Pythagorean cup
BIOGRAPHY Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and the putative founder of the movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him. He was born on the island of Samos, and travelled, visiting Egypt and Greece, and maybe India. Around 530 BC, he moved to Croton, in Magna Graecia, and there established some kind of school or guild. In 520 BC, he returned to Samos. Pythagoras made influential contributions to philosophy and religion in the late 6th century BC. He is often revered as a great mathematician and scientist and
is best known for the Pythagorean theorem which bears his name. However, because legend and obfuscation cloud his work even more than that of the other preSocratic philosophers, one can give only a tentative account of his
teachings, and some have questioned whether he contributed much to mathematics or natural philosophy. Many of the accomplishments credited to Pythagoras may actually have been accom-
plishments of his colleagues and successors. Some accounts mention that the philosophy associated with Pythagoras was related to mathematics and that numbers were important. It was said that he was the first man to call himself a philosopher, or lover of wisdom, and Pythagorean ideas exercised a marked influence on Plato, and through him, all of Western philosophy.
A few words about the project A Pythagorean cup looks like a normal drinking cup, except that the bowl has a central column in it – giving it a shape like a Bundt pan. The central column of the bowl is positioned directly over the stem of the cup and over the hole at the bottom of the stem. A small open pipe runs from this hole almost to the top of the central column, where there is an open chamber. The chamber is connected by a second pipe to the bottom of the central column, where a hole in the column exposes the pipe to (the contents of) the bowl of the cup. When the cup is filled, liquid rises through the second pipe up to the chamber at the top of the central column, following Pascal’s principle of communicating vessels. As long as the level of the liquid does not rise beyond the level of the chamber, the cup functions as normal. If the level rises further, however, the liquid spills through the chamber into the first pipe and out the bottom. Gravity then creates a siphon through the central column, causing the entire contents of the cup to be emptied through the hole at the bottom of the stem. Some modern toilets operate on the same principle: when the water level in the bowl rises high enough, a siphon is created, flushing the toilet.
Pascal’s Hydrostatic Pressure Pascal’s principle is defined as A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. This principle is stated mathematically as: is the hydrostatic pressure (given in pascals in the SI system), or the difference in pressure at two points within a fluid column, due to the weight of the fluid; ρ is the fluid density (in kilograms per cubic meter in the SI system); g is acceleration due to gravity (normally using the sea level acceleration due to Earth’s gravity, in SI in metres per second squared); is the height of fluid above the point of measurement, or the difference in elevation between the two points within the fluid column (in metres in SI). The intuitive explanation of this formula is that the change in pressure between 2 elevations is due to the weight of the fluid between the elevations. A more correct interpretation, though, is that the pressure change is caused by the change of potential energy per unit volume of the liquid due to the existence of the gravitational field. Note that the variation with height does not depend on any additional pressures. Therefore, Pascal’s law can be interpreted as saying that any change in pressure applied at any given point of the fluid is transmitted undiminished throughout the fluid.
The formula that gives the P pressure on an object submerged in a fluid is therefore:
P=r*g*h r (rho) is the density of the fluid, g is the acceleration of gravity h is the height of the fluid above the object
O RT HO G R A P H IC D R AW I N G
RENDERING Everything in moderation
THE PRODUCT