Why is the Fermi surface called a sphere in 1D and 2D?

[helpcometk]

Homework Statement

Consider an electron gas in ONE and TWO dimensions i.e N electrons in a metal wire with length L or in metal sheet with area L^2.

Pictures must be drwan of the fermi 'sphere' and the Fermi 'surface' .
Why are the two words in quotation marks ?

Homework Equations

The Attempt at a Solution

From hours of research i did on the WEB .(Im not by no means an expert in SOLID STATE PHYSICS), i managed to find only that in one Dimension the fermi surface is 2 planes separted by distance 2Kf.

Ascroft and Mermin as well as Kittel to my knowledge cannot answer this Question.
Any Experts in Solid state Physics who can Help ?

 

[member 553083]

The two words are in quotation marks because Fermi surfaces and Fermi spheres are not actually surfaces or spheres; they are mathematical abstractions used to conceptualize the behavior of electrons in a solid.