NUMBER PATTERN USING 1, 2, 8 AND 9

                      9 x 2 = 18

              99 x 2 = 198

            999 x 2 = 1998

          9999 x 2 = 19998

        99999 x 2 = 199998

      999999 x 2 = 1999998

    9999999 x 2 = 19999998

  99999999 x 2 = 199999998

999999999 x 2 = 1999999998

PALINDROMIC NUMBER PATTERN WITH 1

111111111
               * 111111111
--------------------------
 12345678987654321

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.

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.