Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Display Omitted Scissor shears are affine transformations in 3-space that, in analogy with the usual rotations, can be understood as hyperbolic rotations about a fixed line, in a fixed coordinate frame.  study algebraic surfaces invariant under scissor shears, and investigate their similarities and differences with the algebraic surfaces invariant under the usual rotations, namely the algebraic surfaces of revolution. In particular,  provide a necessary condition for an algebraic surface to be invariant under scissor shears, and  prove that such shear invariant surfaces can have either one, three, or infinitely many scissor axes. Furthermore,  characterize the surfaces with either three or infinitely many scissor axes. Additionally, in each case  show how to calculate the location of these scissor axes as ll as the rest of the coordinate frame.
['Juan Gerardo Alcázar', 'Ron Goldman', 'Carlos Hermoso']
I am writing a research paper on a idea Algebraic surfaces invariant under scissor shears
[{"from": "human", "value": "I am writing a research paper on a idea Algebraic surfaces invariant under scissor shears"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Display Omitted Scissor shears are affine transformations in 3-space that, in analogy with the usual rotations, can be understood as hyperbolic rotations about a fixed line, in a fixed coordinate frame.  study algebraic surfaces invariant under scissor shears, and investigate their similarities and differences with the algebraic surfaces invariant under the usual rotations, namely the algebraic surfaces of revolution. In particular,  provide a necessary condition for an algebraic surface to be invariant under scissor shears, and  prove that such shear invariant surfaces can have either one, three, or infinitely many scissor axes. Furthermore,  characterize the surfaces with either three or infinitely many scissor axes. Additionally, in each case  show how to calculate the location of these scissor axes as ll as the rest of the coordinate frame."}]