Number 5

                                        Importance of 5

1.      It is the fifth number of Fibonacci sequence. In Fibonacci sequence the next number is the sum of the previous two. Example: - 1, 1, 2, 3, 5, …

2.      With naked eye we can see 5 planets – Mercury, Venus, Mars, Saturn and Jupiter.

3.      Plato the Greek Philosopher reckoned the classic elements (Earth, Air, Fire and Water) were composed of regular shaped solids of which there are five. They are called Platonic solids. The five Platonic solids are – Tetrahedron (4), Cube (6), Octahedron (8),

Dodecahedron (12), and Icosahedrons (20). These are the only convex regular solids possible to construct.

                                          

4.      Any power of 5 ends with 5 except the power 0.                                                                            

                      5² = 25                                                   5³ = 125                                                                                     5⁴ = 625                                                5⁵ = 3125

5.      A five sided polygon is known as Pentagon. Pentagon is the only shape in which the number of sides and number of diagonals are same. 

6.      A number that ends with 0 or 5 is divisible by 5. Example- 1000, 645

7.      Pentagram, Pentangle, and Pentacle are all names for a five pointed star. The Pentagram or five folded star was endorsed by Pythagoreans because in its regular form it contains the Golden ratio (1.618)

                                

8.      Five pointed symmetry is found in an apple.

9.      Five can be partitioned in 7 ways.

      10.  It is a Fermat Prime.

11.  It is the first Wilson Prime. A Wilson Prime is a prime number p such that p² divides     (p – 1 )! + 1, where! denotes the factorial of a number. This is named after the English mathematician John Wilson.

12.  Vulgar fractions with 5 or 2 in the denominator don’t yield infinite decimal expansion. A real number having the denominator in the form of 2ⁿ x 5^m will have a terminating decimal expansion.

13.  Atomic number of Boron is 5

14.  5 is the hypotenuse of the smallest Pythagorean Triangle with its other two sides 3 and 4.                                                                         

          5² = 3² + 4².                                                                                                         

   This is the only Pythagorean Triangles with its sides arranged in Arithmetic Progression.

15.   It is the first prime which is in the form of 4n + 1 from which it follows that it is the sum of 2 squares expressed in one way only.                                                                                        

16.  It is the first prime of the form 6n – 1. All other primes are one more or one less than a multiple of 6 except 2 and 3.

17.  Every number can be expressed as the sum of 5 positive or negative cubes in an infinite numbers of ways.

18.  The general algebraic equation of the 5^th degree cannot be solved in radicals. This was proved by Abel in 1824.

19. One of math's perplexing mysteries. A sphere in five dimensional space has a larger volume (8π^2/15) than in any other dimension for a unit radius. From two dimensions up to five the volume increases, then decreases forever after.

20. 1084 is the smallest integer whose spelling, one thousand eighty-four, contains the 5 vowels (a, e, i, o, u) in order (Jim Wilder)

21. The sum of the first five integers raised to their own power, is prime, 

1^1+2^2+3^3+4^4+5^5=3413

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Rajesh Kumar Thakur

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