Five

The five (5) is an odd natural number that follows four and precedes six.

• Pronunciation of five, version Spain. (?·i)
• Pronunciation of five, Spanish version. (?·i)
• Number five in morse code. (?·i)

Math

Typical figure format of number five

Arithmetic and Algebra

• It's 3.♪ prime number, after 3 and before 7 with them forms the only terna that are terms of an arithmetic progression of three consecutive cousins with reason 2.
• Square pyramidal number ^{[chuckles]required]}.
• It's a pitagric prime number: 2²+ 1²= 5 = 4·1+1.^{[chuckles]required]}
• Like (2+i)(2-i)= (1+2i)(1-2i)=5,m the five is not a Gaussian cousin.
• The K set of congruence remnants module 5 has 5 elements: 0,1,2,3 and 4. These with the addition form an abelian group of order 5.
• The 1 has five fifth roots, a real 1, four imaginary roots and at the same time primitive roots.
• There are five Peano postulates for the construction of the system of natural numbers.
• It is the fifth term of Fibonacci succession after 3 and before 8, it is also the only number of Fibonacci in which the cardinal and the ordinal refer to the same number.
• The power set of a set A of 5 elements has exactly 2⁵=32 subsets of A.
• It's Fermat's second number, after 3 and before 17.
• According to the Abel-Ruffini Theorem, the fifth grade equation is the least grade that has no formula for its resolution.
• If we multiply any pair number (to 0) by 5, the last digit of the product always ends at zero.
• A grade 5 polynomial has six terms.
• A grade 5 algebraic equation, with integer coefficients, necessarily has at least one actual root.
• (a+b)⁵ that is the fifth power of 5 has six terms.

Geometry

• 5 is the hypotenuse of a rectangle triangle whose ghettos are 3 and 4. Known and used results by Egyptians and Babylonians.
• 5 is the cathet of a rectangle triangle whose hypotenuse is 13 and the other cathet is 12.
• There are exactly 5 regular polyhedrons, called platonic solids.
• The five-sided polygon is named pentagon. The regular pentagon has certain properties like the reason between the length of its diagonal and the length of its side is the golden number.
• The convex pentagon has 5 sides and 5 diagonals.
• The regular pentagon has 5 axes of symmetry that pass through any vertex and the midpoint of the opposite side.
• There are 5 postulates of Euclides.
• The dodecahedron is the only one of the five regular polyhedrons whose faces are all regular pentagons.

Number Theory

• It's a pentagonal number.^{[chuckles]required]}
• It's a Catalan number.
• It's a Pell number.
• It's a Bell number.
• It is a term of the succession of Padovan.
• A Sierpinski number.
• Only number that is part of more than a couple of twin cousins. Five is also the only cousin who is the sum of two consecutive cousins, namely, 2 and 3.
• A prime number of Wilson
• He's an Eisenstein cousin with no imaginary part and a real part of form 3 n - 1.
• A Perrin number.
• Form a pair of sexy prime numbers along with 11.
• Number of Thabit.^{[chuckles]required]}

Quinary numbering systems

Evolution of the representative sign of the five in the system of numeration

When the concept of number became broad enough, the various peoples of antiquity were the need to express it in a symbolic language. Since the human being has five fingers on each hand, ten and twenty on both, taking into account the toes, these numbers are emerging as the preferred base of the different numbering systems. The base five system is called quinary.

A study carried out on pre-Columbian cultures determined that close to a third used some decimal numbering system; slightly less than a third some quinary or quinary-decimal system, a little less still were those who used some binary system, around 10% maintained some vigesimal system, 1% some ternary system and the rest used systems not identifiable with these numbering bases. All this is a sample of how important this number is for different human cultures.

Chemistry

• Atomic Boro Number (B).
• Group 5 of the periodic table is also called the vanadium family.

Astronomy

• Messier M5 object is a globular cluster found in the Serpens constellation.

Stave

In mathematics, a "pentagram" (also called a "pentacle," "pentalpha," or "pentangle") is a five-pointed star drawn with five straight strokes. The importance of this figure is that if we take the five segments that are easy to find in the graphs, ordered from largest to smallest and calculate the relationship between the length of one with respect to the other, the golden number is obtained.

Although initially appearing associated with the cosmos god or Babylonian sorcerer order, this figure was very closely related to the Pythagoreans, who used it as a symbol. The Pythagoras numbers in relation to different attributes, elements or physical object, so that the staff was associated with the number five, life, power and invulnerability. Many authors believe that the pentagram is one of the many elements borrowed from the Pythagoreans from the Babylonians, but others doubt it. In turn, it is believed that the end of the philosophical doctrine of Pythagoras is closely related to the geometric discovery that the ratio of the diagonal of the pentagon and its side is not a rational number, which actually occurred before the algebraic demonstration of irrationality. √ 2. But the pentagram continued its existence in Platonic philosophy.

Over time it took on its own mystical value, which in some conceptions represents purity, perfection or beauty, while in others it is a symbol associated with the demonic and imperfect, being the ancestor of six, valued for being a perfect number.

Although the Pythagoreans gave great importance to music and made extensive studies of it, the musical staff has nothing to do with them or their philosophy. It was created in the year 1025 by the Italian musician Guido of Arezzo.

In nature

Construction of a logarithmic spiral

Oreaster reticulatus, typical sea star of five arms.

In nature, biological evolution determined that certain patterns of symmetry were repeated frequently, either for aesthetics or functionality. One of the most frequent cases is when there are five axes of symmetry, which is known as pentaradial symmetry.

In botany it is common to find flowers with five petals, a fact related to solar illumination, a distribution that responds to Ludwig's Law.

In turn, the distance from the elbow to the end of the hand is one fifth of the total height of the person.

The pyritohedron is a crystal of pyrite in the shape of an irregular dodecahedron.

Pentamerism

pentamerism is an exclusive quality of sea stars, consisting of a pentaradial symmetry that some members of this class develop from the larval stage. Although not all are pentameric, they do have bilateral symmetry, with a spectrum ranging from five to sixteen arms.

The golden ratio

The golden number as a ratio appears numerous times, both in plant animal species or natural phenomena, product of the physical balance that occurs in logarithmic spiral-shaped distributions.

Several inflorescences have arcs that start from the center and deviate clockwise and anticlockwise, the seeds being at their intersections. Because it is the most efficient packing, the quotient between them is the golden ratio. The shell of some cephalopods, such as the Nautilus, or the shell of some molluscs, such as the snail, have the shape of a logarithmic spiral.

The Bode Galaxy has the shape of a double logarithmic spiral.

Origin of the five fingers

Most species of terrestrial vertebrates are descended from a class of lungfish called sarcopterygians. Fossils between 359 and 345 million years old show that the legs of the earliest amphibians had bones in common with the fins of a 377 million-year-old fish of this class. This type structure, for the primitive limbs, is called chyrid and is estimated to have appeared 365 million years ago.

One of its characteristics is that it has five fingers. The descendants of the holders of the quiridian amphibians have preserved or decreased the number of fingers, since it is believed that these primitive terrestrial species were more than five fingers (polydactyly), they are descendants of the different classes of sarcopterygians. Reaffirm the evolutionary competition as the best quiridian and tetrapod locomotion system, as its main representative, making the pentadactyly predominate. Humans are tetrapods, so we have four limbs, thus the explanation why most humans have five fingers on each limb. It is then reflected in most current numbering systems, based on the importance of this account number.

Cultural aspects

• In the popular Andean culture the number five is a special number, perhaps sacred. For since the fifth day of a person's death, after pichcada (the fifth day or final farewell), the soul of the deceased withdraws from his house.
• In the Aymara language, the numbering system is base five, or a five-year model.
• Only number for which the number of letters matches the number you name. No other number written in Spanish gives this same coincidence.

The 5 on television

• XHGC-TDT: Mexican open television network.