Blog Space :D Sine of One Degree

[Frank74]

I spent 10 years studying natural mathematical patterns and geometry. The importance of Phi and the Fibonacci sequence. And am resolved in my conviction that the '0' used as a place holder in the decimal system is wrong, and we should only use digits 1-9, with a '0' meaning something different than a numerical exponent. As it was supposed to have been implemented in its inception.

Look up vedic mathematics to get some examples of its application.

I worked out that there is a recurring pattern to infinity in the Fibonacci sequence when the totals are mod 9'd. And it explains natural growth. The number pattern forms a geometry that follows the law of the path of least resistance. And the geometry shows polarity of energy as well as force/amount.

Useless comment over.

Cheers.

[ExtremeDude2]

Binary!

[HatCat]

^ Ignore this Dude of Extreme dumbness; he is so dumb he cannot even properly solve for x in a basic equation like (x - 5)(x + 3) = 0.

http://forum.pj64-emu.com/showpost.p...8&postcount=53

Originally Posted by Frank74

And am resolved in my conviction that the '0' used as a place holder in the decimal system is wrong, and we should only use digits 1-9, with a '0' meaning something different than a numerical exponent. As it was supposed to have been implemented in its inception.

That still is a mostly new idea to me, but at least in things like C you get a partial implementation of that. The use of 0 as a leading digit in C numbers prevents the integer from being parsed as a decimal--a literal like `089` should fail to compile in C as it should be 89 without the leading 0.

[Frank74]

I should have said the decimal system is wrong in terms of explaining the real world At least for calculation. The '0' is used in the result, but not the calculation. '0' = '9'. Its a method I was drawn to in Vortex Based Mathematics. I was one of the first members at http://vbm369.ning.com/.

I like ancient mathematics. The oldest forms are the closest to how computers calculate today. Powers of two, no multiplication, just adding. BINARY!

A 5000 year old method:

56 X	25
1	25	0	
2	50	0	
4	100	0	
8	200	1	200 +
16	400	1	400 +
32	800	1	800 = 1400

Phi is derived from the Fibonacci sequence. 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13, 8+13=21, 13+21=34, 21+34=55 etc.
Two numbers in sequence, the higher divided by the next lower, equals perfect Phi after so many iterations. Also the sequence when mod 9'd, follows a pattern, and has a mod 9 doubling (1,2,4,8,7,5) and dividing (1,5,7,8,4,2) pattern running through it.
Fibonaccci in column sequence.

1	5	34	233	1597	10946
1	8	55	377	2584	17711
2	13	89	610	4181	28657
3	21	144	987	6765	46368
					
Mod 9'd.
1	5	7	8	4	2
1	8	1	8	1	8
2	4	8	7	5	1
3	3	9	6	6	9

Doubling.
1,2,4,8,16,32,64,128,256,1024,2048,4096 = 1,2,4,8,7,5,1,2,4,8,7,5 etc.
Dividing.
1, 0,5, 0.25, 0.125, 0.0625, 0.03125 = 1,5,7,8,4,2 etc.

Plotted on a 9 point circle. The red plots the doubling/dividing pattern, and represents matter/current. The green the spirit/magnetic field (Right angles to the current, as in today's text books).

[ExtremeDude2]

Originally Posted by HatCat

^ Ignore this Dude of Extreme dumbness; he is so dumb he cannot even properly solve for x in a basic equation like (x - 5)(x + 3) = 0.

http://forum.pj64-emu.com/showpost.p...8&postcount=53



That still is a mostly new idea to me, but at least in things like C you get a partial implementation of that. The use of 0 as a leading digit in C numbers prevents the integer from being parsed as a decimal--a literal like `089` should fail to compile in C as it should be 89 without the leading 0.

Bro, don't make delete that post with ur posting it everywhere.

[HatCat]

That is an interesting number of patterns revolving around the Fibonacci. I was actually never taught any rudimentary examples of sequences like that in primary school and had to have read about it later on my own. But I never thought that deeply about all the patterns.

Actually, I was never beforehand taught about Phi either (or "the golden ratio" as I usually see it being called in geometry). So, for some reason, the Fibonacci sequence after infinite iterations of (n[i] / n[i - 1]), converges into a limit of Phi = 1/2 * (1 + sqrt(5)).

So far in my computations of sin(1 deg) I have only ever countered the nested expression sqrt(5 + sqrt(5)) so many repeated times, but not quite Phi itself.

But the graph of matter and current versus the spirit/magnetic field looks particularly interesting...I like both philosophy and math but, until the sound of things like that, never really thought the two were co-relative. When I keep looking up this Vedic stuff it sounds more and more like the way math used to be done back then involved a lot more philosophy.

[HatCat]

Not as big of a success update as I was hoping, but I've successfully derived the cubic sine of one degree (or pi/180 radians).

Now my handwriting is very neat, in my not-so-humble opinion, but I still feel the need to post these images to this forum after all my scratches, scribbles and pseudo-erasures over 5 pages of notebook ink trying to calculate these expressions.

So for clean reading purposes to my own note-taking in trying to figure this out:


Haven't decided where to go from here. One thing I've observed is that (a^2 - b^2) is 64, so I can substitute 64 replaced with a*a - b*b or 4 with cuberoot(a*a - b*b) to try further to get rid of this imaginary cruft and the annoying radicals.

[Frank74]

Have you ever played with Primes? Just seen this > https://en.wikipedia.org/wiki/Prime_...c_progressions

Another example of the use of mod 9.

I have spent many years studying ancient scripture and science. Newton was a theologian. Tesla grew up reading from his father's library of ancient scripture, his father was a strict religious person. Einstein/Oppenheimer read Indian scripture. Oppenheimer used a passage from the Mahabharata to describe the first atomic explosion.

We've not yet made it back into the Golden Age. That I believe existed 14000 years ago. Disaster sent mankind into the dark ages, and we've still not achieved what was written in ancient times. A Golden Age is another 1000 years away.

It was Ed Leedskalnin's Coral Castle codes that got me first interested in this sort of stuff. An 85 pound man, built a castle on his own, he quarried every stone by himself, and positioned them by himself. Some of the blocks are several tonnes in weight. He wrote a book called Magnetic Current. I have a pdf I made of it here. https://dl.dropboxusercontent.com/u/...ic_current.pdf

[HatCat]

Some crazy amazing people centuries back. Crazy enduring, composing...light too. 85 pounds lol.
Humm...but why about 1000 years away for another Golden Age? Somehow that just sounds kinda soon to me.

That really is an interesting pattern with the primes. My last research project with prime numbers was merely to optimize the fastest C program to calculate the first 10,000 prime numbers, in the shortest amount of computation time. Several patterns, theorems/conjectures I learned about played a part in the optimizations...but I did not think every alternating 9 primes to mod by could have been one of the implementations.

[ExtremeDude2]

Bro, didn't I tell u that like 2 years ago?