## Saturday, January 10, 2009

### Teach-Learn (all mixed up)

Teach-Learn (all mixed up)

Some say that
one teaches best,
what one needs to learn
the most.

Teach-Learn
Two sides
of the same coin?
Or are they,
one and the same?

GB #8

### Ambigram Poettery

I started a series of blog posts with some "poettery" along with Punya Mishra's ambigrams. These are comments on ambigrams he has made over the years. You can find them here.

I call it poettery, because it is the product of my pottering around the poetry format. Really, its not poetry in the sense of the word-- can't really say I don't really understand the sense of the word.

Ambigrams, though, are something that are really interesting, and people interested in math are likely to like them.

You can read Punya's flattered introduction to ambi-poettary here.

### Binary Pascal's Triangle

Binary Pascal's Triangle

"Bit by bit,
I understand,
the triangle of Sierpinski"
says Pascal?

Math Poettary #1

## Friday, January 09, 2009

### Logical

Logical

Logical
If o looks like a,
Then a looks like o,
and conversely.
Look at the mirror g
and tell me,
what can you see?

Through the looking glass
they say,
beyond what is
logical,
you can find
the meaning of life --
the universe, everything:
The number 42.

GB #7

## Thursday, January 08, 2009

I'
m
front to back
and back to front.
I,
and
m.
And surprise,
so does

GB #6

### A-life (artificial life, spiral)

A-life (artificial life, spiral)

A Life
Changing a little
at a time.
A slightly different
point of view,
another shift
in perspective.
A Life,
you would think,
spirals endlessly.
Its an illusion:
Its finite,
like everything else.

GB #5

### A-life (artificial life) III

A-life (artificial life) III

A Life
black and red,
completely Square.
Looks the same
whichever way
you look at it.
Going around
a circle.
That's it?

GB #4

### Punya

Punya

A Pun-
or a good 1,
is just a Pun.
You'll never know,
whether
I say what I mean,
or I mean what I say.
A good pun, ya?

GB #3

### A-life (artificial life) II

A-life (artificial life) II

A Life.
What a life!
It gets further
and further
from itself.
And smaller
and smaller
forever.
And dissolves into
nothingness.

GB #2

### A-life (artificial life) I

A-life (artificial life) I, originally uploaded by punyamishra.

A Life
is no life.
Turn it around
its the same.
What A Life.
From A to E,
not worth living.

GB #1

## Sunday, December 07, 2008

### Get Smart! Maths Concepts

The book Get Smart! Maths Concepts has been released by Penguin Books, India.

The book is a survey of middle school math, and covers concepts that I feel will be useful for all students to know. It may even give a quick review of things you need to know in pre-algebra and algebra, before you encounter them again in a calculus class. The emphasis is on thinking mathematically, rather than just learning the procedures to solve problems.

You can buy the book from flipkart.

## Thursday, November 20, 2008

### Book Released

Maths Concepts has just been released. Check out:
http://www.penguinbooksindia.com/Bookdetail.aspx?bookId=7609

This blog is to answer questions if any from readers, post errata, and discuss solutions of the problems in the Do and Discuss section of the book.

### Acknowledgements

From the book Get Smart! Maths Concepts, Puffin Books, India, 2008.

I acknowledge the debt I owe to Professor Richard Askey of the University of Wisconsin. Most of the topics of this book are included in a beautiful handout made by Professor Askey. The handout outlines the essential aspects of algebra and geometry that students should know before they learn the Calculus.

I would also like to thank Vatsala Kaul, Penguin’s Editor for this book. Vatsala conceptualised this book creatively, and has clarified the exposition throughout this book. Further, I thank Shubhank Bhadauria and Tarun Sachdeva for creating the graphics in this book.

I thank the following people who are an integral part of my life, and who have encouraged me in one way or the other during the writing of this book: My school friends—Hartosh Singh Bal, Punya Mishra, Poonam Madan, Gaurav Suri, and Vikram Jamalabad. My colleagues— Jagdish Prakash, Shantanu Prakash, Abhinav Dhar, Sangeeta Gulati, and Meena Raju. And my family—Hem Bhatnagar, S. S. Bhatnagar, Saurabh Kumar, Amit Bhatnagar, Jayshree Bhalerao, and Priti Kumar.
Last but not the least, I wish to thank my daughter Tejasi. It is because of Tejasi and her friends that I rediscovered the joy of doing mathematics at the primary and middle school level.

## Wednesday, November 19, 2008

### Contents

1. What is Counting?
3. Multiplication and Areas
4. Division
5. Divisors and Multiples
6. Prime Factorization
7. Addition and Subtraction of Fractions
8. GCD and LCM
9. Integers
10. Rational Numbers
11. Decimals and Measurement
12. Linear Equations
13. Symbols and Their Algebra
14. Division of Polynomials
15. Basic Constructs of Geometry
16. Congruent Triangles
17. Parallel Lines
18. Area and Perimeter
19. Pythagoras Theorem
20. Coordinate Geometry
21. The Square Root of 2
22. How to Study Math
164 Pages

### Dedication

Dedicated to Mrs. Asha Sarin and the late Mr. I.S. Chawla, two amazing math teachers, who got me hooked to math in the late 70s and early 80s in Modern School, Barakhamba Road, New Delhi.
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