Friday, June 04, 2010

The q-disease

Special Functions,
by Andrews, Askey and Roy.
Here's a belated review,
and a thank you.

~*~*~*~*~*~

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

Everything
in The Book
is as elegant,
as could be.

Everything
as simple,
as effortless,
as should be.

Everything
as beautiful,
as it is.

~*~*~*~*~*~

Thursday, May 14, 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

Sunday, April 05, 2009

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.

Saturday, April 04, 2009

Watson-Crick


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

Friday, February 27, 2009

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

Friday, February 20, 2009

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.

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