section_path: Moduli spaces
section_name: Moduli spaces
paragraph_text: Moduli spaces
  
  Considering constants and variables can lead to the concept of moduli spaces. For illustration, consider the equation for a parabola, y = a x 2 + b x + c, {\displaystyle y=ax^{2}+bx+c,} where a, b, c, x {\displaystyle a,b,c,x} and y {\displaystyle y} are all considered to be real. The set of points (x, y) {\displaystyle (x,y)} in the 2D plane satisfying this equation trace out the graph of a parabola. Here, a, b {\displaystyle a,b} and c {\displaystyle c} are regarded as constants, which specify the parabola, while x {\displaystyle x} and y {\displaystyle y} are variables.
  
  Then instead regarding a, b {\displaystyle a,b} and c {\displaystyle c} as variables, we observe that each set of 3-tuples (a, b, c) {\displaystyle (a,b,c)} corresponds to a different parabola. That is, they specify coordinates on the 'space of parabolas': this is known as a moduli space of parabolas.