<P> In about 964 AD, the Persian astronomer Abd al - Rahman al - Sufi, writing in his Book of Fixed Stars, described a "nebulous spot" in the Andromeda constellation, the first definitive reference to what we now know is the Andromeda Galaxy, the nearest spiral galaxy to our galaxy . Nasir al - Din al - Tusi invented a geometrical technique called a Tusi - couple, which generates linear motion from the sum of two circular motions to replace Ptolemy's problematic equant . The Tusi couple was later employed in Ibn al - Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model although it is not known who the intermediary is or if Copernicus rediscovered the technique independently . </P> <P> Alhazen played a role in the development of optics . One of the prevailing theories of vision in his time and place was the emission theory supported by Euclid and Ptolemy, where sight worked by the eye emitting rays of light, and the other was the Aristotelean theory that sight worked when the essence of objects flows into the eyes . Alhazen correctly argued that vision occurred when light, traveling in straight lines, reflects off an object into the eyes . Al - Biruni wrote of his insights into light, stating that its velocity must be immense when compared to the speed of sound . </P> <P> Al - Kindi warned against alchemists attempting the transmutation of simple, base metals into precious ones like gold in the ninth century . </P> <P> Al - Biruni (973 - 1048) estimated the radius of the earth as 6339.6 km (modern value is c. 6,371 km), the best estimate at that time . </P>

Which of these scientific achievements happened during the islamic golden age