Working an Āyādi Reckoning by Hand

1. The plan, in hastas

Take a house 21 hastas wide and 32 hastas long. At the engine’s default hasta of 0.4572 m (18 inches) that is 9.60 m by 14.63 m, or 31.5 ft by 48 ft. The Mayamata’s measure is the half-perimeter, the breadth plus the length: 21 + 32 = 53 hastas. Other traditions measure other things — the Mānasāra takes the length, the breadth and the circumference separately, and the Viśvakarma Prakāśa the area — so the same house gives different remainders under each, as the Āyādi chapter sets out.

2. The three remainders

• Āya = (53 × 8) mod 12 = 424 mod 12 = 4
• Vyaya = (53 × 9) mod 10 = 477 mod 10 = 7
• Yoni = (53 × 3) mod 8 = 159 mod 8 = 7, which is Gaja

A remainder of zero is read as the modulus for the āya and vyaya (12 and 10) and as the eighth yoni, Kāka. The texts count the odd yonis good, and Gaja is the seventh. The rule that the āya should exceed the vyaya is not met here: 4 is less than 7.

3. What one hasta does

Add one hasta to the half-perimeter — about 46 cm on a wall — and every remainder moves. Here are the same three figures for 53, 54 and 55 hastas.

That is the point of working it by hand: the remainder is a property of a whole number of hastas, not of the house. It moves by a hasta’s worth of wall. For that reason the reference reports these figures as a traditional reading with its tradition and cubit stated, and does not tell anyone to change a plan for a remainder. Whether to move a wall is a design decision, bound by the sanctioned plan and the setbacks the bye-laws require (see Multi-storey stacking & building codes).