How did Egyptian architecture influence early Greek and Roman architecture?

One of the most important influences of Egyptian architecture on greek and roman architecture was the establishment of basic elements of the column. The Egyptians established the basic design of a column, which consists of three parts: a pedestal (at the bottom), the column itself, and the capital (at the top). The Greeks stole the basic Egyptian design and took off with it. They developed three classical orders of architecture, distinguished by the style of the capitals and the shape and size of the columns. These three orders (Doric, Ionic and Corinthian), along with two more (Composite and Tuscan) added by the Romans, persist into this day.

Text quoted from History of architecture 1 handouts

I would add that the Greeks developed the fluted column (not completely round but 'scalloped'), which the Egyptians did not use. The Greek columns got smaller towards the top, so the column actually looks taller than it is. Also, note that the Greeks needed to place the columns close together, otherwise the flat stone held up by two neighboring columns would crack in the middle. The Romans invented the arch, unknown to the early Greeks and Egyptians, allowing more space between columns. The principle of the arch was the same as the domed roof, allowing a huge, empty space underneath. (Cf. the Parthenon in Rome). --- It is probable that Egyptian mathematics, highly developed for land-surveying in relation to Nile-irrigated agriculture, was a necessary precursor to the calculations necessary for building the Greek and Roman temples and other monuments.