Al-Jayyani: The father of modern spherical trigonometry

Modern spherical trigonometry

Al-Jayyani was an Islamic 𝘮𝘢𝘵𝘩𝘦𝘮𝘢𝘵𝘪𝘤𝘪𝘢𝘯. He wrote many important commentaries on Euclid's Elements and was the first to make spherical trigonometry. fyi spherical trigonometry is the metrical relationships between the sides and angles of spherical triangles.

The Spanish scholar was an expert in the Qur'an, also being knowledgeable in Arabic philology, inheritance laws and arithmetic. Al-Jayyani's work on ratio is the most interesting mathematical work. Line, surface, angle, and solid were the four magnitudes used in geometry. He was the first to consider "number" as geometrical magnitude.

We are going to learn about Al-Jayyani’s "The book of Unknown Arcs of a Sphere", considered the first treatise on spherical trigonometry. In his book he describes formula for right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle. He had sketched some figures to prove these formulas. His works influenced many European mathematicians. Some argues that one of Regiomontanus sources was The book of unknown arcs of a sphere. Among the similarities between al-Jayyani’s treatise and that of Regiomontanus are the definition of ratios as numbers, the lack of a tangent function, and a similar method of solving a spherical triangle when all sides are unknown.

Work by al-Jayyani on 𝘢𝘴𝘵𝘳𝘰𝘯𝘰𝘮𝘺 was also important. He wrote on the morning and evening twilight, computing the fairly accurate value of 18° for the angle of the sun below the horizon at the start on morning twilight and at the end of the evening twilight.

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