Sumerian Board

Formula

Value = (Col3 × 3600) + (Col2 × 60) + Col1

Positional system based on powers of 60. Columns accumulate values up to 59 before carrying over.

Worked Examples

Example 1: Number 70

Problem:70 in Base 60

Solution:70 = 60 + 10. 1 in the 60s column. 10 in the 1s column.

Result:1, 10

Frequently Asked Questions

What is the Sumerian number system?

The Sumerians (and later Babylonians) used a base-60 (sexagesimal) system. It originated around 3000 BCE and is the reason we have 60 seconds in a minute and 360 degrees in a circle.

What are the tokens?

Early Sumerians used clay tokens. A small cone represented 1, a small ball represented 10, a large cone 60, and a large cone with a hole 600. Sumerian Board simplifies this into a positional board.

How do I convert decimal to Sumerian?

Divide the decimal number by 60 repeatedly. The remainders become the digits in each column, reading from right (units) to left (60s, 3600s).

What is the difference between Sumerian and Babylonian math?

Sumerian math laid the foundation with the base-60 system and tokens. Babylonian mathematicians (who came later in the same region) refined this into a fully positional system and developed advanced algebra and geometry.

Background & Theory

The Sumerian system is positional sexagesimal (Base 60). **Place Values:** * **Right column (Dish):** $60^0$ (Values 1-59) * **Middle column (Gesh):** $60^1$ (Values 60-3540) * **Left column (Shar):** $60^2$ (Values 3600-215999) **Within a Column:** It functions additively (base 10 sub-base). * **▼ (Vertical Wedge):** Value 1. * **◀ (Corner Wedge):** Value 10. * Values up to 59 are formed by grouping these wedges (e.g., 23 is ◀◀▼▼▼). **Example:** The number 75 is written as [1, 15]. 1 × 60 + 15 × 1 = 75.

History

The Sumerian civilization in ancient Mesopotamia (modern Iraq) developed one of the world's earliest writing and counting systems around 3100 BCE. Originally using clay tokens for accounting, they evolved into Cuneiform script on clay tablets. Their mathematical legacy persists today in our measurement of time (hours, minutes, seconds) and angles (degrees). The system began as a collection of physical tokens representing different goods. Over centuries, these tokens were impressed onto clay envelopes, leading to written numerals. The positional system (where the value of a digit depends on its position) was a revolutionary development that allowed for representing arbitrarily large numbers with a small set of symbols.