Teach-Learn (all mixed up)
Originally uploaded by punyamishra
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
Teach-Learn (all mixed up)
Teach-Learn (all mixed up)
Originally uploaded by punyamishra
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.
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
Originally uploaded by GauravBhatnagar
"Bit by bit,
I understand,
the triangle of Sierpinski"
says Pascal?
Math Poettary #1
Logical
Logical
Originally uploaded by punyamishra
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
ADAM
ADAM
Originally uploaded by punyamishra
Madam
I'
m
Adam.
Reads the same
front to back
and back to front.
So does Madam,
I,
and
m.
And surprise,
so does
Adam.
GB #6
A-life (artificial life, spiral)
A-life (artificial life, spiral)
Originally uploaded by punyamishra
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
Originally uploaded by punyamishra
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
Originally uploaded by punyamishra
A Pun-
A bad one,
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
Originally uploaded by punyamishra
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
is no life.
Turn it around
its the same.
What A Life.
From A to E,
not worth living.
GB #1
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.
Book Released
Maths Concepts has just been released. Check out:
http://www.penguinbooksindia.com/Bookdetail.aspx?bookId=7609
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.
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.
Contents
- What this Book is About
- What is Counting?
- Addition and Subtraction
- Multiplication and Areas
- Division
- Divisors and Multiples
- Prime Factorization
- Addition and Subtraction of Fractions
- GCD and LCM
- Integers
- Rational Numbers
- Decimals and Measurement
- Linear Equations
- Symbols and Their Algebra
- Division of Polynomials
- Basic Constructs of Geometry
- Congruent Triangles
- Parallel Lines
- Area and Perimeter
- Pythagoras Theorem
- Coordinate Geometry
- The Square Root of 2 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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