Saturday, February 14, 2009

Dog


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

Thursday, February 12, 2009

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.

Monday, February 09, 2009

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

Sunday, February 08, 2009

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

Saturday, February 07, 2009

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

Friday, February 06, 2009

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.

Thursday, February 05, 2009

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