108 (number)

← 107 108 109 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred eight
Ordinal	108th (one hundred and eighth)
Factorization	2^2× 3^3
Divisors	1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Roman numeral	CVIII
Binary	11011002
Ternary	110003
Quaternary	12304
Quinary	4135
Senary	3006
Octal	1548
Duodecimal	9012
Hexadecimal	6C16
Vigesimal	5820
Base 36	3036

108 (one hundred [and] eight) is the natural number following 107 and preceding 109.

In mathematics

108 is:

• an abundant number.
• a semiperfect number.
• a tetranacci number.^[1]
• the hyperfactorial of 3 since it is of the form $1^{1}\cdot 2^{2}\cdot 3^{3}$.
• divisible by the value of its φ function, which is 36.
• divisible by the total number of its divisors (12), hence it is a refactorable number.
• the angle in degrees of the interior angles of a regular pentagon in Euclidean space.
• palindromic in bases 11 (99₁₁), 17 (66₁₇), 26 (44₂₆), 35 (33₃₅) and 53 (22₅₃)
• a Harshad number in bases 2, 3, 4, 6, 7, 9, 10, 11, 12, 13 and 16
• a self number.^[2]
• nine dozen

There are 108 free polyominoes of order 7.

The equation $2\sin \left({\frac {108^{\circ }}{2}}\right)=\phi$ results in the golden ratio.

Religion and the arts

The number 108 is considered sacred by the Dharmic Religions, such as Hinduism, Buddhism, Jainism.

Hinduism

Mukhya Shivaganas are 108 in number and hence Shaiva sects, particularly Lingayats, use 108 rudraksha beaded lace for japa. Also they recite supreme lord Shiva's 108 (AshtaaShatanaamaavaLi) names daily during their morning Shivapuja.
In Gaudiya Vaishnavism, there are 108 gopis of Vrindavan. Recital of these names, often accompanied by the counting of a 108-beaded mala, is considered sacred and often done during religious ceremonies. The recital is called namajapa. Accordingly, a japa mala usually has beads for 108 repetitions of a mantra. The Sri Vaishnavite Tradition has 108 Divya Kshetras of Lord Vishnu, called as 108 Divya Desams. The 12 Prolific Poet Saints called Alwars of the Sri Vaishnavites wrote devotional poetry about these 108 abodes of Lord Vishnu which was later compiled by Nathamuni as the Divya Prabhandams which are sacred texts in the philosophy.

The well known bas-relief carving at the famous Angkor Wat temple in Cambodia relates the Hindu story of a serpent being pulled back and forth by 108 gods and asuras (demons), 54 gods pulling one way, and 54 asuras pulling the other, to churn the ocean of milk in order to produce the elixir of immortality. According to the Oriental Architecture site there are 5 monumental guardian gates to the fortified temple city of Angkor Thom.^[3] In front of each gate stand giant statues of 54 gods (to the left of the causeway) and 54 demons (to the right of the causeway) which represent the churning of the ocean.

Buddhism

Likewise, Tibetan Buddhist malas or rosaries (Tib. ཕྲེང་བ Wyl. phreng ba, "Trengwa") are usually 108 beads;^[4] sometimes 111 including the guru bead(s), reflecting the words of the Buddha called in Tibetan the Kangyur (Wylie: Bka'-'gyur) in 108 volumes. Zen priests wear juzu (a ring of prayer beads) around their wrists, which consists of 108 beads.^[5]

Japa mala, or japa beads, made from tulasi wood, consisting of 108 beads plus the head bead.

The Lankavatara Sutra has a section where the Bodhisattva Mahamati asks Buddha 108 questions^[6] and another section where Buddha lists 108 statements of negation in the form of "A statement concerning X is not statement concerning X".^[7] In a footnote, D.T. Suzuki explains that the Sanskrit word translated as "statement" is pada which can also mean "foot-step" or "a position." This confusion over the word "pada" explains why some have mistakenly held that the reference to 108 statements in the Lankavatara refer to the 108 steps that many temples have.^[8]

In some schools of Buddhism it is believed that there are 108 feelings. According to Bhante Gunaratana^[9] this number is reached by multiplying the senses smell, touch, taste, hearing, sight, and consciousness by whether they are painful, pleasant or neutral, and then again by whether these are internally generated or externally occurring, and yet again by past, present and future, finally we get 108 feelings. 6 × 3 × 2 × 3 = 108. In Japan, at the end of the year, a bell is chimed 108 times in Buddhist temples to finish the old year and welcome the new one. Each ring represents one of 108 earthly temptations (Bonnō) a person must overcome to achieve nirvana.

In Jewish culture and numerology

Jews often give gifts and charitable donations in multiples of the number 18, associated with the Hebrew word 'chai(חי)', meaning 'alive', 'living', or 'life'. See Chai (symbol). The number 108 both is a multiple of 18 (6 times 18) and contains the numbers 1 and 8 that compose the number 18.

Other references

In the neo-Gnostic teachings of Samael Aun Weor, an individual has 108 chances (lifetimes) to eliminate his egos and transcend the material world before "devolving" and having the egos forcefully removed in the infradimensions.^[10]

Martial arts

Many East Asian martial arts trace their roots back to Buddhism, specifically, to the Buddhist Shaolin Temple. Because of their ties to Buddhism, 108 has become an important symbolic number in a number of martial arts styles.

• According to Marma Adi and Ayurveda, there are 108 pressure points in the body, where consciousness and flesh intersect to give life to the living being.^[11]
• The Chinese school of martial arts agrees with the South Indian school of martial arts on the principle of 108 pressure points.^[12][13]
• 108 number figures prominently in the symbolism associated with karate, particularly the Gōjū-ryū discipline. The ultimate Gōjū-ryū kata, Suparinpei, literally translates to 108. Suparinpei is the Japanese pronunciation of the number 108, while gojūshi of Gojūshiho is the Japanese pronunciation of the number 54. The other Gōjū-ryū kata, Sanseru (meaning "36") and Seipai ("18") are factors of the number 108.^[5]
• The 108 moves of the Yang Taijiquan long form and 108 moves in the Wing Chun wooden dummy form, taught by Yip Man, are noted in this regard.^[8]
• The Eagle Claw Kung Fu style has a form known as the 108 Locking Hand Techniques.^[14] This form is considered the essence of the style, consisting of an encyclopedia of Chin Na techniques, and is said to be passed down from the founder General Yue Fei.^[14]
• Paek Pal Ki Hyung, the 7th form taught in the art of Kuk Sool Won, translates literally to "108 technique" form. It is also frequently referred to as the "eliminate 108 torments" form. Each motion corresponds with one of the 108 Buddhist torments or defilements.

In literature

• In Homer's Odyssey, the number of suitors coveting Penelope, wife of Odysseus.
• There are 108 outlaws in the Chinese classic Water Margin/Outlaws of the Marsh by Shi Nai'an.
• There are 108 love sonnets in Astrophil and Stella, the first English sonnet sequence by Sir Philip Sidney.

In science

• 108 is the atomic number of hassium.
• 108 degrees Fahrenheit is the internal temperature at which the human body's vital organs begin to fail from overheating.
• The distance of Earth from the Sun is about 108 times the diameter of the Sun (actually closer to 107.51, as per definition of the AU). Actual ratio varies between 105.7 (Perihelion) and 109.3 (Aphelion).

In technology

• The number of Mbit/s of a non-standard extension of IEEE 802.11g wireless network using channel bonding.
• 108 is the name of a community of and for open source developers, created by Red Hat.^[15]

In sports

• 108 is the number that the Belgian cyclist Wouter Weylandt wore when he crashed fatally in the Giro d'Italia on May 9, 2011. As a tribute, many supporters held replicas of his race number by the side of the road the next day. The organization of the Giro d'Italia decided not to issue race number 108 in future editions, to commemorate him.
• An official Major League Baseball baseball has 108 stitches.^[16]
• In 2016 the Chicago Cubs (MLB) won the World Series for the first time in 108 years, ending the longest championship drought in North American professional sports. The Cubs' win came in the 10th inning with 8 runs (108).

In other fields

• There are 108 cards in a deck of UNO cards.
• In India, 108 (1-0-8) is the toll-free emergency telephone number.
• 108 stories in the Sears Tower (Willis Tower) in Chicago, Illinois.

See also

• 108 (band)
• List of highways numbered 108
• Zero one infinity rule

Notes

1. "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
2. "Sloane's A003052 : Self numbers or Colombian numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. http://www.orientalarchitecture.com/cambodia/angkor/angkorthom.php
4. Chapter 5 of 'Generating the Deity' ISBN 1-55939-055-7
5. Hyaku Hachi No Bonno: The Influence of The 108 Defilements and Other Buddhist Concepts on Karate Thought and Practice By Charles C. Goodin. The article has appeared in Issue #7, Winter 1996-97 of Furyu: The Budo Journal.
6. The Lankavatara Sutra translated by Daisetz Teitaro Suzuki, Chapter Two, Section II,
7. The Lankavatara Sutra translated by Daisetz Teitaro Suzuki, Chapter Two, Section III,
8. 108 STEPS: The Sino-Indian Connection in the Martial Arts by Joyotpaul Chaudhuri....
9. Bhante Gunaratana, Four Foundations of Mindfulness in Plain English 2012, Wisdom Publications page 86
10. Samael Aun Weor (2005) [1983]. The Pistis Sophia Unveiled. Glorian Publishing. pp. 211–214. ISBN 0-9745916-8-8.
11. A Western Journalist on India: The Ferengi's Columns By François Gautier. pg 158. ISBN 81-241-0795-5
12. Subramaniam Phd., P., (general editors) Dr. Shu Hikosaka, Asst. Prof. Norinaga Shimizu, & Dr. G. John Samuel, (translator) Dr. M. Radhika (1994). Varma Cuttiram வர்ம சுத்திரம்: A Tamil Text on Martial Art from Palm-Leaf Manuscript. Madras: Institute of Asian Studies. pp. 90 & 91.
13. Reid Phd., Howard, Michael Croucher (1991). The Way of the Warrior: The Paradox of the Martial Arts. New York: Outlook Press. pp. 58–85. ISBN 0-87951-433-7.
14. Leung, Shum and Jeanne Chin. The Secrets of Eagle Claw Kung Fu: Ying Jow Pai. Tuttle martial arts. Boston: Tuttle Pub, 2001, p. 15
15. Red Hat Announces First Red Hat Developer Day In India @ ENTERPRISE OPEN SOURCE MAGAZINE
16. Official Major League Baseball by Rawlings

9. '108' in the anime series 'Tokko' is the number of pieces in the Box of Dirge Chinese puzzle box created by alchemy as a doorway between the world of demons and this one. The puzzle box was used in all of the Hellraiser films but there was no reference to its number of shards.

References

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134

External links

• The Significance of the number 108
• Meaning of 108 beads on a mala
• Article on the symbolism of the number 108
• Our Sun, Planet Earth and the Hoary 108 - (domain is closed)
• The Mystical 108 in the Bible, Eastern Religions and the TV Show LOST - (domain is closed)
• The spiritual meaning of 108