The Nile was of utmost importance to the Ancient Egyptians in many ways. It brought water and fertile soil, and in addition it was perfect for transportation. Once a year, however, the Nile would inundate the land, bringing disaster in its wake by destroying crops and villages. This eventually led these Ancient Egyptians to organize their efforts to avoid this early disaster under one leader. This led to the first type of government, which quickly became more complex.
In time the Egyptians realized, that although the floods destroyed their crops, the silt left behind fertilized the land and created a new, rich layer of top soil, perfect for crops. It was decided that the cycle of the water would have to be studied in order to avoid the destruction of crops each year and take advantage of the fertility provided by the inundation. As a result they invented the nilometer, consisting of a slab, a well and a series of smaller steps. All three, though, were calibrated to the same units of measurement, the so-called cubit. The nilometers, spaced out along the river banks, allowed them to study the cycle, predict the coming of the next flood and plant their crops at the right time to avoid destruction.
The floods had another, unwanted, side effect. Each year, the boundaries between fields were erased by flood waters and silt, and had to be re-established. The work of measuring the land and redefining the borders was known as geometry, and it was regarded as re-establishing the principle of law and order on earth. This yearly activity became the foundation for the science of natural laws, as it was embodied in the archetypal shapes of triangle, square and circle. This is how the inundation of the Nile contributed to geometry.