1.
Hexagram
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A hexagram or sexagram is a six-pointed geometric star figure with the Schläfli symbol,2, or. It is the compound of two equilateral triangles, the intersection is a regular hexagon. It is used in historical, religious and cultural contexts, for example in Hanafism, Jewish identity, in mathematics, the root system for the simple Lie group G2 is in the form of a hexagram, with six long roots and six short roots. A six-pointed star, like a hexagon, can be created using a compass. Without changing the radius of the compass, set its pivot on the circles circumference, with the pivot on the last point found, similarly find a third point on the circumference, and repeat until six such points have been marked. With a straight edge, join alternate points on the circumference to form two overlapping equilateral triangles. It is possible that as a geometric shape, like for example the triangle, circle, or square. The hexagram is a symbol called satkona yantra or sadkona yantra found on ancient South Indian Hindu temples. It symbolizes the nara-narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in moksha, or nirvana, some researchers have theorized that the hexagram represents the astrological chart at the time of Davids birth or anointment as king. The hexagram is also known as the Kings Star in astrological circles, in antique papyri, pentagrams, together with stars and other signs, are frequently found on amulets bearing the Jewish names of God, and used to guard against fever and other diseases. Curiously the hexagram is not found among these signs, in the Greek Magical Papyri at Paris and London there are 22 signs side by side, and a circle with twelve signs, but neither a pentagram nor a hexagram. Six-pointed stars have also found in cosmological diagrams in Hinduism, Buddhism. The reasons behind this symbols common appearance in Indic religions and the West are unknown, one possibility is that they have a common origin. The other possibility is that artists and religious people from several cultures independently created the hexagram shape, within Indic lore, the shape is generally understood to consist of two triangles—one pointed up and the other down—locked in harmonious embrace. The two components are called Om and the Hrim in Sanskrit, and symbolize mans position between earth and sky, the downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni Tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the union of male and female. The two locked triangles are known as Shanmukha—the six-faced, representing the six faces of Shiva & Shaktis progeny Kartikeya. This symbol is also a part of several yantras and has significance in Hindu ritual worship

2.
Chinese checkers
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Chinese Checkers or Chinese chequers is a strategy board game of German origin which can be played by two, three, four, or six people, playing individually or with partners. The game is a modern and simplified variation of the American game Halma, the remaining players continue the game to establish second-, third-, fourth-, fifth-, and last-place finishers. The rules are simple, so young children can play. Despite its name, the game is not a variation of checkers, the game was invented in Germany in 1892 under the name Stern-Halma as a variation of the older American game Halma. The Stern refers to the star shape. The name Chinese Checkers originated in the United States as a scheme by Bill. The Pressman companys game was originally called Hop Ching Checkers, the game was introduced to Chinese-speaking regions mostly by the Japanese. The aim is to all ones pieces into the star corner on the opposite side of the board before opponents do the same. The destination corner is called home, each player has 10 pieces, except in games between two players when 15 are sometimes used. In hop across, the most popular variation, each starts with their colored pieces on one of the six points or corners of the star. A player may not combine hopping with a single-step move – a move consists of one or the other, there is no capturing in Chinese Checkers, so hopped pieces remain active and in play. Turns proceed clockwise around the board, in the diagram, Green might move the topmost piece one space diagonally forward as shown. A hop consists of jumping over an adjacent piece, either ones own or an opponents. Red might advance the indicated piece by a chain of three hops in a single move and it is not mandatory to make the most number of hops possible. Can be played all versus all, or three teams of two, when playing teams, teammates usually sit at opposite corners of the star, with each team member controlling their own colored set of pieces. The first team to both sets to their home destination corners is the winner. The remaining players usually play to determine second- and third-place finishers. The four-player game is the same as the game for six players, in a three-player game, all players control either one or two sets of pieces each

3.
1 (number)
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1, is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement, for example, a line segment of unit length is a line segment of length 1. It is also the first of the series of natural numbers. The word one can be used as a noun, an adjective and it comes from the English word an, which comes from the Proto-Germanic root *ainaz. The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-, compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish een, Dutch een, German eins and Old Norse einn. Compare the Proto-Indo-European root *oi-no- to Greek oinos, Latin unus, Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin, One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number, any number multiplied by one is that number, as one is the identity for multiplication. As a result,1 is its own factorial, its own square, its own cube, One is also the result of the empty product, as any number multiplied by one is itself. It is also the natural number that is neither composite nor prime with respect to division. The Gupta wrote it as a line, and the Nagari sometimes added a small circle on the left. The Nepali also rotated it to the right but kept the circle small and this eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. Where the 1 is written with an upstroke, the number 7 has a horizontal stroke through the vertical line. While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used,1 cannot be used as the base of a positional numeral system, as the only digit that would be permitted in such a system would be 0. Since the base 1 exponential function always equals 1, its inverse does not exist, there are two ways to write the real number 1 as a recurring decimal, as 1.000. and as 0.999. There is only one way to represent the real number 1 as a Dedekind cut, in a multiplicative group or monoid, the identity element is sometimes denoted 1, but e is also traditional. However,1 is especially common for the identity of a ring. When such a ring has characteristic n not equal to 0,1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few

4.
37 (number)
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37 is the natural number following 36 and preceding 38. Thirty-seven is the 12th prime number, a prime with 73. It is a hexagonal number and a star number. Every positive integer is the sum of at most 37 fifth powers,37 appears in the Padovan sequence, preceded by the terms 16,21, and 28. Since the greatest prime factor of 372 +1 =1370 is 137, the atomic number of rubidium The normal human body temperature in degrees Celsius Messier object M37, a magnitude 6. The duration of Saros series 37 was 1298.1 years, the Saros number of the lunar eclipse series which began on -1492 April 3 and ended on -194 May 22. The duration of Saros series 37 was 1298.1 years, kepler-37b is the smallest known planet. The New York Yankees, also for Stengel and this honor made him the first manager to have had his number retired by two different teams. In the NFL, The Detroit Lions, for Doak Walker, the San Francisco 49ers, for Jimmy Johnson. Thirty-seven is, The number of plays William Shakespeare is thought to have written, today the +37 prefix is shared by Lithuania, Latvia, Estonia, Moldova, Armenia, Belarus, Andorra, Monaco, San Marino and Vatican City. A television channel reserved for radio astronomy in the United States The number people are most likely to state when asked to give a number between 0 and 100. The inspiration for the album 37 Everywhere by Punchline List of highways numbered 37 Number Thirty-Seven, Pennsylvania, unincorporated community in Cambria County, Pennsylvania I37

5.
121 (number)
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121 is the natural number following 120 and preceding 122. One hundred twenty-one is a square and is the sum of three consecutive primes, there are no squares besides 121 known to be of the form 1 + p + p 2 + p 3 + p 4, where p is prime. Other such squares must have at least 35 digits, there are only two other squares known to be of the form n. Another example of 121 being of the few examples supporting a conjecture is that Fermat conjectured that 4 and 121 are the perfect squares of the form x3 -4. It is also a number and a centered octagonal number. In base 10, it is a Smith number since its digits add up to the value as its factorization. But it can not be expressed as the sum of any other number plus that numbers digits, making 121 a self number