Is there anything like an experiment in mathematics? And if this is the case, what would distinguish a mathematical from thought experiment? In present paper, framework for practice of mathematics will be put forward, which consider as experimenting activity and proving activity. The relationship between these two activities explored more importantly distinction thought-experiments, real experi...

Beginning with digitized volumetric data, we wish to rapidly and efficiently extract and represent surfaces defined as isosurfaces in the interpolated data. The Marching Cubes algorithm is a standard approach to this problem. We instead perform a decomposition of each 8-cell associated with a voxel into five tetrahedra, as in the PayneToga algorithm [Payne and Toga, 1990]. Following the ideas o...

The author and Rohatgi recently proved a ‘shuffling theorem’ for doubly-dented hexagons. In particular, they showed that shuffling removed unit triangles along horizontal axis in hexagon changes the tiling number by only simple multiplicative factor. this paper, we consider similar phenomenon symmetry class of tilings, namely, reflectively symmetric tilings. We also prove several theorems halved

It is well known that primitive Pythagorean triangles have integer inradius and exradii. We investigate the generalization to primitive Heronian triangles. In particular, we study the special cases of isosceles triangles and triangles with sides in arithmetic progression. We also give two families of primitive Heronian triangles, one decomposable and one indecomposable, which have integer inrad...