For inductors, the word "form" is used for the thing you wind the coil on. It is what gives form to the coil while winding it.
- In some inductors, the form is removed after winding. These are usually coils made of stiff wire that will keep its shape without the form.
- In some inductors, the form remains in the inductor after winding. These inductors usually have fine wire or are very small - the wire can't hold the coil shape by itself.
- In some inductors, the form is part of the inductor. The form in such cases may be of metal or pressed ferrite particles. The metal or ferrite core increases the inductance, making it possible to get a higher inductance in a smaller volume.
Hobbyists used to wind their own inductors rather than order a specific value from a manufacturer. In such hand made parts, it was common to wind the inductor around the body of a resistor. If the wire was stiff, you could later remove the resistor. If not, the carbon composition contruction of the resistor body meant that it wouldn't have any noticeable effect on the inductance of the coil.
In really olden days, people made simple AM radios using large air-core coils. They would wind the coil around a cylinder shaped box of oatmeal, thethen remove the box when the coil was complete.
The oatmeal box was the form.