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

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

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

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:

(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.

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

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

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.

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

is also continuous.

"This does not mean,"

the Modulus Function

points out,

"that every continuous function

is differentiable too."

Math Poettary #5

A continuous function

Going along nicely

without lifting pencil

from paper.

Ouch!

This sharp point

got me,

its not differentiable.

Math Poettary #4

Going along nicely

without lifting pencil

from paper.

Ouch!

This sharp point

got me,

its not differentiable.

Math Poettary #4

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

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: 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

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

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

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