devotion & mathematics

  TETRAHEDRON : A tetrahedron is a third dimensional structure having 4 triangles as faces, six edges and four vertices.  A tetrahedron is also called a triangular pyramid.   In a tetrahedron if all four triangles are equilateral triangles then the tetrahedron is called a regular tetrahedron. The volume of a tetrahedron is one-third the area of the base times the height i.e. volume V= (1/3)bh, where b is base and h is height. Also the total surface area is the sum of the surface areas of all it's faces. Here We see some properties of a regular tetrahedron.  Volume = a^3/6√2 Total surface area= (a^2)√3 surface area of each face = (1/4)(a^2)√3 Height =a√6/3,                             here a is the side of regular tetrahedron. #tetrahedron #volume #surfacearea #height #dimension

  HYPERCUBE :                          A hypercube is 4th dimensional analog of a cube . Hypercube is essentially a cube extended into a fourth  dimension.    A hypercube has 8  cubes(3D) as faces, 16 vertices(0 D), 32 edges(1D),24 faces  which are 2D squares.                     { Here D indicates the dimension}   In this hypercube all edges meet at right angles.          Basically if we take a 3D cube , a 3D cube has height, width, breath and area whereas the 4D cube i.e. a hypercube has all the above height, width, breath and area thrice i.e. inner, outer and total.  That means hypercube has inner height, outer height and total height,  inner width, outer width and total width just like the  other two breath and area are also measured for inner, outer and total . Hence totally a hypercube has...

  Why |-2| = 2?                     Everyone know any number which is positive or negative in the modulus turns into positive     i.e. for example |-2|=2 and |2|=2.                 why this happened? Now I explain it in brief.    Before going to that first we see the meaning of | x-y |.     | x-y | means the distance between x and y.          Now |2|= |2-0|                              = the distance between 0 and 2.                              = 2.      Therefor |2|= 2.   Also |-2| = |-2-0|                          = the distance between 0 and -2                 ...

    DIMENSION   :           we often see the 2 dimensional, 3 dimensional objects.           for example square, rectangle, circle are 2 dimensional where as cube, cuboid and sphere are 3 dimensional objects.                                                                    but here a curiosity is that how to measure the  dimension of an object. " An object is said to be of dimension n if its boundary is of dimension n-1 "   for example if we see a square which has boundary 4 lines and since each line is of one dimensional , the total object i.e.,square is of dimension 2.   similarly if we take a cube which is surrounded by 6 squares. since each square is  of dimension 2 , the dimension of cube is 3.  Also here I i...