108 is a Harshad Number. A Harshad number is any number divisible by the sum of its digits. 1 plus 8 equals 9 and nine is a factor of 108 (9 times 12). It's a curious property of 9 that so many of its products are Harshad numbers but not all. 99 is divisible by nine but 99 is not divisible by 18, so 99 is not Harshad. Harshad is Sanskrit for "great joy". These numbers were discovered by an Indian mathematician. The first 50 Harshad numbers are: 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 102, 108, 110, 111, 112, 114, 117, 120, 126, 132, 133, 135, 140, 144, 150, 152, 153, 156, 162, 171, 180, 190, 192, 195, 198, 200.

All that is interesting enough in and of itself, but 108 has other curious properties as well. Mathematically it is the sum of six squared plus six squared plus six squared and we all know you don't want to mess around with 666, the number of the Beast even though it is generally discredited by true number mavens.

108 is also a number divisible by the number of its divisors--there are twelve of them: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. If that wasn't strange enough, 108 is the sum of 9 consecutive numbers: 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 = 108. 108 equals the sum of the first 9 multiples of 3, viz. 0, 3, 6, 9, 12, 15, 18, 21 and 24.

In astronomical terms 108 is really interesting. The sun is exactly 108 times its diameter away from Earth. So is the moon. It is exactly this size to distance ratio that makes both bodies the same size during an eclipse. The diameter of the sun is almost exactly 108 times the dianeter of the earth's. Coincidence? I don't think so.

Culturally 108 is deeply mystical. The Buddhists claim there are 108 desires. There are 108 forms of ignorance and 108 lies. Hindus will tell you there are 108 chakras leading to the heart chakra. 108 refers to god in Islam. One represents the one god; zero represents completeness; and eight is infinity. The number 108 is considered sacred in many Eastern religions and traditions, such as Hinduism, Buddhism, Jainism, Sikhism and connected yoga and dharma based practices. For example, Hindu deities have 108 names. Recital of these names, often accompanied by counting of 108-beaded Mala, is considered sacred and often done during religious ceremonies. The recital is called namajapa. Accordingly, a mala usually has beads for 108 repetitions of a mantra.

Likewise, Zen priests wear juzu (a ring of prayer beads) around their wrists, which consists of 108 beads. The Lankavatara Sutra repeatedly refers to the 108 steps Hindu temples have. In Tibetan Buddhism, it is believed that there are 108 sins. And in Japan, at the end of the year, a bell is chimed 108 times to finish the old year and welcome the new one. Each ring represents one of 108 earthly temptations a person must overcome to achieve nirvana.
The 108th element is Hassium a relatively long lived transuranic first isolated in 1994.

A baseball has 108 stitches.

2013-09-09 09:03:03 micheledutcher - Although also any number can be dissected to reveal hidden properties, I appreciate the author bringing us this number's properties so eloquently. I especially enjoyed the last sentence - seemingly unimpressive after the article's references to religion - but there are some to whom baseball is a religion.

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