A star is a fire ball in space. When you are on the earth you can see that it is a star shape. Why is this so?

Answer 1

It's caused by viewing them through the Earth's atmosphere. Seeing them from space, they do not 'twinkle'.

Answer 2

What is a star shape? How do you define it? There is a mathematical definition for any other 3-D shape:
Cube:
The cube is the Platonic solid P_1 (also called the regular hexahedron). It is composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron U_6 and Wenninger model W_3. It is described by the Schläfli symbol {4,3} and Wythoff symbol 3|24.

Sphere:
A sphere is defined as the set of all points in three-dimensional Euclidean space R^3 that are located at a distance r (the "radius") from a given point (the "center"). Twice the radius is called the diameter, and pairs of points on the sphere on opposite sides of a diameter are called antipodes.

Pyramid:
A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right pyramid is a pyramid for which the line joining the centroid of the base and the apex is perpendicular to the base. A regular pyramid is a right pyramid whose base is a regular polygon. An n-gonal regular pyramid (denoted Y_n) having equilateral triangles as sides is possible only for n==3, 4, 5. These correspond to the tetrahedron, square pyramid, and pentagonal pyramid, respectively.

A star is a 3-D object in the space, yet we only have a definition for its 2-D form:

Star:
A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a circumference. The number q is called the density of the star polygon. Without loss of generality, take q

Answer 3

That's due to aperture effects in your eye or atmospheric effects.

Ground based telescopes show the expected images of stars.

Answer 4

The way the light comes off it and the Earth's atmosphere.