The Justicar: The Good, The Bad, The Profoundly Stupid

No, this isn't about Rebecca Watson. This is about a mathematics, err 'mathematics', cough 'book' I was introduced to today by the sheerest of accidents. I 'found' a new blog I hadn't before heard of, and I was reading a rather detailed discussion on category theory (absolutely interesting subject one notes). So, there are some mathematically bright people there, which is probably why I enjoyed the discussion.

The host of the place goes by the name MarkCC, and I must say that in my first few minutes of reading over there I am suitably impressed to have included his blog in my google reader doohickey.

However, his about page has a link on it left by a commenter. This link is um, special. Yeah, it's special. That's it. Mm hmm. It's to an online book which seeks to properly determine the value of pi. It is, I am assured, not ~3.14. No, it's 3.125. Oh here, take a look for yourself.

Well, I'm glad we have this all settled. I'll pick up the red math phone and let everyone know. First, I want to point out a couple other of the, um, interesting bits.

Squares are properly handled in 3 discrete cases.
Group 1.) perimeter> area
Group 2.) perimeter = area
Group 3.) area > perimeter

Now, I don't want to let mathematical genius of this caliber (calibre if you prefer) evade detection and proper citation, so I'll quote him directly (note u.l. and u.a. mean units of length/area as pertinent):

Squares with sides of 4 u.l. have a perimeter of 16 u.l. and an area of
16 u.a. Perimeter = 16 u.l. and area = 16 u.a. What I immediately
observed was the common number for the perimeter and the area.

So, our steely-eyed mathematician has discovered the secret most of us mathematicians have been too afraid to make known: 4s = s^2 for s = 4.

Now I know what some of you cynical fuckers out there just might be thinking, but please, please, hold your fingers. There is a method to his madness, or madness to his method. Or something.

If we ~~circumscribe a circle~~ if we draw a square around a circle, we immediately note there are four points of tangency. This is key here. For,

It is most important that one realise that circles are depended of
squares. This law does not imply for rectangles or triangles.

It is obvious that the squares (but not rectangles one notes) of the three different Groups from earlier can be ~~used to circumscribe~~ drawn around any circle. Since this can be easily shown, it is obvious that the circle will ~~inscribe~~ be inside the squares. Therefore, circles (and their areas!) will fit into one of those three categories above. Or, in the author's words:

Now we know that the square with 4.u.l is unique and solitary. And we also
recognize the unique circle with a diameter 4.u.l, which is placed inside the
square. The question is which constant or value is useable for calculation of a
circle.
By now we know that the squares grading-system is a law of nature. If in
every square there is a circle with its diameter equal as the side of the
square there must be a grading system for circles as well. The circle
grading-system is also a law of nature.

Now, we skip ahead slightly to see the real magic at work here. I promise you, Archimedes himself would indeed be taken aback by this process.

This is a consequence directly of taking the natural logarithm of the common logarithm of e. Except, of course, in cases where we take log[ln(e)]. Please see:

The first formulae is constructed and it with using into that ln of logarithm e,
which the formula are based on that. (1)
The basis I started with is logarithm e^ since I chose the ln of logarithm e^. The
squares side is put into the formulae which one give some values for each square.(2)

For more on this brilliant and shining beacon of intellectual light, please see the whole paper.
It's worth noting that you can earn yourself a copy of the book, which--I can state without any concern of peradventure--has even more information!