SNIPPETS...

Meteor strikes again!

A meteor is caused by a tiny particle of dust which enters the earth’s atmosphere. As it moves downward, it experiences collision with air molecules, and the friction generated causes the particle to glow and eventually burn up. Most meteors burn up at altitudes of around 100 km.

It is an exceptional celestial manifestation for sky observers. Geminid meteor showers will illuminate the sky on the nights of December 13 and 14 in India this year. The Geminids should produce a fine display of one to two meteor every minute for North American observers with dark skies, weather permitting.

Brief bursts of activity could produce even higher rates. In Europe, Asia and Australia, the peak will come during local daylight hours. Observers in these parts of the world should still see a very good meteor display on the night of December 13 and 14.  

Geminids are several times denser than the cometary dust flakes that supply most meteor showers. Under normal conditions and during ideal dark-sky conditions, 60 to 120 Geminid meteors can be expected to burst across the sky every hour on an average.

If you wish to see a maximum number of meteors then the best time would be during the night. You don’t even need a telescope to see them.

S A Mohan Krishna

12-12-12: sublime, unique

The year 2012 is drawing to a close. The twelfth of December of the year, i.e. 12-12-12 is now here. We can write this again only after hundred years (in 2112)! Whatever be the Mayan basis, the number 12 has its own unique property.
It is what has been called a sublime number. Of course, 12 is used commonly in everyday parlance to denote a dozen (not counting a baker’s dozen!) A gross is a dozen times dozen! Apart from this, there are umpteen references and phrases with the 12 prefix. The play ‘Twelfth Night’, and the twelve apostles, etc.

Now to come to the sublime part. For this, we need to invoke the perfect numbers, which are numbers the sum of whose divisors add up to the number itself. Six and 28 are examples. Thus 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.

They become rarer as we go to larger and larger numbers. The 30th perfect number was found using Cray Supercomputer in 1985. Hardly 40 of them are known. No odd perfect numbers are known. They have many interesting properties like the sum of their reciprocals (of their divisors) is always 2! Except for six, they can be expressed as the sum of cubes of consecutive odd numbers. Sublime numbers are far rarer! A number is sublime if the number of its divisors and the sum of the divisors of the number are both perfect numbers.

Twelve is the first sublime number (6 divisors adding up to 28). The next one is a horrendously large 78 digit number, starting from 6086.1264! These are the only two sublime numbers known. So, 12 is really unique! Only one other number has this property and that is a really large 78-digit number.

Even with the biggest supercomputer, we may not be able to discover the third such number. So, on 12-12-12, let us ponder on this.

C Sivaram

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