GB: 2009

Design II

Design II
Ambigram by punyamishra

A great design:
Everything fits in nicely
into one complete whole.

Not a hair out of place,
and not one thing
more
than what is
needed.

The form
and the function,
made for each other.

GB #32

Paradox

Paradox
Ambigram by punyamishra

All Cretans are liars
said Epiminedes,
a Cretan,
a classic Paradox.

If Epiminedes tells the truth
then he must be lying.
And if he is lying,
he is telling the truth.

Watson-Crick
Ambigram by punyamishra

Watson and Crick
show
what fun it is
to be
a scientist.

What fun it is
to discover
something new.

What fun it is
to compete
with the best
and win.

Watson and Crick
discovered
the secret of life
itself.
GB #30

Internet

Internet
Ambigram by punyamishra

The Internet
inking pacts
across the world.

Linking
and connecting
all humanity.

Shakily
connecting
all the dots
into one
continuous whole.

GB #29

Internet II

Internet II
Ambigram by punyamishra

Small knots
woven together
become a net.
Flexible, stable,
and very strong.

Small computers
inter-connected
become the Net.

Unleashing
the power
of communication,
of creativity,
and
of community.

Small individuals,
linked together
become the
Internet.

GB #28

Douglas R Hofstadter

Sides-reversed-is
Ambigram by punyamishra

Douglas R Hofstadter
sides reversed is
Retdatsfoh R Salgoud
sides reversed is
Douglas R Hofstadter
...
is one Strange Loop.

Hofstadter wrote
Godel, Escher and Bach:
An eternal golden braid.

A personal review follows.

Dog
Originally uploaded by punyamishra

A dog,
wags his tail,
seeks attention.
And licks your face,
without asking for
your permission.

Comes up close
and becomes
personal.

And becomes
your best friend.

GB #26

God

God
Originally uploaded by punyamishra

GOD
looks the same
whichever way
you look at it.

Look down from the top
or up from bottom --
and find GOD.

Look in the mirror
and see GOD.

Just like the 0,
symbol for
nothingness.

But still,
required,
to count from
one to infinity.

GB #25

I Love My India

Tejasi made this using My Paint Free, on my iPhone.

Trees

Birds

Flowers

Math Poettary - Infinite

Check out the post here.

A brief explanation

The post mentions the sphere as a "one-point compactification" of the (complex) plane (by adding a point at infinity). The property of the sphere being compact somehow makes it a little closer to being "finite" and therefore easier to handle. But to understand more precisely what all this means you need to take a good course in Complex Analysis or Topology.

When studying complex analysis, I thought that the theorems are simpler, more beautiful, and closer to the finite case than analogous theorems in Real Analysis. I don't know whether that is due to the relationship with the sphere, but I suspect it is so.

Here is an example: You know that a polynomial p(x) with real coefficients (and a finite degree) can be written as a product of factors of the form (x-a) where a is a zero of the polynomial. (The root a is of-course a complex number). Turns out, under certain conditions, we can write a function (which can be viewed as an infinite series) as an (infinite) product of its zeros. For example, consider this formula:

Euler's Product:

Euler Product

(The formula above taken from Wikipedia's entry on the Wallis Product.)

The formula looks nicer if you replace x by (pi)x. Then the expression on the left has zeros at +1, +2, +3, ... and -1, -2, -3, .... And on the right you get factors of the form (1-x/n)(1+x/n) which is zero for x = +n and -n.
In fact, the way we write the product is something to do with making the product "converge" (or make sense).

This formula is definitely something I will write about one day. I think I need to pick up a complex analysis book again...its been too long...and have almost forgotten the beautiful stuff I used to see everyday.

Darwin

Darwin
Ambigram by punyamishra

"Beauty in mathematics,"
says Polya,
"is seeing the truth
without effort."

Polya's dictum applies
to Science
as well.

Darwin explained
nature's bounty --
from simplicity
emerged complexity,
adapting by competing.

Darwin explained
so much, so simply,
so beautifully.

GB #24

Infinite

Infinite
Originally uploaded by punyamishra
Infinite plane
made compact
becomes a sphere.

Still infinite,
but compact,
somehow closer to
being finite.

GB # 23 (also Math Poettary)

Look here too.

The Modulus Function

Every differentiable function
is also continuous.
"This does not mean,"
the Modulus Function
points out,
"that every continuous function
is differentiable too."

Math Poettary #5

Not differentiable

A continuous function
Going along nicely
without lifting pencil
from paper.

Ouch!
This sharp point
got me,
its not differentiable.

Math Poettary #4

Continuous function

A continuous function,
draw it without
picking up pencil
from paper.

At all points,
the left hand limit
the same as
the right hand limit,
the same as
the value of the function
at the point.

At all points
its value
what it should be.

Math Poettary #3

Book Review by Tejasi Bhatnagar

BOOK REVIEW: GET SMART! MATHS CONCEPTS
DAILY BARD RATING: 4.5 STARS

Maths Concepts is a book written by Dr. Gaurav Bhatnagar for classes 6th to 8th. The interesting part of this book is that it has jokes and conversations related to maths. A child who gets 60% in maths may get above 90% after reading this book. It contains interesting problems which may look easy but are difficult to solve. It even teaches the ten important ways to do well in mathematics.

FULL DISCLOSURE
Tejasi is the author's daughter. This telegraphic book review was written for a school assignment to write a newspaper (which she named THE DAILY BARD). A character named Tejasi has also featured as one of the many kids having the 'conversations' mentioned in Tejasi's review. This fact may have influenced her interest in the book.

No-x-in-Nixon

No-x-in-Nixon
Originally uploaded by punyamishra

NO X IN NIXON

A palindrome
but False.

NO X IN NIXON
sides reversed is
NO X IN NIXON

Truly
a longer palindrome.

sides reversed is
sides reversed is
sides reversed is

(repeated ad infinitum)

truly
the longest
palindrome.

GB #22

Sense-non-Sense

Sense-Non-Sense
Originally uploaded by punyamishra

Image in
No Og
de Nash,
No Jabber
wock soever.

No pun
ya at all.
No Ji,
No Bee,
No ambi,
just potty.

Life sans
non-sense,
makes no sense:

It is
like this sentence.
Meaning less,
or none at all.

Or like this one.
Not funny;
no fun at all.

GB #21

Love

Love
Originally uploaded by punyamishra

Fools marry the girl they love,
Wise men love the girl they marry,
goes an old dictum.

Love turns
most of us
backwards --
into a fool.

Eventually,
all turn wise.

GB #20

Play

Play
Originally uploaded by punyamishra

"Come back soon from play,
and finish your work"
is what you hear.

Until work becomes work,
and play, play.

Play hard enough,
and play becomes work.

But, work hard enough,
and work becomes play.

And if you look hard enough,
PLAY becomes LEARN.

Now you don't need,
to hurry back from play.

GB #19

Discover

Discover
Ambigram by punyamishra

The scientific training,
teaches how to discover.

The artistic training
teaches how to uncover.

The mathematician uncovers,
only to discover --
new things to uncover.

GB #18 (Also Math Poettary)

Isosceles Triangle

An Isosceles Triangle
looks in the mirror,
and finds itself un-reversed.
"My base angles are equal,"
it says.

Math Poettary #2

Darpan (rotates to mirror)

Darpan (rotates to mirror)
Originally uploaded by punyamishra

When you read something in Hindi,
do you turn it around in your mind,
and think it through in English?

When you speak in English,
do you think it through in Hindi,
and turn it around in your mind?

Does your mind let you see
what you really are,
when you look in the mirror?

GB #17

Blogger

Blogger
Originally uploaded by punyamishra

I may not write very well
but still,
I do write.

I may be confused,
but still,
I do express myself.

I may not have much to say,
but still,
I do say it.

I may not think too deeply,
but still,
I do think.

I am
a Blogger.

GB #16

Ali

Ali
Originally uploaded by punyamishra

Ali said to himself:
"I'm the Greatest".
And for many,
he was
The Greatest

What do you
tell yourself?

GB #15

Visual Wordplay

Visual Wordplay
Originally uploaded by punyamishra

A picture, they say,
is worth a thousand words.

Then what about words,
that are also pictures?

What about
Visual wordplay?

GB#14

Anand (reflection)

Anand (reflection)
Originally uploaded by punyamishra

Anand.
Simple,
humble,
down-to-earth,
impassive.
A nice guy.

Aggressive.
Listens to
his opponent's
breathing,
to read
their mind.

And works his own
with lightening speed.

Anand,
chess champion.

GB #13

How to buy the book

Here is a list of addresses and contracts in case you are having trouble finding the book.

Delhi: Variety Book Depot – 23412567 / Mr.John

Chennai: India Book Distributors – 044 28353173 / Vinay Anchan
Desh kumar (Penguin Rep) - 9789087712

Mumbai: Strand Mumbai - 022-22086109 / Madhu
Ketan Patel (Penguin Rep) - 9867189490

For online book store you can go to www.firstandsecond.com

Here is another online book store link.

If all else fails, please write to: customer.service@in.penguingroup.com.

Smita

Smita
Originally uploaded by punyamishra

P-Smita,
A love story.

Psmita,
listened patiently,
to every story
through the night.
While the Other
dropped off.

Psmita,
flipped P over,
for ever
and ever.

Psmita,
continues to
listen patiently --
even though
this P
is never silent.

Gb #12

Good-Evil

Good-Evil
Originally uploaded by punyamishra

Good and Evil,
black and white.

One cannot exist
without the other.

When you remove
the evil,
is good
left-over?

GB # 11

Madam-i'm-Adam

Madam-i'm-Adam
Originally uploaded by punyamishra

Madam I'm Adam.
Could be the first
sentence ever spoken,
the first
palindrome.

It reads the same
front to back
and back to front.
Flip it over,
and still,
its the same.

First ever sentence,
an ambigram.

GB #10

Teach-Learn

Teach-Learn
Originally uploaded by punyamishra

We are here
to teach what we learn,
and to learn what we teach.

We are here
to learn when we teach,
and teach when we learn.

We are here,
to give what we have,
and take what we can.

GB #9

Teach-Learn (all mixed up)

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

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
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

GB #1