### 1 Neettal Azhavu (Length)

ellu (til/sesame) | $8$ siRu-kadagu (mustard) |

nellu (rice grain) | $8$ ellu |

viral | $8$ nellu ($1.9444\dots $ cm) |

saaN | $12$ viral ($23.3333\dots $ cm) |

(distance from tip of thumb ﬁnger to tip of little ﬁnger) | |

muzham | $2$ saaN ($46.6666\dots $ cm) |

(distance from elbow to tip of middle ﬁnger) | |

kajam | $2$ muzham |

paagam | $2$ kajam |

sangili (chain) | $22$ kajam |

furlong | $220$ kajam |

kilo metre | $5$ furlong |

mile | $8$ furlong |

### 2 Niraththal Azhavu (Weights/Balance)

Gold Weights | |

kunRimaNi | weight of $4$ nellu (rice grain) |

kazhanchu | $10$ kunRimaNi |

sovereign/pawan | $1.5$ kazhanchu ($8$ grams) |

Grain and Fluid Volume | Moogathal Azhavu (Volume) |

sittigai | a pinch |

sevidu | $360$ nellu (rice grain) |

aazhaakku | $5$ sevidu |

uzhakku | $2$ aazhaakku |

uri | $2$ uzhakku |

padi | $2$ uri |

marakkaal (kuRuNi) | $8$ padi |

pothi (mootai) | $120$ padi |

Kottai | $21$ marakkaal |

### 3 Parapa Azhavu (Area)

kuzhi | $576$ sq. ft |

marakkal vedaipaadu | $8$ cent; area required to sow $8$ padi |

rice grain | |

acre | $100$ cents = $12.5$ marakkal vedaipaadu |

acre | $300$ kuzhi |

kaani | $100$ kuzhi = $132$ cent |

veli | $7$ kaani |

### 4 Fractions

These small fractions, in the table below, were used by ancient stone sculptors of south India.

mukkaal | $\frac{3}{4}$ |

arai/paadhi | $\frac{1}{2}$ |

kaal | $\frac{1}{4}$ |

arai-kaal | $\frac{1}{8}$ |

veesam (or maakaani) | $\frac{1}{16}$ (one Aana in currency) |

mundru veesam | $\frac{3}{16}$ |

oru maa | $\frac{1}{20}$ |

iru maa | $\frac{1}{10}$ |

mundru maa | $\frac{3}{20}$ |

naal maa | $\frac{1}{5}$ |

arai veesam | $\frac{1}{32}$ |

arai maa | $\frac{1}{40}$ |

kaal veesam | $\frac{1}{64}$ |

mukkaal veesam | $\frac{3}{64}$ |

kaani | $\frac{1}{80}$ |

mukkaani | $\frac{3}{80}$ |

arai-kaani | $\frac{1}{160}$ |

munthiri | $\frac{1}{320}$ |

keel-munthiri | $\frac{1}{102400}=\frac{1}{{\left(320\right)}^{2}}$ |

immi | $\frac{1}{2150400}=\frac{1}{21\times {\left(320\right)}^{2}}$ |

mummi | $\frac{1}{23654400}=\frac{1}{11\times 2150400}$ |

aNu | $\frac{1}{165580800}=\frac{1}{7\times 23654400}$ |

kuNam | $\frac{1}{1490227200}=\frac{1}{9\times 165580800}$ |

panDam | $\frac{1}{7451136000}=\frac{1}{5\times 1490227200}$ |

pAgam | $\frac{1}{44706816000}=\frac{1}{6\times 7451136000}$ |

vinDam | $\frac{1}{312947712000}=\frac{1}{7\times 44706816000}$ |

naga-vinDam | $\frac{1}{5320111104000}=\frac{1}{17\times 312947712000}$ |

sinDai | $\frac{1}{74481555456000}=\frac{1}{14\times 5320111104000}$ |

kathirmunai | $\frac{1}{489631109120000}$ |

kuralvalaippadi | $\frac{1}{9585244364800000}$ |

veLLam | $\frac{1}{575114661888000000}$ |

nuN-maNal | $\frac{1}{100\times 575114661888000000}$ |

Therthukkal | $\frac{1}{2323824530227200000000}$ |

Till recently, the sale and purchase of land used the decimal form $a.b.c$ in kaani units which is equal to $\left(132\times a\right)+\left(8.25\times b\right)+\left(0.515625\times c\right)$ cents. The decimal form is in base 16. In other words, both $b$ and $c$ takes value between $0$ and $15$ because $8.25\times 16=132$ and $0.515625\times 16=8.25$. For instance, to represent $132$ cents, they write $1.0.0$ kaani. Similarly, $0.4.0$ represented $33$ cents. So, when poet Bharathiyar asked “kaani niLam Vendum, parasakthi!” (Oh Lord! give me one kaani land) did he has ask for 132 cents. Probably, not! He probably meant the fraction $1\u221580$ of the smallest saleable land that existed during his time.

### 5 War Batallion

The batallion of an army had measurements. In mahabharat, there is a mention that Arjun destroyed $8$ akkroni batallions in a single day — the day after his son Abhimanyu was killed in war– while trying to locate Jayadharth before sunset. One akkroni batallion must have had $24300$ entities. An entity refers to one of these: a Chariot, an elephant, a horse or one foot soldier. A paththi is a group containing one Chariot, one elephant, three horses and 5 foot soldiers (10 entities). Three paththi makes one kulmam (30 entites). Three kulmam made one kaNam (90 entities). Three kaNam made one bhagini (270 entities). Three bhagini made one kridalai (810 entities) and three kridalai made one samu (2430 entities). Ten samu made one akkroni. This means Arjun killed $1,94,400$ entities. Was it possible? What was the population then?