Re: [math-fun] Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine

I tried to find equations in R^3 for the trefoil defined initially in R^4 = {(x,y,z,w)}: (x+iy)^2 + (z+iw)^3 = 0 and x^2 + y^2 + z^2 + w^2 = 1 but which is then stereographically projected into R^3 = {(X,Y,Z)} via X = x/(1-w), Y = y/(1-w), Z = z/(1-w). If my algebra is right, the final (two) equations are 4(X^2 - Y^2)(X^2 + Y^2 + Z^2 + 1) + 8 Z^3 - 6 Z W^2 = 0 & 8 X Y (X^2 + Y^2 + Z^2 + 1) + 12 Z^2 W - W^3 = 0 where W is short for (X^2 + Y^2 + Z^2 - 1). I can't tell for sure if it looks right when I try to plot it in 3D using Mac "Grapher". —Dan