Tamil Fractions

A friend asks for REASONS:

A who to the what now? A twelve-letter word, a thaerrhugaL, representing a number somewhere in the region of twenty-three ninety-ninths of a sextillionth.

It's hardly unreasonable to demand REASONS. It's not an 'obvious' number - a power of anything, for example. Its reciprocal is (brilliantly) $\frac{9,800,000}{27}\times 18!$; dear readers, I shall be honest with you: that wasn't the first thing I guessed.

The Wikipedia page on Tamil fractions sheds a little more light, though:

  • 1/160= araikkaaNi
  • 1/320= munthiri
  • 1/102,400= keezh munthiri
  • 1/2,150,400= immi
  • 1/23,654,400= mummi
  • 1/165,580,800= aNu
  • 1/1,490,227,200= kuNam
  • 1/7,451,136,000= pantham
  • 1/44,706,816,000= sggtta
  • 1/312,947,712,000= vintham
  • 1/5,320,111,104,000= naagavintham
  • 1/74,481,555,456,000= sinthai
  • 1/1,489,631,109,120,000= kathirmunai
  • 1/59,585,244,364,800,000= kuralvaLaippidi
  • 1/3,575,114,661,888,000,000= veLLam
  • 1/357,511,466,188,800,000,000= nuNNmaNl
  • 1/2,323,824,530,227,200,000,000= thaertthugaL

Spot the pattern? No, me either. However, it turns out that each fraction is related to the one before:

$\frac{1}{160} = \frac{2}{320}$
$\frac{1}{320} = \frac{320}{102,400}$ - this could be a square measurement, perhaps?
$\frac{1}{102400} = \frac{21}{2150400}$
$\frac{1}{2150400} = \frac{11}{23654400}$
$\frac{1}{23654400} = \frac{7}{165580800}$
$\frac{1}{165580800} = \frac{9}{1490227200}$
$\frac{1}{1490227200} = \frac{5}{7451136000}$
$\frac{1}{7451136000} = \frac{6}{44706816000}$
$\frac{1}{44706816000} = \frac{7}{312947712000}$
$\frac{1}{312947712000} = \frac{17}{5320111104000}$
$\frac{1}{5320111104000} = \frac{14}{74481555456000}$
$\frac{1}{74481555456000} = \frac{20}{1489631109120000}$
$\frac{1}{1489631109120000} = \frac{40}{59585244364800000}$
$\frac{1}{59585244364800000} = \frac{60}{3575114661888000000}$
$\frac{1}{3575114661888000000} = \frac{100}{357511466188800000000}$
$\frac{1}{357511466188800000000} = \frac{13}{2\times 2323824530227200000000}$

Oh, those wacky Tamils! What a ludicrous way of dealing with naming fractions! Where does that 17 come from, for example? Why suddenly $\frac{13}{2}$ as a divisor? There's no way you'd catch us modern-day cosmopolitan Westerners dividing - let's say - a mile into 4,561,920 equal parts and calling them each a point, eh? That would be completely preposterous and backwards.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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