Circles And Squares

Blog post # 39:

(This following puzzle/poem looks messed up in any font that is not fixed-width.)
Follow the words through the grid. If you take every path, a maze is formed.
This is sort of like a word-search puzzle, but the words go around corners and form sentences. The periods are the dead-ends. The multi-branched poem answer is in the comments to this blog post.

This Maze (a poem)
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T H I S L A B Y R I N T V E S T E T
H I S G R I D E P P A H E R I A R H
. S P O E M . A T O N D N E X S O A
T S A D E I S R S W I A D N A A M N
R . O S N O B U T T H B O U T N Y I
U N V I S I . D L O E P A T H S S T
T E E B C I H W : E Z A M A N I O W
H E O O H . E L D D I S A , Y F O N
: V U T D I R E C T R I T N T C K L
E A R S M H W H T I Y . S I R E C A
V H G O E I S I E O R E V A T I F E
E E L A E C I E V N , A S I N L A ,
R W ? F S H H C A O T S O L F O R E
Y N O O R A L L I S S A W L O T E W
T H G Y L O P A H G U C H A R A N D
H I N G I S A S W U O R H T E N I O
I , I S S O . . E P U L E . T O L M
N G T I T I L L , A Z Z Y E T B E .

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I am going to do something that is sure to lose me readers. I will post some math, BUT I will try to write it up in a way accessible to non-math people. Sit around and learn something... If you dare!

Of Scalene Existence


Such A Metaphorical Arctangent


Arctangents Of The Shell


X To The Y


(And the least mathematical of the picture-names in today's post)
Of Ambidextrous Refraction


Slice of pi...

Okay, this is a basic and relatively simple math result that I didn't learn until I was out of highschool. It relates to pi, the ratio of a perfect circle's circumference to its diameter (3.14159...etc; the digits go on forever). The result is NOT one of my own original results, since I think this result has been known for hundreds of years. But I am surprised they don't teach it in school until calculus class at the earliest.

Start by writing down the first half-dozen to a dozen or so ODD positive integers, in order starting with 1. (The number of these integers you write down is unimportant.) Put a little space between each integer.
1 3 5 7 9 11 13 15,
for example.
(Note, this is not the same sequence as the prime numbers. It is just the odd whole numbers.)

Write "1/" immediately before each of the integers you just wrote down. Now you should have a series of fractions, 1 divided by 1, followed by 1 divided by 3, followed by 1 divided by 5, etc.

1/1 1/3 1/5 1/7 1/9 1/11 ...

Next, put a "+" before the "1/1", a "-" before the "1/3", a "+" before the "1/5", a "-" before the "1/7".
Continue alternating back and forth, placing a "+" before every fraction following {any fraction with a "-" before it}, and placing a "-" before every fraction following {any fraction with a "+" before it}.

+1/1-1/3+1/5-1/7+1/9-1/11 ...etc

(Note that the plusses and minuses alternate.)

Now, let's pretend that we didn't write out just a half-dozen to a dozen fractions, but continued doing this, instead writing fractions for MANY MANY such fractions. Well, the result of our addition/subtraction, as the number of terms gets bigger (and the denominator in the fractions gets bigger, the fractions get smaller), would get closer and closer to a mysterious constant, a decimal. Whenever we add a fraction, the sum/subtraction is a little bigger than that constant. Whenever we subtract, the sum/subtraction is a little smaller than that constant. As we take more and more terms, the error approaches zero.

If we were to, say, take the sum/subtraction out to an INFINITE number of terms, then the sum/subtraction would equal that constant exactly.

Call that constant x. (Its decimal representation starts x=0.785...)
Now, last step, multiply that constant x by 4.

What do you get?

3.14159...

pi!

Now, what use is this formula for calculating pi? Actually, the sum/subtraction approaches pi/4 (=x) so slowly that is is almost completely useless for calculating the digits of pi.
(Pi is now known to MANY MANY digits. But you would have to take MANY fractions in the sum/subtraction to get even a few digits of pi accurately.)

But you can do things with the sum/subtraction, if you are a math person, that makes knowing this result useful (If you are into math).
Trust me. (Or not.)

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[Politics alert! Politics alert!]

One last thing today.

More in regards to the Supreme Court ruling on corporations basically having more free speech than individuals:
(See my earlier blog posts for more on this topic.)

It occurred to me that one way to help nullify the evil effect of this ruling is for certain news media organizations to SELF-IMPOSE a limit on how much corporations can spend on campaign and issue ads on their networks, in their magazines, etc.
The news media organizations would proclaim far and wide that they have such a limit. They indeed deserve good press for having the limit.
Both sides of an issue would be allowed to spend up to a predetermined level on the network, say, according to each media organization's own rules.

But...
Does anyone really think that media organizations, corporate swine themselves, will voluntarily limit how much is spent on their media outlets, especially when profits are at stake!?

Ha! Ha! Ha! Ha! Ha! Ha! Ha! Ha!!!!!!!!

We are screwed.

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Leroy