The Groogle's Doodle and the Strudel Bugle

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I put Lewis Carroll, Dr. Seuss, and Shel Silverstein into my mental blender, and this is what came out.

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A groogle named Dougal made a doodle of a noodle-eating poodle

"Oh, what fine work I've done!" said the groogle

the groogle blew a bugle, the signal for strudel

but even after the groogle blew the strudel bugle

the groogle's servant came without a strudel

"Apologies, my lord Dougal", said the abashed servant 

who had to muddle through a puddle on the double 

"We're out of strudels and I lack the recipe"

At this, the groogle (named Dougal) used Google to find strudel

"Ah ha!" said the droogle named Dougal, "let's take the flagon wagon"

and so the droogle and his servant named Foozle set out for strudel

the flagon wagon stout and sure, for it was a gift from a dragon

thus the droogle named Dougal and his servant named Foozle set out

in the dragon flagon wagon in search of strudel found on Google

"When you see the strudel", said the groogle named Dougal 

to his servant named Foozle, "be sure to blow the strudel bugle"

Blowing the strudel bugle was the only way to scare off the

noodle-eating poodle that the groogle named Dougal had doodled

Their journey was not easy; they had to muddle through a puddle

in the dragon flagon wagon; there was a bungle in the jungle 

when a killer gorilla flotilla from Manilla attacked the groogle

named Dougal and his servant named Foozle just as Foozle spotted

the strudel and blew the strudel bugle from the dragon flagon wagon

a killer gorilla from the Manilla flotilla grabbed a paddle for the battle

that was a jungle bungle and the groogle and Foozle tried to muddle through a puddle

but the puddle paddle battle with the killer gorilla flotilla from Manilla for

the dragon flagon wagon began just as Foozle blew the strudel bugle

It was a raucous melee when entered the fray none other than the noodle-eating poodle

whom the droogle named Dougal had doodled before he Googled for strudel!

For you see, when Foozle blew the strudel bugle, he summoned the noodle-eating poodle

named Kitten Kaboodle to the midst of the dragon flagon wagon puddle paddle battle

with the killer gorilla flotilla from Manilla 

Kitten Kaboodle seized and blew the strudel bugle which signaled all the noodle poodles

to converge on the dragon flagon wagon of the droogle named Dougal and his servant named Foozle

The killer gorilla flotilla from Manilla was about to flee when the poodle named Kitten Kaboodle

offered strudel to them, for that is the custom whenever a noodle poodle hears the call of the strudel bugle

In thanks for the strudel, the droogle named Dougal passed the strudel bugle to the noodle poodle

named Kitten Kaboodle and ended the dragon flagon wagon puddle paddle battle with the killer gorilla flotilla from Manilla 

Once back at home, the groogle named Dougal made another doodle of the noodle poodle named Kitten Kaboodle who now was the keeper of the strudel bugle

perfect squares and the factorization of semiprimes

 I'll start with a few simple examples. 

11*13 = 143

12*12 = 144

13 - 12 = 1

12 - 11 = 1

144 - 143 = 1

1 = 1^2

Hmm. Interesting. 

7*11 = 77

9*9 = 81

11 - 9 = 2

9 - 7 = 2 

81 - 77 = 4

4 = 2^2

So if a and b are prime, and c is an integer halfway between them, then: 

sqrt(c^2 - a*b) = a - c = c - b

So given any semiprime, if we round it up to the nearest perfect square and find the difference between that and the semiprime, we can quickly factorize. The integer factorization problem is currently believed to be too hard to solve with current methods. It is also the basis for RSA encryption. 

I like to visualize semiprimes as rectangles made up of unit squares. If you take one of the rows/columns from the short side and stick it onto the long side, you'll see a gap of how many unit squares must be added to make the whole thing a perfect square. That gap will be the shape of a square.

Semiprimes can be thought of as perfect squares with a missing square-shaped piece of one corner. 

OK, time for a bigger example.

991*997 = 988027

Assume we want to factorize 988027. If we take the square root of that, we get almost 994, which is halfway between 991 and 997. If we square 994 and subtract it from the semiprime, we get a difference of 9 which is a perfect square. This proves that 994 is halfway between the factors of the semiprime and that the difference between each factor and 994 is 3 (square root of 9).

Is this end of the integer factorization problem? Maybe. Rigorous proofs are not my strength. 

Good Storytelling vs. Good Writing

These two lists might explain the difference:

List of English-language books considered the best - Wikipedia

List of best-selling books - Wikipedia

only sold well (over a million copies)

Alice in Wonderland, Dune, Pride and Prejudice, The Adventures of Huckleberry Finn, Black Beauty

only called the best

Animal Farm, Lord of the Flies, Ulysses, Heart of Darkness, 1984, Catch-22

sold well and called the best

Lord of the Rings, The Great Gatsby, To Kill a Mockingbird, Lolita, Catcher in the Rye

My conclusion: good storytelling makes money; good writing impresses critics.

I remember reading several of the "only called the best" books as assignments in school. I think schools should include more best-sellers in the curriculum. The Great Gatsby and To Kill a Mockingbird are often assigned, but younger readers seem to prefer fantasy, hence the popularity of the Harry Potter books. 

Another minor mathematical insight: chords and cyclic quadrilaterals - squaring the circle?

Any two intersecting chords of a circle will each get divided into two segments. If one chord has segments of length A and B, and the other chord has segments of length C and D, then A*B = C*D because of the  similar triangles that are formed. 

Thus, if the diagonals of a quadrilateral have the same property, it must be a cyclic quadrilateral because the diagonals are chords of a circle touching the corners of the quadrilateral.

However, except for a square, the intersection of the diagonals or chords cannot be the center of the circle because that would make two pairs of identical triangles. 

Lockhart noted that if one connects the midpoints of the sides of ANY quadrilateral, the result is a parallelogram. 

The World of Mathematical Reality – Paul Lockhart

What Lockhart ought to investigate is whether the diagonals of any quadrilateral are chords of a circle. Of course, the answer is no, but why?

The proof is left as an exercise for the reader. 

 

abolition haiku and limerick - poems 55 and 56

an abolition

is perhaps the final word 

sometimes not the end

for some great evil, "abolition!" cries the angry crowd

pomp and circumstance with fiery speeches read aloud

but in their zest they forgot their plans contain a certain fatal flaw

which is that changing minds takes more than just changing the law

for some care less about justice and more about feeling proud

aberration haiku and limerick - poems 53 and 54

an aberration

is not always the worst thing

variety is spice

it's an aberration when what we get

doesn't follow the plan we set

but it's better to roll with the punches

and when needed act on our hunches

than to frown, curse, grouse, and fret

abdomen haiku and limerick - poems 51 and 52

arthropod segments

head, thorax, and abdomen

home of the stinger

for abdomen is garbled Greek

and for those who knowledge seek

know the fondness scholars bold

had for the languages of old

even for tongues they could not speak

abbey haiku and limerick - poems 49 and 50

silent house of god

many monks in prayer are awed

from just the stained glass

Vikings looted an abbey Hibernian

and the monk who was most learned in

Latin mourned the stolen Book of Kells

But from Norse hands it fell 

And now we can tell the tale recorded therein

abalone haiku and limerick - poems 45 and 46

a marine mollusk

taken from cold, autumn seas

a dinner delight

a mollusk from the sea

known as the abalone

has a flat spiral shell

and by that you can tell

whether to take or leave it be 

abattoir haiku and limerick - poems 47 and 48

an abattoir grim

for the cattle that go in 

a job most macabre 

from a grisly abattoir comes our beef

and the doomed, fatted cattle come to grief

but later when I dine 

on a juicy steak so fine

vegetarians are beyond belief

abacus haiku and limerick - poems 43 and 44

still used in Asia

an ancient adding machine

first calculator

though the computer is most fabulous

there is plain beauty in the abacus

for wooden rods and beads

are all that one needs

to reckon even sums tremendous

aardvark haiku and limerick - poems 41 and 42

note: here begin my alphabetical poems

I don't think I can write a poem about every word in my dictionary (65,000 entries) but I will try.

burrowing mammal

eater of ants and termites

nature's pest control

the aardvark from Africa south

has a most unusual mouth 

with a tongue long and sticky

it can afford to be picky

and prefers ant over louse