit) to Celsius, before making any decisions, such as whether to wear a coat etc..
Similarly some Curves are isomorphisms of one another. For example a set of (date, discount factors) is isomorphic to a set of (date, continuously compounded zero coupon rates) which is isomorphic to a set of (date, overnight rates).