Why was the battle of gaugamela so important in alexander’s conquest of the persian empire?

the answer for 3 is b and the answer for 4 is d

the revival of interest in greek and roman influences also stimulated developments in math and science. the mathematical traditions that governed the conception of the universe were based in greek mathematics that had been preserved and built upon by scientists in muslim lands, such as nasir al-din in the 13th century. the catholic church endorsed the views of ptolemy, the greek philosopher and astronomer who constructed a geocentric theory where all planets, the moon, and the sun revolved around the earth. using calculations from al-din, polish monk and mathematician, nicholas copernicus, concluded that the geocentric theory did not make sense. instead, his data indicated that the earth and all the other planets rotated around the sun, a conclusion that he did not share widely, for fear of retaliation from the church. in fact, his heliocentric theory was not published until after his death in 1543.

the scientist that really got into trouble over the heliocentric theory was italian galileo galilei, who strengthened and improved copernicus' theory. other scientists, such as johannes kepler, had demonstrated that planets also moved in elliptical orbits, and galileo confirmed those theories as well. perhaps most famously, he built a telescope that allowed him to observe the phenomena directly, recording details of heavenly bodies that the ancients could never have known about. galileo's theories were published in the starry messenger in 1610, a highly controversial book criticized by other scientists, as well as officials of the church. galileo made the mistake of making fun of people that disagreed with him, and he was arrested and put on trial, eventually recanting his theory publicly in order to save his own life.