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the_sexagesimal_place_value_notation [2015/10/25 21:41] – gombert | the_sexagesimal_place_value_notation [2016/03/16 22:10] (current) – [The Sexagesimal Place Value Notation] gombert | ||
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====== The Sexagesimal Place Value Notation ====== | ====== The Sexagesimal Place Value Notation ====== | ||
- | The Sexagesimal Place Value Notation (SPVN thereafter) is a notation of numbers using a positional principle and the base 60. It was used mainly in mathematical texts from the end of 3< | + | The Sexagesimal Place Value Notation (SPVN thereafter) is a notation of numbers using a positional principle and the base 60. It was used mainly in mathematical texts from the end of 3< |
- | \\ To understand this notation, the best is to look at school exercises intended to teach it in Old Babylonian scribal schools, for example a multiplication table. Table 2 shows the photographs and a copy of a multiplication table by 9 from Nippur (HS 217a < [[http:// | + | To understand this notation, the best is to look at school exercises intended to teach it in Old Babylonian scribal schools, for example a multiplication table. Table 2 shows the photographs and a copy of a multiplication table by 9 from Nippur ([[http:// |
- | Obverse\\ | + | Obverse\\ |
- | | + | '' |
- | \\ 8.20 | + | \\ Reverse\\ |
+ | '' | ||
+ | \\ 8.20 a-ra< | ||
- | **Table 2: transliteration of HS 217a, school tablet from Nippur, multiplication table by 9** | + | **transliteration of [[http:// |
- | \\ Thus, in front of 7, we expect the number 63. Instead, we see the notation {{mathematics-CP%20(1)_html_4362eb2d.gif? | + | Thus, in front of 7, we expect the number 63. Instead, we see the notation {{mathematics-CP (1)_html_4362eb2d.png? |
- | \\ However, there is a difference with the modern time system. If we continue the reading of the multiplication table, in front of 20, we expect 180, that is, 3×60, or 3.0 in our modern sexagesimal system, but we see {{mathematics-CP%20(1)_html_m606456ac.gif?17x21}}. This means that 3×60 is noted with exactly the same sign as the “3” in the third row of the left column. In other words, at the same time the sign {{mathematics-CP%20(1)_html_m606456ac.gif?16x20}} denotes 3 and 3×60. When we see the sign {{mathematics-CP%20(1)_html_m606456ac.gif?18x18}} in a multiplication table, we do not know if the wedges represent units, sixties, sixtieth, etc. The floating character of the cuneiform SPVN is a general feature in mathematical texts. | + | However, there is a difference with the modern time system. If we continue the reading of the multiplication table, in front of 20, we expect 180, that is, 3×60, or 3.0 in our modern sexagesimal system, but we see {{mathematics-CP (1)_html_m606456ac.png?17x21}}. This means that 3×60 is noted with exactly the same sign as the “3” in the third row of the left column. In other words, at the same time the sign {{mathematics-CP (1)_html_m606456ac.png?16x20}} denotes 3 and 3×60. When we see the sign {{mathematics-CP (1)_html_m606456ac.png?18x18}} in a multiplication table, we do not know if the wedges represent units, sixties, sixtieth, etc. The floating character of the cuneiform SPVN is a general feature in mathematical texts.\\ |
- | \\ The reader can facilitate his/her calculations with SPVN by using the online tool developed by Baptiste Mélès, | + | The reader can facilitate his/her calculations with SPVN by using the online tool developed by Baptiste Mélès, [[http:// |
- | \\ ===== Bibliography ===== | + | ===== Bibliography ===== |
* Neugebauer, Otto. 1957. //The exact sciences in antiquity// | * Neugebauer, Otto. 1957. //The exact sciences in antiquity// | ||
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* Proust, Christine. 2013. Du calcul flottant en Mésopotamie. //La Gazette des Mathématiciens// | * Proust, Christine. 2013. Du calcul flottant en Mésopotamie. //La Gazette des Mathématiciens// | ||
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* Thureau-Dangin, | * Thureau-Dangin, | ||
\\ CP | \\ CP | ||
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+ | Return to [[mathematics]] |