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Monday, November 9, 2009

EUCLID



FATHER OF MATHEMATICS

The Greek mathematician Euclid’s referred to as “THE FATHER OF GEOMETRY” is well known for his most famous work “ The Elements” which is a collection of geometrical theorems and “Euclidean theorem”.


EUCLID’S FAMOUS QUOTES:
“The laws of nature are but the mathematical thoughts of God”


“ There is no other Royal path which leads to geometry”.
THE ELEMENTS:

The Elements is divided into 13 books.
  • The first 6 books deals with plane geometry.
  • Books  7to 9 deals with number theory.
  • Book 10 deals with the theory of irrational numbers .
  • Books 11 to 13 deals with three-dimensional geometry .

Euclid's Elements is remarkable for the clarity with which the theorems are stated and proved.


EUCLID'S OTHER WORKS :       
  • ON DIVISION deals with plane geometry.
  • The book DATA discusses plane geometry and contains propositions.
  • PHAENOMENA is a work by what we call today as applied mathematics, concerning the  geometry of spheres for use in astronomy. 
  • THE OPTICS, corrects the belief held at the time that the sun and other heavenly bodies are actually the size they appear to be to the eye.
  • CONICS was a work on conic sections.
 EUCLID'S APPROACH:

Euclid used an approach called the "synthetic approach" to present his theorems. Using this method, one progresses in a series of logical steps from the known to the unknown.

EUCLID’S CLASSICAL PROOF ON PRIME NUMBERS:

Euclid proved that it is impossible to find the "largest prime number," because if you take the largest known prime number, add 1 to the product of all the primes up to and including it, you will get another prime number. Euclid's proof for this theorem is generally accepted as one of the "classic" proofs because of its conciseness and clarity. Millions of prime numbers are known to exist, and more are being added by mathematicians and computer scientists.

Sunday, November 8, 2009

A MATH POEM ON FRIENDSHIP

0% INVEST AND 100% INTEREST

Friendship is infinity,
containing only plus points.
So, my friend you are a Modulus.
If the world is a circle,
You are a point on the circumference,
I am a tangent,
which will touch the circle at that point.
If I am a straight lineYou are a lso the same my friend.
For we are not perpendicular,
but always coincide.

ARCHIMEDES





FATHER OF MATHEMATICS

CONTRIBUTIONS TO MATHEMATICS
Archimedes, a Greek mathematician is considered one of the three great mathematicians along with Isaac Newton and Carl Fredrick Gauss. . His greatest contributions to mathematics were in the area of Geometry. Archimedes was also an accomplished engineer and an inventor.



  • Discovered the method to determine the area and volumes of circles, spheres and cones. 
  • Discovered the actual value of PI.
  • Archimedes‘s investigation on Method of Exhaustion led way to current form of Integral Calculus which is now updated. Though it is outdated it is believed that he invented the method of Integral Calculus 2000 years before Newton and Leibniz.

OTHER CONTRIBUTIONS
  • Archimedes performed countless experiments on screws, levers, and pulleys. 
  • Archimedes invented the water screw, a machine for raising water to bring it to fields.  
  • His work with levers and pulleys led to the inventions of compound pulley systems and cranes.  
  • His compound pulleys are highlighted in a story that reports that Archimedes moved a fully-loaded ship single-handedly while seated at a distance.  
  • His crane was reportedly used in warfare during the Roman siege of his home, Syracuse. 
  • Wartime inventions attributed to Archimedes include rock-throwing catapults, grappling hooks, and lenses or mirrors that could allegedly reflect thesun's rays and cause ships to catch on fire.
  • Another invention was a miniature planetarium, a sphere whose motion imitated that of the earth, sun, moon, and the five planets that were then known to exist.

 A FAMOUS STORY 
There are many stories about how Archimedes made his discoveries. A famous one tells how he uncovered an attempt to cheat King Hieron.


The king ordered a golden crown and gave the crown's maker the exact amount of gold needed. The maker delivered a crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to think about the matter. One day Archimedes was considering it while he was getting into a bathtub. He noticed that the amount of water overflowing the tub was proportional (related consistently) to the amount of his body that was being immersed (covered by water). This gave him an idea for solving the problem of the crown. He was so thrilled that he ran naked through the streets shouting, "Eureka!" (Greek for "I have discovered it!").


There are several ways Archimedes may have determined the amount of silver in the crown. One likely method relies on an idea that is now called Archimedes's principle. It states that a body immersed in a fluid is buoyed up (pushed up) by a force that is equal to the weight of fluid that is displaced (pushed out of place) by the body. Using this method, he would have first taken two equal weights of gold and silver and compared their weights when immersed in water. Next he would have compared the weight of the crown and an equal weight of pure silver in water in the same way. The difference between these two comparisons would indicate that the crown was not pure gold. 

Saturday, November 7, 2009

MATH LIMERICK


A Dozen, a Gross, and a Score,

plus three times the square root of four,
divided by seven,
plus five times eleven,
equals nine squared and not a bit more.







-- Jon Saxton

Thursday, November 5, 2009

CAREERS IN MATHEMATICS


Actuary
Actuaries are hired by insurance companies (life, health, casualty, etc.), pension plans, businesses, consulting firms (business and actuarial), and government agencies. To become an actuary (an Associate or a Fellow), one must pass a series of examinations administered by the Society of Actuaries. The initial exams are primarily mathematics, including probability and statistics, and can be taken while still an undergraduate student.


Computational Scientist
A computational scientist is an applied mathematician who interprets problems arising from the physical sciences and engineering in mathematical form and develops mathematical solutions to these problems. Very large and sophisticated computers are used intensively. Potential employers include government laboratories, the chemical industry, and the biotech industry. 

Operations Research Analyst
Also called management science analysts, operations research analysts help organizations coordinate activities and operate in the most efficient manner, by applying scientific methods and mathematical principles to organizational problems. Computers are used extensively in their work.

Systems Engineer or Systems Analyst
A systems engineer or analyst usually has substantial course work in engineering or another technical field. This enables him/her to apply mathematical techniques to solve the problems unique to the industry of their employer.

Scientific Communication
The scientific publishing industry has a need for scientifically trained individuals for sales and editing.

Software Engineer or Software Consultant
A software engineer generally designs and writes software that performs nonnumerical functions, such as graphics. A background in math and computer science is needed. Employers include consulting firms and large corporations which do their own software development. There is also room in this field for the entrepreneur or consultant.

 Statistician
Statistics is both a very applied field and also a theoretical one. Many, but not all, statisticians are active in both applications and the development of new theory, but the greatest potential in terms of jobs is in applied statistics. Statisticians generally work with people in other fields, therefore communication skills are very important. Statistical
applications nearly always include the analysis of data and hence some knowledge and experience in computing is very important. There are opportunities for statisticians in the government, in industry, business, medicine, and in academia

Wednesday, November 4, 2009

FLORENCE NIGHTINGALE'S CONTRIBUTION TO MATHEMATICS


The rare photograph of Florence Nightingale was taken by Lizzie Caswall Smith in 1910 .The black and white image of the silver-haired nursing pioneer shows her in the imposing bedroom of her home just off London's Park Lane, before her death in 1910 at the age of 90.


Florence Nightingale is most remembered as a pioneer of nursing and a reformer of hospital sanitation methods. For most of her ninety years, Nightingale pushed for reform of the British military health-care system and with that the profession of nursing started to gain the respect it deserved.

During the American Civil War, Nightingale was a consultant on army health to the United States government. She also responded to a British war office request for advice on army medical care in Canada. Her mathematical activities included ascertaining "the average speed of transport by sledge" and calculating "the time required to transport the sick over the immense distances of Canada."

Unknown to many, Florence Nightingale is credited with developing a form of the pie chart now known as the polar area diagram, or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram to dramatize the needless deaths caused by unsanitary conditions and the need for reform during the Crimean War .


The legend reads:

The Areas of the blue, red, & black wedges are each measured from the
centre as the common vertex.

The blue wedges measured from the centre of the
circle represent area for area the deaths from Preventable or Mitigable
Zymotic diseases, the red wedges measured from the centre the deaths from
wounds, & the black wedges measured from the centre the deaths from all
other causes.

The black line across the red triangle in Nov. 1854 marks the
boundary of the deaths from all other causes during the month.

In October 1854, & April 1855, the black area coincides with the red, in January
& February 1855,(*) the blue coincides with the black.

The entire areas may be compared by following the blue, the red, & the black lines
enclosing them.



With her analysis, Florence Nightingale revolutionized the idea that social phenomena could be objectively measured and subjected to mathematical analysis.

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