# 5

Nov 30 2011

5 represent a numeral, a number, and it is also serves as the name of the glyph. Glyph is a unique mark placed on a written medium which serves to the meaning of what is written.

It is one of the natural number lies between 4 and 6.

How “5” is used in Mathematics?

In the prime number series 5 stands in the 3rd position (1, 3, 5, 7…).

5 can be written as 221+1, so it is classified as a Fermat prime.

5 serve as

: The 3rd Germain prime

: The 1st safe prime

: The 3rd Mersenne prime exponent

: The 3rd factorial prime

&

: The 3rd Catalan number

Five is the first known good prime which is an Eisenstein prime number that neither have imaginary  part nor it have real part. Eisenstein prime takes the form 3n − 1.

5 is the 5th number in the Fibonacci series (1,1,2,3,5,8…).5 appears in all the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), … so it is also serves as the Markov number.

In numbers whose base is 10 or 20, 5 serves as a 1-automorphic number.

Normally in mathematics polynomial equations of degree 4 and the below like 3, 2 can be easily solved with radicals. But the degree of equation is 5 and above those can’t be solved.

This is called as the Abel–Ruffini theorem. It is due to the fact, that the symmetric group Sn is solvable if the group is in the order n ≤ 4 and it is not solvable if n ≥ 5.

A graph which is having four or fewer vertices is usually a planar but there some kind of graphs exists with 5 vertices those are usually not planar: K5, the complete graph with 5 vertices.

Generally a planar graph is a graph which can be drawn on the plane. In these graph edges of the vertices intersect only at their endpoints. Other way around, it can be said edges of vertices will not cross each other.

If a polygon is made up of five sides then it is called as pentagon.

A polygon with five sides is a pentagon. Polygonal numbers representing pentagons which also called as the pentagonal numbers.

Another one fact about 5 is the only prime number that ends with the digit 5. It is because all other numbers written with 5 in their one’s place are multiples of 5. So normally the 5 in base 10, five is called as 1- automorphic number.

called as 1- automorphic number.

Table of Elementary operations

Multiplication

 Multiplication 1 2 3 4 5 6 7 8 9 10 … 1000 5* X 5 10 15 20 25 30 35 40 45 50 … 5000

Division

 Division 1 2 3 4 5 6 7 8 9 10 … 15 5/ X 5 2.5 1.66 1.25 1 0.833 0.625 0.5 .. x/5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 3

Exponentiation

 Division 1 2 3 4 5 6 7 8 9 10 5x 5 25 125 652 3125 15625 78125 390625 1953125 9765625 X5 1 32 243 1024 3125 7776 16807 32768 59049 100000

Glyph evaluation history

The evolution history of the current modern glyph of five cannot be traced back to the Brahmin Indians such that we have done for the numbers 1 to 4. Indian Empires of Gupta  and Kushana had many different glyphs. Interestingly they had no similarity with our modern glyph of 5.

The empires of Punjabi and Nagari have taken these glyphs those are similar to the lowercase letter “h” rotated to 180°. Later on The Ghubar Arabs has transformed the glyph in many different ways just as Gupta empires. This time more or less it was similar to 4 or 3 than the number 5. From these character representations Europeans finally have given the shape of modern 5.

How five is represented in various languages and numbering systems

 Cardinal 5 five Ordinal 5th fifth Numeral system quinary Factorization prime Divisors 1, 5 Roman numeral V Roman numeral (Unicode) Ⅴ, ⅴ Greek ε (or Ε) Arabic ٥,5 Arabic (Persian,Urdu) ۵ Ge’ez ፭ Bengali ৫ Punjabi ੫ Chinese numeral 五，伍 Devanāgarī ५ Hebrew ה (Hey) Khmer ៥ Telugu ౫ Malayalam ൫ Tamil ௫ Thai ๕ prefixes penta-/pent- (fromGreek)quinque-/quinqu-/quint-(from Latin) Binary 101 Octal 5 Duodecimal 5 Hexadecimal 5

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