Risālah al-muḥīṭīyya
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The Risālah al-muḥīṭiyyah is a significant work by the Persian mathematician and astronomer Ghiyāth al-Dīn Jamshīd al-Kāshī. Written around 1424, this treatise is a masterpiece of computation, primarily focused on determining the value of pi (2π) with remarkable precision.12
Al-Kāshī calculated pi to nine sexagesimal places, which translates to an accuracy of 16 decimal places. This achievement surpassed previous records and remained unsurpassed for nearly two centuries. He employed a polygon with an immense number of sides (3 × 2²⁸) to achieve this accuracy, aiming for an error smaller than the width of a horse's hair. The work highlights the importance of precise calculations in astronomy, particularly for determining the size of the universe.1
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