quoting from the paper: Although innocent at the first glance, origami surpasses the power of “compass and straight-edge”and can solve third-order mathematical

quoting from the paper: Although innocent at the first glance, origami surpasses the power of “compass and straight-edge”and can solve third-order mathematical problems including the “angle trisection” and “doubling the cube” quoting from the paper: From the technological side, origami is a generic methodology to transform between 2d and 3dgeometries. Does anyone know if you had a mechanical "liquid paper notebook" where the marks on the notebook are rotating micro-balls (from 0% to 100% black) if you could use origami as a way of expanding out an originally folded sheet of a large size (say 11 x 14 - legal size paper) where the folded version might be the size of a paperback book? On a different note, I think I know what angle trisection is, but I'm not sure what "doubling the cube" might mean. Does anyone know what geometric problem the author is referencing ?