Wednesday, 19 April 2017

Ramanujan museum

The Ramanujan museum for math

12 AUGUST 2009 NO COMMENT
S Sundaram and Nirmala Raman
PK Srinivasan, or PKS as he was known, was a dreamer with his head in the world of mathematics but feet fi rmly on the ground. He was an ardent admirer and practically a devotee of the Indian mathematical genius Srinivasa Ramanujan.
Ramanujan-Museum
This is what he wrote in a preface to Volume 1 of the Ramanujan Memorial Number: Letters and Reminiscences he helped publish in 1968; “(the dream is to set up a) Ramanujan Memorial Foundation with the object of setting up a permanent memorial to Ramanujan in the shape of a multistoried building in Madras, housing a planetarium, mathematical exhibition wings, auditorium, library and showrooms displaying applications of mathematics in industry. It will be a house of entertainment par excellence for the layman and it will strive to make mathematics almost as popular as dance and music. We solicit generous support and help from the readers and institutions all over the globe for translation of the dream into reality.”
He had to wait for almost 25 years to atleast have a room for the memorabilia of this great mathematician and finally could accommodate it in the premises of the Avvai Cultural Academy, Royapuram, and the man who helped him realise his dream, at least partially, was Shri A.T.B Bose, a businessman interested in education.
The story of PKS’s fascination with Ramanujan and how he came to collect letters and other memorablia related to Ramanujan and how these came to be housed in the Ramanujan Museum in Chennai is a story worth recounting if only to show the power of dreams and a single-minded devotion to a cause.
PKS was introduced to the life and works of Ramanujan in 1948 through a book on “Indian Scientists’ published by G A Natesan & Co. The life sketch of Ramanujan moved him and created in him a desire to discover more about the genius.
At that time, PKS was working as a mathematics teacher in Muthialpet High School in Chennai. Through his innovative methods of teaching, PKS managed to kindle an interest in mathematics amongst his students.
PKS felt that Ramanujan’s life taught you that it was possible to reach great heights of achievement irrespective of your background if only you are true to yourself. This was something he wanted all his students to realise. He was one of the founder members of the Association of Mathematics Teachers in India (AMTI) in 1965 because of a conviction that mathematics teachers needed to have a professional platform to exchange ideas.
In 1954 PKS met Janaki Ammal and S Thirunarayanan, wife and brother of Shri Ramanujan. Subsequently he also met Ananda Rao, who was a contemporary of Ramanujan in England. He was fascinated listening to the many small and hitherto unknown incidences in Ramanujan’s life. This meeting and subsequent contacts with relatives and friends of Ramanujan encouraged PKS into thinking about collecting letters and reminiscences related to Ramanujan’s remarkable life.
In 1962, the Government of India announced the release of a special commemoration stamp marking Ramanujan’s 75th birthday on 22nd December. PKS decided to use this opportunity to bring out a memorial number on Ramanujan, containing letters and reminiscences.
With the help of his students, both former and current, he formed a committee for this purpose in October 1962. They then set about searching for contacts and institutions in India and abroad that who were connected in any way with Ramanujan.
The committee placed ads in local papers, interviewed people who had known Ramanujan and gathered letters. When he got a response to an ad or found a contact, he would immediately follow up. Often he found himself just patiently sitting while some one rummaged around in an old trunk for some half-remembered letter. Sometimes he would bring in a stenographer skilled in both English and Tamil to record a conversation.

Thursday, 13 April 2017

2D SHAPES

2D Shapes

Regular Polygons
polygon is a plane (2D) shape with straight sides.
To be a regular polygon all the sides and angles must be the same:
2d triangle
Triangle - 3 Sides
2d square
Square - 4 Sides
2d pentagon
Pentagon - 5 Sides
2d hexagon
Hexagon - 6 sides
2d heptagon
Heptagon - 7 Sides
2d octagon
Octagon - 8 Sides
2d nonagon
Nonagon - 9 Sides
2d decagon
Decagon - 10 Sides
More ...

Other Common Polygons
2d quadrilateral
Quadrilateral
Any 4 sided 2D shape
2d rectangle
Rectangle - 4 Sides
All right angles
And many more!

Curved Shapes
These 2D shapes have curves, so are not polygons:

2d circle
Circle
2d ellipse
Ellipse

Tuesday, 11 April 2017

amazing maths facts

Interesting and amazing maths facts

Article Category: Units  |  14 Comments

The more one studies mathematics, the more mysterious it becomes, with powers that seem quite ‘spooky’ and almost magical at times.
Maths fun - photo
Consider the Power of Pi: it seems such a simple concept, the ratio between the circumference of a circle and its diameter. As a fraction, that’s simply 22 over 7 but as an actual number, Pi is unknowable.
See the box for an approximate (!) statement of the value of Pi but in fact you could go on calculating it into eternity and never find a pattern or reach the end. So we just call it 3.142.
But consider how this “irrational” number seems to crop up everywhere. Pi is all over the natural world, wherever there’s a circle, of course, measuring patterns in the DNA double helix spiral or how ripples travel outward in water. It helps describe wave patterns or the meandering patterns of rivers.
π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823...
But Pi isn’t just connected with circles. For example, the probability that any two whole numbers among a random collection are "relatively prime" with no common factor is equal to 6 over Pi squared. Pi even enters into Heisenberg's Uncertainty Principle; the equation that defines how precisely we can know the state of the universe.
So Pi is just one example of the ‘magic’ of math. If you want more proof of this, consider the following:

Pi and pizzas are linked

You multiply Pi multiplied by the radius squared to find the area and multiply area by height to find the volume, That means the volume of a pizza that has a nominal radius of (z) and height (a) will, of course, be: Pi × z × z × a
And strangely, if you enter Pi to two decimal places (3.14) in the your calculator and look at it in the mirror, you’ll see it spells ‘pie’.

Nature loves Fibonacci sequences

The spiral shapes of sunflowers and other patterns in nature follow a Fibonacci sequence, where adding the two preceding numbers in the sequence gives you the next (1, 1, 2, 3, 5, 8, etc.)

In a crowded room, two people probably share a birthday

It only takes 23 people to enter a room to give you an evens chance that two of them have the same birthday. With 75 people in the room the chances rise to 99 per cent!

Multiplying ones always gives you palindromic numbers

If you multiply 111,111,111 × 111,111,111 you get 12,345,678,987,654,321 - a palindrome number that reads the same forwards or backwards. And that works all the way back down to 11 x 11 (121) or just 1 x 1 (1).

The universe isn't big enough for Googolplex

A googolplex is 10 to the power of a googol, or 10 to the power of 10 to the power of 100. Our known universe doesn’t have enough space to actually write that out on paper. If you try to do that sum on a computer, you’ll never get the answer, because it won’t have enough memory.

Seven is the favorite number

Playing cards in pocket - all sevens
You might have guessed that most people’s favorite number is 7 but that’s now been proven.
A recent online poll of 3,000 people by Alex Bellos found that around 10% of them chose seven, with three as the runner-up.
That might be because seven has so many favorable connections (seven wonders of the world, pillars of wisdom, seven seas, seven dwarves, seven days, seven colors in the rainbow). But it’s also true that seven is “arithmetically unique” - the only single number you can’t multiply or divide while keeping the answer within the 1-10 group.

Prime numbers help Cicadas survive

Cicadas incubate underground for long periods of time before coming out to mate. Sometimes they spend 13 years underground, sometimes 17. Why? Both those intervals are prime numbers and biologists now believe cicadas adopted those life-cycles to minimize their contact with predators with more round numbered life-cycles.

Monday, 10 April 2017

maths life skills

Life Skills Learned In Math Class

One of the hardest questions for many math teachers to answer in a way that is relevant to students is: “why do I need to know this?”  “For the next course you take”, the easiest answer in many cases, does not answer the question that was usually being asked. My answers to this question obviously depend on the topic being studied at moment, and I don’t have “good” answers for all topics…  but here is my list of key life skills I learned directly or indirectly from math class, with some examples of situations where I find them indispensable.

Sums and differences

How much will all three of these items cost? How much more would I have to spend to get that one instead of this one?

Integer products and quotients

How much would three of this one item cost? Which is cheaper per unit: the 10oz or the 16oz size (when cost per unit is not displayed)? If our four person band will receive $160 for this gig, how much will my share be?

Decimal products (percentages, multiplication by reciprocals)

What dollar difference will a 3% raise in my weekly paycheck represent? How much am I saving if this item is discounted by 20%? How much should I tip the server at the restaurant?

Mental Math Skills

The above calculations usually arise when I do not have a calculator handy

Algebra

Mastery of and comfort with the rules of algebra allows me to re-arrange problems to make them easier to solve… particularly when I am trying to work them without a calculator or something to write on. 17 x 12 is much easier to calculate in my head if I think of it as
(17)(10 + 2) = (17)(10) + (17)(2) = 170 + 34 = 204
Algebra has also taught me to be comfortable tackling problems that will take many steps to solve, by first breaking the problem down into smaller tasks or goals, then solving each in turn (sort of like writing a 20 page research paper). Or, if that approach does not work, to try working backwards from the desired solution… or perhaps even starting “in the middle”, and working from there to both the start and the end. These problem solving approaches are useful in many walks of life, even non-quantitative ones.

Word Problems

Word problems often present information in a less structured, more true-to-life way. I have to think a bit to figure out what information is relevant to the question being asked, along with how best to use it. They give me better practice determining what mathematical tools might be relevant to the situation than problems which are already expressed either entirely in numerical form or as equations. In other words, they help me learn to better apply what I know about math to the world around me.

Geometric Proofs

Deductive reasoning is very broadly useful (ask any lawyer), and influences all of my attempts at communication greatly. It was easiest for me to grasp as a concept in the context of developing geometric proofs, which provide a visual aid to the deductive part of the reasoning. “Problem solving” involves tackling problems that are new to me, which I have the tools to solve, but for which I do not know “where to start” from prior experience. Most students struggle with this process as they learn it, and I see proofs as an easier place to learn this challenging and valuable skill than others.

Thursday, 6 April 2017

maths in graph

Make your own Graphs

Explore the wonderful world of graphs. Create your own, and see what different functions produce. Get to understand what is really happening.

What type of Graph do you want?
You can explore ...
graph straight line
... the properties of a Straight Line Graph
graph quadratic
... the properties of a Quadratic Equation Graph
cartesian coordinates thumb
And also:
 
cool graphs
Try some Sample Graphs
graphapplet1
Make up a function like you use a calculator, then graph the result
Bar Graphs