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Alhazen's problem, also known as Alhazen's billiard problem, is a mathematical problem in geometrical optics first formulated by Ptolemy in 150 AD. [1] It is named for the 11th-century Arab mathematician Alhazen ( Ibn al-Haytham ) who presented a geometric solution in his Book of Optics .
His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point.
The Book of Optics (Arabic: كتاب المناظر, romanized: Kitāb al-Manāẓir; Latin: De Aspectibus or Perspectiva; Italian: Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al-Haytham, known in the West as Alhazen or Alhacen (965–c. 1040 AD).
Alhazen (Ibn al-Haytham), "the father of Optics" [14] Ibn al-Haytham (known in as Alhacen or Alhazen in Western Europe), writing in the 1010s, received both Ibn Sahl's treatise and a partial Arabic translation of Ptolemy's Optics. He produced a comprehensive and systematic analysis of Greek optical theories. [15]
Early in the 11th century Alhazen wrote a scathing critique of Ptolemy's model in his Doubts on Ptolemy (c. 1028), which some have interpreted to imply he was criticizing Ptolemy's geocentrism, [14] but most agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism. [15]
Alhazen was the first person to explain that vision occurs when light reflects from an object into one's eyes. [ 7 ] The rise of rationalist physics in the 17th century led to a novel version of the intromissionist theory that proved extremely influential and displaced any legacies of the old emissive theories.
Ptolemy I was a general in the army of Alexander the Great and after Alexander’s death had taken over the province of Egypt as a satrap (local governor). Along with the other successors to Alexander he did not hold the title of king until 305, but was still an important player in the affairs of the Macedonian Empire in the east.
Ptolemy XI was succeeded by a son of Ptolemy IX, Ptolemy XII Neos Dionysos, nicknamed Auletes, the flute-player. By now Rome was the arbiter of Egyptian affairs, and annexed both Libya and Cyprus . In 58 BC Auletes was driven out by the Alexandrian mob, but the Romans restored him to power three years later.