i am habituated doing mathematical problems involving some widely known basic theories and facts. as the basic building blocks of mathematics are so common in use that i hardly think of how truthfulness of facts were proved. in spite of solving hundreds of problems based on circle area, i can't figure out how to prove the irrationality of pi. if i search for value of this constant, i may get value accurate up to 500 decimal places but it doesn't help me to know how pi was established as irrational entity. i look back and think of all mathematics books i read up to +12, i never crossed any basic book explaining proof of this truth. i searched the proof in wikipedia, but things explained is hard to grasp for me. handling pi is still tough.
is it hypothesis of geometry or rigorously proved that the area of rectangle is 'length x breadth' and volume of cuboid is 'length x breadth x height' ??? they interpreted dimensional features of real world and devised these two most basic form of tools to explain geometrical meaning of shape and size. it seems to be surprisingly unbelievable, some smart thinkers gave solid reasons for foundation of these formulae to calculate area and volume many centuries ago, in spite our course books fail to provide the logics how did mathematicians derived them. any kind of regular or irregular two dimensional geometrical shape is summation of n number of rectangles. any three dimensional figure is composed of n number of small cuboids. we explain everything in terms of these formulae but one one asks to explain these formulae.
2 comments:
hi ritesh
after reading ur blog i realized one thing that u must have bunked many classes in your school level.
everything is there dude. if u want to know, how the area of rectangle is L*B, its simple, imagine rectale to be the pile having lenth as rectangle lenth and 1 unit as breadth and no. of pile equals to value of breadth, so when u multiply them u will get the area. these are very basic things dude
get ur basics right??
Truely Ritesh, We are very far from the basics and we have need to brush up them but that doesn't mean that these basics are baseless unless u have thouroghly searched for the rerason behind their existance even after many centuries...Do u think ppl haven't raise their voice against stg wrong in that time..I can definitely say that if there might be some worng with them it must have correctd till now... Moreover the example u have taken is not at all correct. there is proof of each mathematical formula available and someone can easily find out it..
Let us try to think in a different way...Imagine, If many things or formulas which u r using today may become just basics for our new generations...but that doesn't mean that what we r using today is incorrect...This is the process of develoment ...we cann't always stick to some bascis ...there is a need as per a particular time and we just have to apply the bascis available at that time in a proper way to be part of that development.It is just a plus point if u have good basics then only u can use them effectively.
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