Christiaan Huygens is best known for his work in astronomy and physics, but he also did important work in mathematics. Although he advanced no new theories, Huygens made improvements to existing methods of calculation and applied them to solving problems in the natural sciences. Had he not been diverted from mathematics by astronomy and physics, he might have be one of history's greatest mathematicians. However, the modern world might be lacking the pendulum clock and the wave theory of light, Huygens' greatest accomplishments.
Born April 14, 1629, at The Hague in the Netherlands, Christiaan Huygens was the son of a family of diplomats. His grandfather, also named Christiaan, had been secretary to William the Silent and Prince Maurice, and his father, Constantjin, had been in service to Prince Frederic Henry and the House of Orange his whole life. Young Christiaan was expected to follow the family path (his brother Constantjin, like his father, served the House of Orange), but he was far too interested in the sciences.
Huygens studied law and mathematics at the University of Leiden and the Collegium Arausicum at Breda. There, he studied classical mathematics and the more modern techniques of René Descartes and others. At the end of these formal studies, Huygens was able to live at home from 1650 to 1666, thanks to support from his father. Those sixteen years at home were the most fruitful of his scientific career.
During this period, Huygens made a number of trips to Paris and London. On his first journey, to Paris in September 1655, he met the men who would become the core of the Académie Royale des Sciences, which was founded in 1666 (Huygens soon became a member early). He traveled to Paris again and stayed from October 1660 to March 1661; he then spent two months in London, attending meetings at Gresham College and meeting some of England's great thinkers. Huygens eventually settled in Paris and lived there from 1666 to 1680, but political unrest and ill health made it essential for him to return to The Hague, where he died in 1695.
Huygens first studied mathematics, concentrating on determinations of quadraturesand cubatures. He published Theoremata de quadratura hyperboles, ellipses et ciculi; in it, he related the quadriture and the center of gravity of these various shapes. His next book, De circuili magnitudine inventa, appeared in 1654.
After Huygens heard about Blaise Pascal's work in probability, he began to investigate it. He published Tractatus de ratiociniis in alea ludo(a book about the theory of probabilty) in 1657, and applied the theory to calculating life expectancy. It remained the only book on the subject until the 18th century.
Huygens was known as a Cartesian--that is, he followed the ideas of René Descartes. As such, he did not believe in the action of forces as Isaac Newton proposed, believing instead that there could be a mechanical explanation for everything. Huygens' great gift to others was demonstrating how mathematics could be applied to natural problems, and his work, Holorogium oscillatorium, shows the strength of this approach.
Huygen's first major achievement was the development of the pendulum clock. Years before, Galileo had observed the movement of a lamp in a church and realized that the time of each swing was nearly the same, no matter the extent of the swing. Despite his brilliance, Galileo never managed to develop a working pendulum, which would have led to more accurate timekeeping (of increasing importance in this era of scientific revolutions). Huygens realized that the circular arcing swings that Galileo had observed were not identical; rather, they were nearly so. For a pendulum to move in swings of equal time, its movement would have to follow a curve known as a cycloid. Huygens designed a clock with such a pendulum that had weights attached near its fulcrum that would make it move in this nearly circular, cyloidian arc; he then attached the pendulum to a clock's works and used a system of falling weights that would keep the pendulum moving despite friction and air resistance. The mechanisms of the modern grandfather clock have changed little from Huygens' first one, which he presented to the Dutch estates general. He described the clock in his work Horologium, published in 1658.
More important than this invention was Huygens' development of the wave theory of light. At the time, it was believed only particles that traveled in a straight line could cast shadows as light did; Newton had advanced the idea of light consisting of such straight-traveling particles. Because of the examples of water waves, it was thought that waves bent around objects. In an effort to correct Newton, Huygens proved that in some cases waves could indeed travel in straight lines. He believed that light was a series of shock waves that disturbed particles existing in the "ether." When struck by the light, these closely packed particles would move and form new wave fronts. Where these wave fronts overlapped, there was light--a concept known as Huygen's principle. Although his theory allowed him to explain refraction and reflection, and predicted that light would more slowly in a denser medium such as water, it did not explain polarization. Newton's theory remained at the forefront; Huygens' idea laid dormant until it was rediscovered and improved on by Thomas Young in the 19th century.
Huygens also worked in optics, creating fine telescopes that led to important astronomical discoveries. Thanks to his improved instrument, he was able to correct Galileo's error that stated Saturn was a triple planet. Galileo's telescope did not have sufficient resolution; Saturn's rings appeared to him as two planets snuggled up to the main body. Huygens was able to discern a single ring around the planet.
Huygens also was the first to guess at the distances of the stars. Assuming that Sirius was as bright as the sun, he calculated it to be 2.5 trillion miles from Earth. We now know that Sirius is far brighter than the sun and its true distance is 20 times Huygens' approximation. Huygens also was the first to notice surface markings on Mars and the largest of Saturn's moons, Titan.
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