A surface of general type with \( p_g =q =0, K^2 =1 \)
  We construct a surface of general type with invariants \( \chi = K^2 = 1 \) and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by finding a plane curve with certain singularities, resolving these, and taking the double cover branched along the resulting smooth curve. 
Caryn Werner