Monday, November 28, 2011

Augustin-Jean Fresnel 1788-1827



     Fresnel was a 19th century French physicist. He was the son of an architect and was schooled by his parents but was considered to be a slow learner when at the age of 8 he still had difficulties reading. When he was sent to an actual school for a formal education at the age of 12 it was then that he was introduced to science and mathematics; he excelled greatly at both. 

     He decided he wanted to become an engineer and in 1806 he went to the School of Civil Engineering. After graduating, he worked for several years on engineering projects for the French government departments but due to Napoleon returned from Elba in 1815 he lost his post but only temporarily. During the time when he wasn’t working for the government was when he started to become interested in optics.

     Fresnel came up with formulas that could explain refraction, double refraction, reflection, and the polarization of light reflected from a transparent substance. The work he did supported the concept of transverse vibrations in light waves, which he evaluated mathematically and the wave theory. He also developed a method that ended up producing circularly polarized light. In 1819 he was nominated a commissioner of lighthouses and began to encourage that mirrors be replaced with compound lenses in lighthouses, which he invented a lens for the task. The type of special lens he constructed for lighthouses is called today the Fresnel lens. Here is a little information on those lenses and why he needed to construct them differently. 

     "Faced with the need to construct a large lens for a lighthouse of appropriate focal length, but unable to support the large weight of a double convex lens of that size, French physicist Augustin Fresnel (1788-1827) reasoned that it was the surface curvature which gave the focusing power. He reproduced the surface curvature of the thick lens in sections, maintaining the same focal length with a fraction of the weight. The lens strength in diopters is defined as the inverse of the focal length in meters.http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/fresnellens.html 



     The type of lens he invented is used in many lighthouses around the world and has a very distinctive shape, sort of resembling a beehive with a lamp in the center. 

http://en.wikipedia.org/wiki/Lighthouse 
     "The lens is composed of rings of glass prisms positioned above and below the lamp to bend and concentrate the light into a bright beam. The Fresnel lighthouse lens works so well that the light can be seen from a distance of 20 or more miles." http://micro.magnet.fsu.edu/optics/timeline/people/fresnel.html


     The lighthouses before he invented his lens, the ones that used mirrors, could only reflect light to small distances and reflect barely enough light in fog or misty nights.

     During his lifetime Fresnel was awarded for his work and was was a member of many societies. He read a memoir on diffraction of light in 1818, which he received the prize of the Academie des Sciences at Paris and in 1823 he was unanimously elected a member of the French Academy of Sciences. Two years after that in 1825 he also became a member of the Royal Society of London who later awarded him the Rumford medal. He died shortly after that in1827 of consumption on the 14th of July. 















Sunday, November 13, 2011

John Wallis (1616-1703


      John Wallis was an English mathematician born in Ashford, Kent, England.  He was first intended to be a doctor but his interested circled around mathematics. After receiving his Masters degree he entered the priesthood as a scribe for 6 years. He made many contributions to trigonometry, calculus, geometry and the analysis of infinite series along with other fields in English grammar, Theology, Logic, and Philosophy.. He was also interested in cryptography and he used his interest along with his knowledge in the area to decode Royalist messages for the Parliamentarians. This was during the time of the Civil War between the Royalists and Parliamentarians. Around that time he also joined a group of scientists that were later called the Royal Society and 6 years after that in 1649 he was appointed as chair of Geometry at Oxford University, where he stayed until his death in 1703.

     John Wallis among with all his brilliance was also an insomniac and used to do mental calculations in his head while lying in bed at night. He once calculated the square root of a 53-digit number and later recited it correctly from memory to 27-digit accuracy. He also designed a structure that was cleverly put together by using what we call today as structural analysis, solving a set of 25 simultaneous equations by hand.

“Wallis designed a structure that could span a square space while only being supported at the edges. It was made up of a pattern of short and identical interlocking pieces, each of which is attached to another piece at each end and supporting two other pieces in-between.” 




shelroof.jpg
http://www.soue.org.uk/souenews/issue4/shelroof.jpg




The structure didn’t need any screws, nails or glue since the pieces supported each other imposing only vertical forces.






      Wallis also introduced the symbol for infinity as being represented by \inftyThe Romans commonly used a similar symbol for a thousand. The reason why Wallis thought it was a good symbol to represent infinity was because the "ribbon" that was in the shape of an eight had no ending and just continued on in the same shape. This symbol was also sometimes depicted as another form of the ancient ouroboros snake symbol, which is a snake twisted into a horizontal eight that is eating its own tail that represented endlessness. 

      These examples are just a few of his many accomplishments that he made throughout his life and in the field of mathematics. To know more about his more complicated discoveries about mathematics this website does a good job at explaining them. 

http://scramble.hubpages.com/hub/John-Wallis-Mathematical-Biography



Websites used