# The History Of Mathematics: Number Systems (Essay Sample)

Read Chapter 1 and answer the following questions (when you read, you may skip most of the math examples which will be explained in the videos posted under MP1, and focus on the history part). Page numbers are indicated to help you locate the answers.

1. (2pts) Describe three different ways of tallying before the number systems were invented (pages 1-6). Minimum 100 words.

2. (1.5pts) Describe Mayan number system (must indicate the symbols used, the base, and whether it is a positional system; pages 7-8). Minimum 75 words.

3. (1.5pts) Describe Egyptian number system (must indicate the symbols used, the base, and whether it is a positional system; pages 11-13 and 15-16). Minimum 75 words.

4. (1.5pts) Describe Greek number system (must indicate the symbols used and whether it is a positional system; pages 16-18). Minimum 75 words.

5. (2pts) Describe Babylonian number system (must indicate the symbols used, the base, and whether it is a positional system; pages 23-26). Minimum 100 words.

6. (1.5pt) Describe Chinese number system (must indicate whether it is a positional system; pages 26-28). Minimum 75 words.

Read Chapter 2 (You may skip the solutions of the math problems in the reading because most of them are explained in the video lectures for MP2s. )

1. (2pts) Describe Egyptians' knowledge of Arithmetics(must include: what Arithmetical problems they could solve, Arithmetical skills they had and whether they knew operations of fractions; pages 37-43). Minimum 100 words.

2. (1pt) Describe Egyptians' knowledge of Algebra (must include: what kind of Algebraic problems they solved or what method they used to solve these problems; pages 46=48). Minimum 50 words.

3. (2pts) Describe Egyptians' knowledge of Geometry (must include: what geometrical formulas they had; pages 53-61) . Minimum 100 words.

4. (2pts) Describe Babylonians' knowledge of Arithmetics (must include: what Arithmetical problems they could solve, Arithmetical skills they had and whether they knew operations of fractions; pages 62-64) . Minimum 100 words.

5. (1pt) Describe Babylonians' knowledge of Algebra (must include: what kind of Algebraic problems they solved or what method they used to solve these problems; pages 64-70) . Minimum 50 words.

6. (2pts) Describe Babylonians' knowledge of Geometry (must include: whether they were aware of the Pythagorean Theorem; pages 72-79). Minimum 80 words.

The History of Mathematics

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The History of Mathematics

Describe three different ways of tallying before the number systems were invented?

Tallying was the earliest technique of expressing the notion of numbers physically. The three methods of tallying included, tying knots in strings which had different lengths or colors, making scratches on stones and cutting notches on pieces of bones or on wooden stick (Burton, 2011). Cutting notches on bones was mostly used by the people during the Stone Age to represent kills, and also as a representation of the lunar calendar. The tying of knots was common among the Incas of Peru which represented records of land transactions and population. The scratches on stones was also used to represent the number of physical objects such as sheep.

Describe the Mayan number system?

The Mayan number system was used by the people of the ancient Maya and incorporated a place value numeration system. The Mayan people developed the hieroglyphic writing by use of 1000 glyphs (Burton, 2011). The creation of the Mayan calendar paved the way for the adoption of a vigesimal counting system which was based on 20. The numbers were expressed symbolically using dots and bars. The dots represented 1 and the bar represented 5. Zero was also represented by a stylized shell. The Maya number system was a positional numerical system since it used numerical symbols to represent numbers (Porubsky, 2007).

Describe Egyptian number system?

The Egyptian number system allowed for continuous counting through the inclusion of a new symbol from the macehead of King Narmer (Burton, 2011). The system allowed for the recordings of large numbers as much as millions. The Egyptian hieroglyphic number symbols represented numbers in the powers of 10. The number 1 was represented by a single stroke and the number 10 was represented by a heel bone sign. The number 10 was considered the base of the Egyptian number system which represented the ten human fingers. The use of symbols to represent numbers as well as the inclusion of a base number qualifies the Egyptian number system to be referred to as a positional numbering system.

Describe Greek number system?

The Greek number system incorporated 24 letters of the Greek alphabet which were augmented by three Phoenician letters which were obsolete (Burton, 2011). The three letters were, digamma, koppa and sampi which represented six, nine and nine hundred respectively. The Greek number system was a positional number system since the initial nine letters were symbolized by the first nine letters of the Greek alphabet, whereas, the next nine letters represented the first nine integral multiples of base 10, which ranged from 10-90 (Burton, 2011).

Describe Babylonian number system?

The Babylonian number system was highly developed since it made use of the positional number system which incorporates place values. The system had a limited set of symbols suffices to represent numbers which was of great advantage to the Babylonians since large

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