Do you know the position where God proclaimed that let there be Universe?

Hi Guys

A particle is a point mass. To study its motion we must know its position with respect to a desired point  in one dimension (1D) along a straight line , or two intersecting lines ( axes ) forming plane in 2D or three intersecting lines (axes) forming space in 3D.

Rene desCartes (1596-1650) invented the method of studying Geometry using Algebra by defining Co-ordinate System.

In 2D plane ( an ant be crawling on a floor ) you need two intersecting lines to determine the position of the ant uniquely, called axes. The point of intersection is called origin and the distances of the point from the axes gives us an ordered pair (a,b) called the co-ordinates. desCartes made it easier by considering the axes to be orthogonal ( mutually perpendicular ) and there evolved the analytical geometry with rectangular cartesian system. You know graphs, so you have some idea about it.

Here the ordered pair (x,y) are the coordinates where x is the distance from Y-axis called abscissa or X-coordinate and y is the distance from X-axis called ordinate or Y-coordinate. Thus the coordinates of origin is (0,0).

Identically for 3D space ( a mosquito by flying in that room ) we need another coordinate - distance of the point from floor (XY-plane) called Z-coordinate

and we get a point in space as an ordered triad (x,y,z).

You may understand easily the difference between 3D and 2D as the flying mosquito in the room and the shadow of the mosquito on the floor.

Now I give you something to think on :

Can a particle be at two or more positions at an instant of time?

or,  if a particle changes its position will there be a finite time elapsed during its motion?

So now you see that to study motion we must know the Coordinate Geometry well.

All the best. You are ready now to get into the realms of Physics...

Purpose to learn is always important

Hi Guys

I believe to learn a subject one must know the purpose - why should we study that particular subject?

Let me ask you then why should we study Trigonometry?

This is for our basic instinct...to grab as much land on earth as possible, since ancient times to this date people made their index of power as procurement of larger land. Thus a King gave the object of measurement of his land ( whether that is greater than his rival neighbouring states ) to his department of wisemen; there were two objectives to know - the area ( for his satisfaction/grievance ) and the perimeter ( for defence arrangement ).

In Greece philosopher mathematician Euclid at around 300 BC started his journey to organise the subject of Geometry 
He is called the
Father of Geometry

In fact to me this was the start of 
human beings in deductive
logic. He studied the
most important
of plane figures
- the triangle or
trigon (polygon
with three sides.
He noted that
a triangle
has  some
features:
1. It is a plane figure bounded by least (3) number of straight lines
2. Any polygon can be divided into triangles; any irregular area can be considered to be broken into triangles subject to a very close approximation. So if we know triangles in detail - its area and perimeter, then we know any surface and its boundary (the King's requirement).
3. A triangle has three sides and three angles
4. The sum of all its three angles is two right angles
5. Any two sides are greater than the third one
and finally
6. greater is the side when greater is its opposite angle

The last property was interesting for the wisemen then to find a relation between the sides and angles.

........is it in direct proportionality?  No, there was no match found but already there was that extraordinary Theorem of Pythagorus for a special triangle - right angled triangle in which we have a relation between three sides. Pythagorus ( 570 BC ) was also
a polymath.

Here started the subject of Trigonometry with an intention to find the relation between the sides and angles of any general triangle - scalene. This is somewhat an induction process in forming definitions of trigonometric ratios - sine[sin], cosine[cos], tangent[tan] - in between sides of a right-angled triangles. With the growth of the subject we obtain the Sine Rule in general for scalene.

Sine rule says that a side is proportional to the sine of its opposite angle. We also find area [ Hero's Formula ] and perimeter through a chapter called Properties/Solutions of Triangles in Trigonometry.

Later we see that the measurement of the heights and distances of mountain peaks or other objects were done with the help of Trigonometry. In 1831 Bengali mathematician, Radhanath Sikdar used Trigonometry to find the height of Peak XV as the tallest mountain of the world under a leadership of the surveyor, George Everest. Now you know the name of the peak in the Himalayas.

However, solving the purpose Trigonometry did not get stalled over there; later we find these ratios as trigonometric functions which contributed heavily for the advancement of Mathematics.

Next day I shall speak on the purpose of  learning Co-ordinate Geometry.

All the best

God gave the digits, man made the rest...

My dear friends

I could not post yesterday. Actually last portion on Maths - Calculus is still pending to be discussed. Calculus is developed independently and at the same time by both Newton[1643-1727]  ( at your left)             and     
Leibnitz [1646-1716]  ( down and at your right ) at the end of seventeenth century. Newton applied the same to explain Motion and Gravitation.

Calculus is a latin word meaning stones for counting. Calculus is the branch of Mathematics that deals with the study of changes.
Let us consider that a car be moving along a straight road with constant speed.  If we want to know the distance covered at a given interval of time then we just calculate the product of that speed and time interval. But in general if the car moves with variable speed and along any path, the technique described above cannot solve the problem.

First we must know the speed of that car at each point of its path; we call it instantaneous speed. To determine this we break the path into very small fragments of distances that are travelled in even smaller intervals of time. So speed, in any such small interval, is the ratio of that description of small distance to the very small time interval. This is the speed during that time interval but still not instantaneous. We know that there is no end to reach smallness i.e., whatever small quantity you may think, I can  think even smaller. That is why we call it infinitesimally small. As a matter of fact we approach towards zero but not exactly zero. 

Now if we approach zero for that time interval, we get that ratio as the instantaneous speed. This ratio, subject to the condition of approaching zero, is called the derivative and determination of this derivative is the primary objective of Calculus through its one branch - Differential Calculus. The process to find the derivative is called differentiation. Basically derivative in general is the rate of change of a function (distance) per unit change of the independent variable (time) on which the function is dependent, at a desired value of the variable (time). This is why derivative is also called the rate measurer and Calculus is called study of changes. In every sphere of life we have a dependence to study and is therefore, the importance of the subject.

However, it is not finished yet. We still  need to know the total path described by the car with variable speed during a given finite time interval. For that we need to sum up each product of that ratio  [small distance to the infinitesimally small time interval] and that infinitesimally small time interval all over the path. The summation is called integration and this other branch is called Integral Calculus.

In differentiation you measure the function at each point by breaking whereas in integration you sum up to know the function along a finite interval. Integration is thus reverse process of differentiation.

I hope you now have got some idea about the purpose of this subject. I have seen in many cases the students learn Calculus mechanically without knowing its necessity and purpose.

Please do not learn this branch of Mathematics just for your examination. Be positive. If you love Mathematical Analysis, I am sure that, you will collect enough fuel to go for without looking back.

Wish you all the best

  

Time is the essence...

Hi Guys

I am sure that you now have found me a great bore! Monotonous directives, cliche treatments and rigorous Maths are making your life hell again. Let us discuss something different today. Let us remember a great philosopher ( in ancient times philosopher means a wise person who has authority in his subject ).

You know Human Civilization is nearly 4000 years old at the maximum, whereas the age of Earth is nearly 4500 million years. So our civilization is a tiniest of ticks in the Big Clock. Still there is someone, an extra-ordinary human being in wheelchair, who claimed that if we know the exact status of that precambrian soup, immediately after God has fired His oven to cook  this Universe, then someday we( this human race ) shall also be able to create another! God is God, but His son is no mean.

Rabindranath while dedicating his book on science "Bishwaporichoy" to Satyendranath Bose wrote that

 'human beings are the only living creatures who always questioned his own understandings, refuted illogical reasonings and always found to be happy in defeating contradictions...they always entered into a world beyond their limits to perceive but  came up with the truth'

To start with such human beings I remember the greatest of polymaths, Leonardo da Vinci (1452-1519). Have a look at his self portrait, now it is placed at the Royal Library of Turin. It is drawn in red chalk and most probably in 1512, a few years before his death. 

The portrait depicts a look of the genius that he is not happy with all he has done. May be some more extra-ordinary inventions he thought of but could not finish, may be he is not happy for what he has done...still he is amongst  those few sons of God. They are hand picked by the Father. I am too ignorant to describe even the complete works of  Leonardo. He is the archetype of the 'Renaissance Man' who was a painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, botanist and writer.

Phew...still he is not satisfied. That is the sign of a genius.

And also think of the span of time...all he had done in 67 years. We do not have much time left. If you really want to make a mark please do not waste your time.

Ramkrishnadev said his followers to make a mark. That is the meaning of your existence.

This is not easy now. In last 500 years the height of the pillar of civilization is no small because there are too many contributions from so many geniuses. You have to reach to that top of your branch and then make that mark.  Reference level is high and time is short.

So can you waste your time, my friends?

Continuing with Maths...

I know ALGEBRA is your favourite  portion of Maths over the last few years. Let us see what are coming onto our plates:

1. Ratio and Proportion ( variation )
2. Indices and Logarithm
3. Theory of Quadratic Equations
4. Progressions
5. Permutations and Combinations
6. Binomial Theorem
7. Exponential series; definition of "e"

Here also you have to know the theory only and practice simple problems after studying the basics. Later you will work out more difficult problems in your Maths classes.

In CO-ORDINATE GEOMETRY the task is lesser but knowledge is very important:

1. Coordinate systems- Rectangular and Polar; their transformations
2. Internal section ratios. Centroid of a triangle
3. Straight line; mainly y = mx + c form.
4. Definitions of Circle, Parabola and Ellipse.
5. Basic form and equation of Rectangular Hyperbola  ( xy = c )

Now you are ready to start with the favourite subject of God : Mathematical Analysis or simply called Calculus. In next post we shall discuss the same in detail.

But you are now at the launching station for a journey to cherish all your life. You may love or hate but you cannot avoid this purest form of philosophy in your future.

They say that wisemen are born twice. True. Once - when they learn to count and next when they learn Mathematical Analysis...

All the best understanding God's language

Extent of Mathematics for +2 level Physics

Hi Guys

I hope you have a renewed opinion about Maths now. I also hope in your Class-X,  you liked the following areas and that is the reason you feel yourself confident now.

1. GEOMETRY - Parallel lines, Similarity in  triangles, Pythagorus Theorem, Circle
2. ALGEBRA - Solution of Simultaneous Equations in two unknowns, Ratio and Proportion, Graphs
3. TRIGONOMETRY - Measure of Angles, Definition of Trigonometric Ratios, Problems on Heights and Distances
4. MENSURATION - Areas and Volumes of Rectangular Parallelopiped, Sphere, Cylinder, Cone

Great! I am overwhelmed by the depth of your knowledge in Mathematics. So why do you worry ?

Since you have just completed your Class-X and you are excited in gearing up for the next, this is the right time to go for TRIGONOMETRY where you have to know the following chapters:

1. Radian as a circular measure of angles
2. Trigonometric Ratios of Negative Angles, Allied Angles, Compound Angles, Multiple Angles and Submultiple Angles.
3. Definition of Inverse Circular Functions
4. General Solutions of Trigonometric Equations
5. Sine and Cosine Rules
6. Trigonometric Graphs - Sinusoidal only ( Sine and Cosine )

That is all. Just know the topic and master the formulae. Do some simple sums from your Maths book - only the first 10-20 of the Exercises. Your Maths teacher will take care of the harder ones later. Believe me he will be very happy with your progress then.

In next post I shall discuss the same on ALGEBRA.

Happy going to all of you.

To what extent Mathematics is important to know Physics?

- Sir, is this a Physics class or a Maths class?

A common frustrating question comes out of nearly all students at the Eleventh class and we also feel sometimes helpless to encourage our students to overcome this negativity.

Last day I said about mathematical modelling of a phenomenon and quantifying the physical quantities ( measurable entities ) to predict its value under known physical conditions. To do that you need to know Mathematics that the quantities obey.

Please note that greatest of Physicists are primarily greatest of Mathematicians. Newton, Gauss, Stokes, Riemann, Einstein, Dirac, Feynmann, ...all were basically geniuses to invent Mathematics of quantities to analyse their problems to explain physical  phenomena. There is no second opinion about it that you have to love Mathematics to understand this level of Physics.

All physical quantities do not obey fundamental laws of pure Mathematics even. There are deviations. Like you know that 'displacement' does not obey algebraic rule of addition but they obey geometric rule of addition. This leads to define physical quantities - vectors and formulate a new Mathematics - Vector Algebra.

Some say Mathematics is a tool to know Physics. I hate that word- tool. Mathematics does not care about anything but logic. It is God's own language. Pure in form and absolute in nature. Some say Mathematics is pre-requisite. That is also not adequate to express. Mathematics is necessity to know Physics.


So Guys, my advice to you is not only to prevent your negligence or fear but to build a sheer passion to know Mathematics in your forthcoming days, if you dream to see yourself as a Physicist or to know the subject in depth to reach upto your desired level .


Next day I want to discuss what should be your right plan to know Mathematics at this level to know Physics better. Meanwhile I would request you all to revise your School Geometry once again because it will not be discussed any more although its requirement will be felt throughout your life if you want to see yourself as an Astrophysicist in future.

Happy understanding and bondage with Mathematics...

Love nature and love all His creations

Hi Guys

Please appreciate nature. It will help you to  know the natural phenomenon. Be surprised with the awesome creation of this Universe. In each step, if you think, you will see the excellent intricacies prepared out of tremendous care and thought.

One of my friends, who is a famous teacher, always tells his students:

Do not see only but observe

Do not hear only but listen

Do not touch only but feel

Do not inhale only but  smell

Do not speak only but believe...

I add to tell you that revere this creation around you with solemn wonder...show your  gratitude that you are part of this magnanimity. You are also given a place. Seek the meaning of your existence...Nature will do the rest. If you are honest in your approach you will be shown light and someday you will glow so that others will see light.

Why do we need to study Physics and how?

Let us consider that in this biting cold you are rubbing the palms of your hands to keep yourself warm.You know due to friction the palm surfaces are getting warm. Mechanical energy is transformed into heat energy. But that is only qualitative inference of this observation.

Now if someone asks what is the scale of warmth developed ( temperature ) due to this rubbing; that means we want to measure the amount of temperature, then a quantitative analysis should be made to solve the problem. We study to find the parameters on which this increment of temperature is dependent:

1. area of the palm surfaces- more is the area, more is the rise of temperature
2. speed of palm movement- greater speed, greater increment of temperature
3. time of rubbing- more time of rubbing, more rise in temperature
4. presence of material on palm surfaces- lesser in smoother objects like -oil,powder
greater in coarse objects like- sand,etc.

So we find there are various factors on which the rise of temperature is dependent. Now we seek the nature i.e., the extent of dependence to find an expression of temperature mathematically. We call it mathematical modelling.

And this expression is your so called formula- if you obtain this by studying your observation and subject to actual results ( by plotting a graph ) we call the same as empirical. Whereas if we derive the expression with respect to our existing established theories and analysis, then it is analytical.

But in both cases you have to match the actually observed experimental result, otherwise nobody is going to listen your theory and explanation!

Wish you high analytical thinking and request you to set your mind to do the same all through your Physical existence.

Good Day Guys. All the very best.

Loving this subject of Physics...

Hi Guys

How is your studies going? I think everything is fine and I wish all the very best for your future.

Generally there is a common belief that PHYSICS is the most glamorous of all subjects. I do not actually know why this kind of belief is there. Yes, this subject is developed by some extra-ordinary geniuses who were/are as colourful as the subject but that is true with other subjects as well.

To me it seems at the moment that the subject holds the truth of the creation of this Universe and may be someday we may stand face to face with God. It is the subject that deals with intangible quantities ( force fields ) that resembles Him. This subject takes us to a journey to eternity, it helps us to make our mind like a poet. A poet creates rhythm in his choice of words while a physicist needs to know the rhythm of nature.

In a historic meeting of Rabindranath and Einstein, poet wanted to know about the famous "Relativity". The scientist explained the absoluteness of the speed of light and grossly explained that a particulate matter cannot move with a speed greater than the speed of light; if it has to then it will be converted into light that is energy itself. Then poet asked whether the converse is true or not - if the flow of energy be stopped by some way to create this Materialistic Universe? The scientist at that time could not confirm the converse phenomenon because he has not proven the same.

A poet is not bound by logic. He has written addressing energy as always in motion and vibrating:

If you stop for a moment
Then and then only
This Universe will be created in a flash
Will be filled by stars, planets, mountains... ( Chanchala )



I believe to know Physics make your mind like a poet and justify like a scientist who should only be driven by observation and logical reasoning.

Connecting you...

This is the first time I am speaking to you- my Boys and Girls- like this. I believe I can share your pleasure and pain through this, whenever you require. This is the place where I shall not

put you into classes rather I shall try to be always besides you all, who love the subject of Physics, to the best of my effort.

I am still a student of the subject and I could grasp very little of it but my passion to know this has no upper bound. I failed to keep track with this subject throughout my life due to materialistic reasons. I am sorry for that. But I am happy to share with my students whatever I could understand. I shall only be successful if some of my students put a brick into the pillar of this human civilization .



My dear guys I promise you to be always with you in this journey. By the way do you know that this is PROMISE DAY?

Love you all. I shall come back to you tomorrow with more about me, my dreams, your role, ...

Starting with you all...

This is fascinating to start speaking to you like this... I am a Student of Physics

and helping others to know whatever I find easier to understand the mysteries

of nature. I am ordinary but I know my boys and girls are extraordinary to solve

the unsolved mysteries someday to make me proud. I shall live through them...