## Friday, February 13, 2009

## Thursday, February 12, 2009

### Math Poettary - Infinite

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:

(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

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

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

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

## Saturday, January 31, 2009

### 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

## Friday, January 30, 2009

### 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)

## Wednesday, January 28, 2009

### Isosceles Triangle

looks in the mirror,

and finds itself un-reversed.

"My base angles are equal,"

it says.

Math Poettary #2