
Galileo helped Mathmeticians with his dicoveries of physics!
While Galileo's application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analysis and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid's Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo's life it was being superseded by the algebraic methods of Descartes.
Galileo produced one piece of original and even prophetic work in mathematics: Galileo's paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.
TECHNOLOGY
Galileo made a few contributions to what we now call technology as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo's physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things.
In 1595–1598, Galileo devised and improved a Geometric and Military Compass suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolò Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations.
About 1593, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.
In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons.
In 1610, he used a telescope as a compound microscope, and he made improved microscopes in 1623 and after. This appears to be the first clearly documented use of the compound microscope.
In 1612, having determined the orbital periods of Jupiter's satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for large land surveys; this method, for example, was used by Lewis and Clark. (For sea navigation, where delicate telescopic observations were more difficult, the longitude problem eventually required development of a practical portable marine chronometer, such as that of John Harrison).
In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock, a vectorial model of which may be seen here. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s.
He created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.
By: jwspackerfan  20070522 15:03:50
