REAL LIFE APPLICATION OF

                       MATHEMATICS

Algebra

1. ·         Computer Science
2. ·         Cryptology (and the Protection of financial accounts with encrypted codes)
3. ·         Scheduling tasks on processors in a heterogeneous multiprocessor computing network
4. ·         Alteration of pattern pieces for precise seam alignment
5. ·         Study of crystal symmetry in Chemistry (Group Theory)

EPC 3 - VISUAL PROJECTOR (Eriksons infancy stage)

                     BLAISE PASCAL

Philosophy of mathematics

Pascal's major contribution to the philosophy of mathematics came with his De l'Esprit géométrique ("Of the Geometrical Spirit"), originally written as a preface to a geometry textbook for one of the famous "Petites-Ecoles de Port-Royal" ("Little Schools of Port-Royal"). The work was unpublished until over a century after his death. Here, Pascal looked into the issue of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same time, however, he claimed this was impossible because such established truths would require other truths to back them up—first principles, therefore, cannot be reached. Based on this, Pascal argued that the procedure used in geometry was as perfect as possible, with certain principles assumed and other propositions developed from them. Nevertheless, there was no way to know the assumed principles to be true.

Pascal also used De l'Esprit géométrique to develop a theory of definition. He distinguished between definitions which are conventional labels defined by the writer and definitions which are within the language and understood by everyone because they naturally designate their referent. The second type would be characteristic of the philosophy of essentialism. Pascal claimed that only definitions of the first type were important to science and mathematics, arguing that those fields should adopt the philosophy of formalism as formulated by Descartes.

In De l'Art de persuader ("On the Art of Persuasion"), Pascal looked deeper into geometry's axiomatic method, specifically the question of how people come to be convinced of the axioms upon which later conclusions are based. Pascal agreed with Montaigne that achieving certainty in these axioms and conclusions through human methods is impossible. He asserted that these principles can be grasped only through intuition, and that this fact underscored the necessity for submission to God in searching out truths.

            SOPHIE GERMAIN’S WORK IN    

                    NUMBER THEORY

        Marie-Sophie Germain ( 1 April 1776 – 27 June 1831) was a French mathematician, physicist, and philosopher. Despite initial opposition from her parents and difficulties presented by society, she gained education from books in her father's library including ones by Leonhard Euler and from correspondence with famous mathematicians such as Lagrange, Legendre, and Gauss. One of the pioneers of elasticity theory, she won the grand prize from the Paris Academy of Sciences for her essay on the subject. Her work on Fermat's Last Theorem provided a foundation for mathematicians exploring the subject for hundreds of years after. Because of prejudice against her sex, she was unable to make a career out of mathematics, but she worked independently throughout her life. 

Renewed interest

Germain's best work was in number theory, and her most significant contribution to number theory dealt with Fermat's Last Theorem. In 1815, after the elasticity contest, the Academy offered a prize for a proof of Fermat's Last Theorem. It reawakened Germain's interest in number theory, and she wrote to Gauss again after ten years of no correspondence.

In the letter, Germain said that number theory was her preferred field, and that it was in her mind all the time she was studying elasticity. She outlined a strategy for a general proof of Fermat's Last Theorem, including a proof for a special case. Germain's letter to Gauss contained her substantial progress toward a proof. She asked Gauss if her approach to the theorem was worth pursuing. Gauss never answered.

                   MATHS PUZZLES

1. What is the following number? 18, 21, 24, 27, 30, 33, 36, ______________

           Answer: Here the pattern to be observed is: every successive number is greater by 3. So the sequence will be: 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, and so on.

2. What is the following number? 53, 51, 49, 47, 45, 43, _______________

      Answer: Here the pattern to be observed is: every successive number is smaller by 2. So the sequence will be: 53, 51, 49, 47, 45, 43, 41, 39, 37, 35, and so on.

3. Hari had 6 siblings who were born all born 2 years apart. The youngest is Richa who is only 7 years old while Hari is the oldest. What is Hari’s age?

        Answer: Richa, the youngest sibling is 7 years old. Each sibling was born 2 years apart, and there are total seven children (Hari and his 6 siblings). So Hari’s age is: 7 + 2 + 2 + 2 + 2 + 2 + 2 = 19.

4. The principal is constructing a square playground for the children of her school. She wanted to fence the area with four exits around the playground so that the ground was accessible from all sides. If she used 27 poles on each side of the playground, how many poles would be needed in total?   

          Answer: 104 poles. The 4 corner poles will be common to two sides. Hence: (25 poles x 4 sides) + 4 corner poles= 104 poles

5. What weighs more – A kilo of apples or a kilo of feathers?                                  

        Answer: They weigh the same. Each weighs exactly a kilo.