Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them. We show that there are 16 equivalence classes of minimal convex imaginary cubes, among whose representatives are a hexagonal bipyramid imaginary cube and a triangular antiprism imag...

Unlike the Metelli monochrome transparencies, when overlays and their backgrounds have chromatic content, the inferred surface colors may not always be physically realizable. In these cases, the inferred chromatic transmittance or reflectance of the overlay is imaginary, lying outside the RGB spectral boundaries. Using the classical Metelli configuration, we demonstrate this illusion, and brief...

Presently, factorials of real negative numbers and imaginary numbers, except for zero and negative integers are interpolated using the Euler's gamma function. In the present paper, the concept of factorials has been generalised as applicable to real and imaginary numbers, and multifactorials. New functions based on Euler's factorial function have been proposed for the factorials of real negativ...

The recent detection by the BICEP2 collaboration of a high level of tensor modes seems to exclude the Starobinsky model of inflation. In this paper we show that this conclusion can be avoided: one can embed the Starobinsky model in supergravity and identify the inflaton field with the imaginary (instead of the real) part of the chiral scalaron multiplet in its formulation. Once coupled to matte...

Past research with 152 preschoolers found that having an imaginary companion or impersonating an imaginary character was positively correlated with theory of mind performance. Three years later, 100 children from this study were retested to assess the developmental course of play with imaginary companions and impersonation of imaginary characters and how these types of role play were related to...

The imaginary cone of a Kac-Moody Lie algebra is the convex hull of zero and the positive imaginary roots. This paper studies the imaginary cone for a class of root systems of general Coxeter groups W . It is shown that the imaginary cone of a reflection subgroup of W is contained in that of W , and that for irreducible infinite W of finite rank, the closed imaginary cone is the only non-zero, ...