MesoCalc


A Mesopotamian Calculator

MesoCalc is a Mesopotamian calculator. It computes with integers in sexagesimal place-value notation and operates on measures.

MesoCalc was created in March 2013 by Baptiste MÉLÈS (Archives Henri Poincaré, Université de Lorraine) with the scientific assistance of Christine PROUST (CNRS, Université Paris-Diderot) in the framework of the SAW Project (Mathematical Sciences in the Ancient World), headed by Karine CHEMLA (CNRS, Université Paris-Diderot).

Contents


Introduction


Arithmetics

Conversion and arithmetical properties

Conversions

Conversion from decimal to sexagesimal (10A → 60A/F):

Conversion from sexagesimal to decimal (60A → 10A):

Arithmetical properties

Regular number? (60A/F → yes/no)

Prime factors (60A → 60A/F):

Additive operations

Addition (60A):

+

Substraction (60A):


Multiplicative operations

Multiplication and quotient

Multiplication (60A/F):

×

Multiplication table (60A/F):

Quotient (60F÷60R → 60F):
÷

Reciprocal and regular numbers

Reciprocal number (60F):

(60F)

Table of regular numbers (60A/F)
from to :

Table of regular and reciprocal numbers (60A/F)
from to :

Exponential operations

Squares and square roots

Square (60A/F):

Square root (60A/F):

(60F)

(60F)

Cubes and cube roots

Cube (60A/F):

Cube root (60A/F):

(60F)

Geometric progression

Geometric progression (a × bn):
a = 60A/F (first term)
b = 60A/F (common ratio)
n = 10A (number of terms)

(WARNING: Due to technical limitations, numbers greater than 53.37.35.32.22.29.43.36.32 are just approximations.)


Measures

Lengths

Units of length:

danna ← 30 ← ← 60 ← ninda ← 12 ← kuš ← 30 ← šusi
11 km 360 m 6 m 50 cm 17 mm

Add lengths:

danna ninda kuš šusi
+

Substract lengths:

danna ninda kuš šusi

Multiply a length:

danna ninda kuš šusi
× times

Surfaces

Units of surface:

gan ← 100 ← sar ← 60 ← gin ← 180 ← še
3600 m² 36 m² 0.6 m² 33 cm²
1 ninda × 1 ninda

Multiply lengths to get a surface:

danna ninda kuš šusi
×

Add surfaces:

gan sar gin še
+

Substract surfaces:

gan sar gin še

Multiply a surface:

gan sar gin še
× times

Volumes

Units of volume:

gan ← 100 ← sar ← 60 ← gin ← 180 ← še
1800 m³ 18 m³ 300 dm³ 1.7 dm³
1 (surface-)sar × 1 kuš

Multiply lengths to get a volume:

danna ninda kuš šusi
×
×

Multiply length and surface to get a volume:

danna ninda kuš šusi
× gan sar gin še

Add volumes:

gan sar gin še
+

Substract volumes:

gan sar gin še

Multiply a volume:

gan sar gin še
× times

Capacities

Units of capacity:

gur ← 5 ← bariga ← 6 ← ban ← 10 ← sila ← 60 ← gin ← 180 ← še
300 L 60 L 10 L 1 L 17 mL 0.1 mL

Add capacities:

gur bariga ban sila gin še
+

Substract capacities:

gur bariga ban sila gin še

Multiply a capacity:

gur bariga ban sila gin še
× times

Weights

Units of weight:

gu ← 60 ← mana ← 60 ← gin ← 180 ← še
30 kg 500 g 8 g 0.05 g

Add weights:

gu mana gin še
+

Substract weights:

gu mana gin še

Multiply a weight:

gu mana gin še
× times

System S and system G

System S:

šar-gal ← 6 ← šar'u ← 10 ← šar ← 6 ← gešu ← 10 ← geš ← 6 ← u ← 10 ← diš
216000 36000 3600 600 60 10 1

System G:

šar-gal ← 6 ← šar'u ← 10 ← šar ← 6 ← bur'u ← 10 ← bur ← 3 ← eše ← 6 ← iku
34800 10800 1080 180 18 6 1

Conversion from system S to system G:

šar-gal šar'u šar gešu geš u diš

Conversion from system G to system S:

šar-gal šar'u šar bur'u bur eše iku

About MesoCalc

Can I download MesoCalc?

Yes, you can! To download MesoCalc and use it offline on your computer or smartphone,

Can I read the source code of MesoCalc?

Yes, you can! MesoCalc is a free software. You can read the source code of the present web page. You can even modify the source code and then redistribute your own modifications under the terms of the GNU General Public License (see the license below).

If you want to see the HTML, CSS and JavaScript source code of this program, you will have to find on option like "View > Page Source" or "Tools > Source Code" in your web browser while displaying the present web page.

License

MesoCalc: a Mesopotamian calculator.

Copyright (C) Baptiste MÉLÈS 2013.

Last version: November 9th 2013.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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