November 30, 2016 Wednesday

Bedtime Story 


How Algebra and Analysis Took Over Geometry

Euclidean space is a coordinate space (space with a coordinate system that forms the basis of constructing vector space or a manifold), that allows several real variables (n) to be treated as a single variable.

The idea of coordinate space or space is very interesting and has undergone a remarkable transformation from the times of Euclid when geometry ruled.

In the days of Euclid, the two-dimensional space was largely defined with the Euclidean plane and the three-dimensional space with postulates and built over it, theorems.

Geometry and the structures created out of it were used to define the real numbers.

Such was the hold of geometry over other branches of mathematics.

Then gradually, very gradually over the years, algebra and mathematical analysis developed and took reigns over mathematics.

Mathematical analysis studies limits using calculus (differentiation, integration), derivatives, continuity and so on.  

                                     

This is possibly the most famous limiting equation often stated as limit of (1 + 1/n)ⁿ as n approaches infinity.

It is believed that this equation was first solved by Jacob Bernoulli way back in 1683 when trying to solve a problem on the compound interest.

Solving this, he came across that magical number now known as the letter  or the Euler constant.

This Euler constant is one of the most famous constants that is both irrational (cannot be expresses as a ratio of 2 integers) and transcendental (not a root of any non-zero polynomial with rational coefficients).

So over the years, this remarkable branch of mathematics called analysis and along with it algebra became so powerful and useful that now they began to be used to define geometry.

Stay tuned to the voice of an average story storytelling chimpanzee or login at http://panarrans.blogspot.in/

                              

Good night and my fellow cousin ape.

         

Another great educator and a teacher that I am aware of is Professor Subhashish Chattopadhyay in Bangalore, India.

While I narrate stories, Professor Subhashish an electronic engineer and a former professor at BARC, does and teaches real mathematics and physics.

He started the participation of Indian students at the International Physics Olympiad.

Do visit him here:

http://skmclasses.weebly.com/

All his books can be downloaded for free through this link:

https://zookeepersblog.wordpress.com/science-tuition-chemistry-physics-mathematics-for-iit-jee-aieee-std-11-12-pu-isc-cbse/

For edutainment and English education of your children, may I suggest this large collection of Kids Songs:

https://www.youtube.com/channel/UCMX11Z5SJQ3kgwSsFJLRIcg