Saik Anam Joaddar Siam

The question that I actually I started out was, Is there any way to express transcendental functions using polynomials avoiding the idea of limits or infinitesimal quantities?   Origin of the Question Nowadays,we learn about the Cauchy-Weierstrass interpretation of limits in our calculus classes.Although I genuinely think that it works and it’s more convenient but I thought there would be creative other ways to do this without the idea of estimating infinitesimal quantities.I found one paper named “ The Lost Calculus ”[1],it avoids the idea of abstract limits but fails when it comes to transcendental functions.I knew that if I broke down the sine function to be humble polynomials I could than use something like Descartes’s method[1] of Tangents to that polynomial to get the derivative without using the idea of limits. That’s when I was stumbled upon this question. First thing that came to my mind was a sine function,I was thinking if there was any way to represen...

Date: 9-26-2017 Original Question: By how many different ways a rubik’s cube can be arranged? Solution: A rubik’s cube has 8 corners, which can be arranged in 8! different positions,and have 3 possible orientations,which gives 3^8 possibilities.But only ⅓  of them have the correct corner orientation as the original rubik’s cube. 12 edges give you 12! Different positions and 2 possible orientations give you 2^12 possibilities. ½  of them have the correct edge orientation of the rubik’s cube,and only ½ of the possible combinations is achievable because no two pieces can be moved by isolation,so to sum up, Follow up question,is there any generalized approach for finding out all the possible combinations of NxN dimensional cubes? Trying to solve this problem analytically I met a lot of hurdles,as the possible different combinations for the cubes of even dimensions were different than the ones of odd dimensions, because of orientational parity of even dimensioned ...