Cutting a torus

Here is the problem - a torus must be cut in 4 parts, so that: (1) all parts have exactly the same shape; and (2) all parts are topologically equivalent to a torus (i.e. they have a hole).

This animation shows a solution to this problem. The result is a set of completely interlinked rings. As a side effect, this solution generates a new problem. It is: if the torus is made of metal, i.e. its parts cannot be deformed by hand, would it be still possible to unscrew the four parts as it is shown in this animation? Or would these part be stuck forever in the shape of a torus?

What do you think?

Category:

Film & Animation

Tags:

• Elica
• Logo
• demo
• torus
• cut
• problem

[ElicaTeam]

@jotape1960 It depends on what part of the mathematics you have in mind. For example, the topological definition is quite different from the analytical. If you are curious about the algebraic surface of a torus, in Cartesian coordinates it is:

r^2=(R-sqrt(x^2+y^2)^2+z^2

If you prefer polar parameters (u,v) then it is:

x = [R+r.cos(v)].cos(u)

y = [R+r.cos(v)].sin(u)

z = r.sin(v)

[jotape1960]

How is, mathematically, defined a Torus? ???