Hi! I apologize for not being able to post for the past few weeks; I was a little busy with all the AP testing, but I hope you all had a wonderful weekend and...
In this post, we will be exploring the basic idea and patterns behind some of the earliest number systems!
In this post, we will be exploring the basic idea and patterns behind some of the earliest number systems!
The Egyptians and the Babylonians are known to have come up with one of the first number conventions. These conventions often used symbols that represented specific numbers, known as “Nodal numbers.” Other numbers would be formed by grouping nodal numbers together in certain way. This system is known as the “Additive System.”
The Egyptians adopted this system in their number conventions. For example, in ancient Egyptian notation, the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 40 would be represented by:
From this notation, we can observe that 1 and 10 were nodal numbers; 1 would be represented by a vertical dash, while 10 would be represented by a symbol that looks like an upside-down U.
The Babylonians used 1, 10 and 60 as their nodal numbers. The Babylonians used a sexagesimal positional number system, in which the value of a particular digit depends both on the digit itself and its position within the number. It has been proposed that 60 was used as the base number, as 60 = 2^2 x 3 x 5, which makes it divisible by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.
Other Fun Facts:
- The Babylonians understood the concept of nothingness, but it was not seen as a number. The Babylonians understood “nothingness” as absence of a number, and thus represented nothingness with a space at first. Later on, a placeholding symbol was used to show the nonexistence of a digit in a certain place value.
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This is the placeholding symbol
used by the ancient Babylonians to
represent 0.
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- Nodal numbers are also used in Roman Numerals, in which many of us are familiar with. In the Roman number system the nodal numbers are 1, 5, 10, 50, 100, 500, 1000, represented respectively by the signs I, V, X, L, C, D, M. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 40 would be represented by I, II, III, IV, V, VI, VII, VIII, IX, X, XIX, XL in Roman numerals.
I hope you all enjoyed this post, and please contact me if you have any questions!
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