# History Of The Mathematics: Achievements Of Diophantus (Essay Sample)

QA5

1. (2pts) Describe the achievements of Diophantus (must include what syncopated algebra is; pages 217-220). Minimum 100 words.

2. (2pts) Describe the history of Diophantine equations (pages 223-230). Minimum 100 words.

3. (2pts) Describe the later commentators who followed Diophantus (pages 232-236). Minimum 100 words.

4. (2pts) Describe the Arabic mathematics and the beginning of the name "Algebra"(pages 238-251 skip math examples). Minimum 100 words.

5. (2pts) Describe the Chinese Nine Chapters (page 251-259). Minimum 100 words.

QA6

1. (4pts) Describe the revival of mathematics in the West(must include what led to further development of mathematics in the West; pages 269-277). Minimum 200 words.

2. (5pts) Describe Fibonacci's life and his contributions to Math (pages 277-283). Minimum 250 words.

3. (1pt) Describe Jordanus's contributions to Math (pages 283-285). Minimum 50 words.

History of Mathematics

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History of Mathematics

Question A5

Describe the achievements of Diophantus.

Diophantus liberated algebra through his accomplishments. In his achievements, he brought about modified algebra, which involved using abbreviations and ciphers of quantities and operations. He phrased the epigram problem to the effect and wrote the Arithmetica involving thirteen books, where only six accounts survived. In the 16th century, a computational process in the algebra involved use of symbols and words, which were referred to as the syncopated algebra from Diophantus work “Arithmetica” (Sfard, 1995). Additionally, he came up with polygonal numbers, where only fragments now exist and also developed Porisms, which were part of Arithmetica, although they were lost in the entirety of the book.

Describe the history of Diophantine equations.

Diophantine equation emerged after the “cattle problem of Archimedes.” The complexity of the problem made it difficult to solve. Following the problem, the Pythagorean equation received much attention than the first or second-degree expressions. The Indians developed a system of mathematics covering geometry, with Hindu mathematician, Aryabhata contributing to the subject by examining the summation of geometric and arithmetic series. Later on, Brahmagupta continued with Aryabhata’s work and came up with his own formula, the area of a cyclic quadrilateral. The two mathematicians had repeated most of Diophantus problems, but their solving approach was different. Diophantus pursued solving the equation using irrational numbers, but only positive integers were proclaimed to be solutions by the Indian mathematicians. From the problem, the Diophantine equation resulted and was proclaimed as an equation having one or more unknowns to be solved for the integral values.

Describe the later commentators who followed Diophantus.

The first commentator was Pappus, whose great work on the mathematical collection was originally written in eight books. The mathematics collection included theorems of solid geometry and high plane curves, which by then were considered as part of mathematics. However, Pappus commentary on Ptolemy Almagest was his only work that survived and he generalized results of his precursor by simplifying the Pythagorean on the square of the hypotenuse. The second commentator was Hypatia, the first woman mathematician, who wrote a commentary on six books of Diophantus’s Arithmetica. Other commentators included Roman mathematicians, Boethius and Cassiodorus. Boethius arithmetic involved definition and theorems with no proof from element books (i, ii, and iv), however, “De Institutionae Arthmetica,” his popular work was a paraphrase of Diophantus work. Cassiodorus composed the “Introduction to Divine and Human Writings,” which was devoted to church scriptures.

Describe the Arabic mathematics and the beginning of the name "Algebra."

The new faith emerged after the surge of Arabic power with the new rulers resolving to build a new capital in Baghdad. Baghdad boosted a larger population than Constantinople, making Arabic as the learning language. At the beginning of the tenth century, almost all Greek philosophical and scientific writing was documented in the Arabic language. Hindu numbers and arithmetical approach were accustomed to Arab mathematician, Al-khowarizmi. He compiled the Arithmetica to a book titled “Book of Addition and Subtraction According to the Hindu Calculation.” In European mathematics, the book’s inspiration was immense, although it was written in Arabic despite its Hindu originality. As a result, the Western Europeans learned about algebra from Al-khowarizmi’...

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