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 #geometry

FEW FOURTH DIMENSIONAL OBJECTS   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 ...