The Paradigm of 3

the paradigm of 3:

1 and 2 and 3
then 3 went on to 6

and 9
and 10

now 5 is preceded by 4 is it not
and 7 followed by 8

and 11 by 12

round to 8 again
5 sides
besides 9
how to get to 10?

well 10 divided by 5 is 2 is it not?
add 8 to get to 10 which is
besides 9 or rather
beside 9 which is
beside 8

iff or if and only if you start at the end
which is 10

and it starts with 1 or zero

CLEARCHARGE

Long Division in Mathematics

long division in mathematics:

it seems that when one number is divided by another the result up top could continue with no end in sight after the decimal point, especially when you divide a prime number by another prime number, say 17/19.

the immediate question is whether this result up top continues to infinity. can you keep writing? some of the numbers up top become an eventual repeat after a certain point surely? because if at some point in the calculation when you subtract after writing down the next number up top and performing that multiplication giving you the remainder the same as before at the bottom, surely then from then on the numbers up top are a series repeat while the first few numbers may not be?

divide an even number by an even number, say 8/16, is much easier. most prime numbers are odd.

CLEARCHARGE

The Calculus of Y = 1 + X power 2

the calculus of Y equals One plus X power Two:

if we plot X, like west to east, and Y, like south to north, zero in the lower left corner, and plot the coordinates of X = 1 then Y = 2, and X = 2 then Y = 5, and then X = 3 then Y = 10, we discover a line could be drawn roughly linking these coordinates that resembles an increasingly northerly sloping graph.

obviously, the area if we consider that, depends on the line and its distance to the X axis, so one could say that, the rate of change of area depends on the line drawn. logically, to continue, the rate of change of the line depends on the gradient at any point on the line, which is, a line drawn as parallel to the graph as possible.

if we examine the graph at X = 1 and Y = 2 the gradient looks steep but is obviously going to become much more steep as X goes on. Y/X = 2 and this seems like the gradient depending on how the line is drawn. notice that, ignoring in the equation, 1, that if we multiply the power by X we could write dY/dX = 2X, and that, if X is still 1, that dY/dX = 2. is that the gradient of the line?

if we, so to speak, if you like, reverse engineer that, to examine, how to obtain the area under the graph and, call it integration, we discover that the equation could be like X + 1/3 X power 3. think about it thus, reduce the power, multiply by the power, ignore that without an X after it. and thus in reverse, call it integration. if we let X = 1 then the integral would be 1 + 1/3 which equals about 4/3 which seems about right too.

can anyone prove that there are 3 dimensions to space? even the Universe contains a virtual reality game concept. and i've imagined how that works. imagine turning right, the empty grid of the visuals in front of you shifting left and so on.

CLEARCHARGE

The Odds on That

the odds on that:

correctly flipping and predicting coin throw at rest is very difficult. the odds are against but it happens. what does that mean? psychic for a few seconds?

first throw predicted correct is easy but to 10 throws? that's hard. but has happened with me several times. the odds are like a thousand against.

the odds of predicting 2 throws is like 1 out of four. not bad, but probably not good enough for realizing what the immediate future will be.

let's think about odds in theory. 1:3 what does that mean? 1 right versus 3 wrong? or 1 out of three? in gambling terms 1/3 that's a payout of one third of the bet or stake. like a payout of 3/1 pays three times your stake but a winning bet also returns your original bet size. so five pounds on a horse or dog payout would be a win of 15 pounds plus five the original. three pounds at 1/3 is a win of a quid. not too bad really, but that's like backing a favourite. it doesn't impress anybody, a shame really!

what are the odds on that? that it will succeed? betting, yes please!? the surprising thing about gambling given that you could win, is that the sequence of a winning streak actually is calm throughout.

but what is the point of gambling? is it to prove that you are psychic or to win a huge sum you could spend? i think originally it was to gain knowledge of all things mathematical and to be able to predict!

of course, spending a win always feels good!

CLEARCHARGE

Mathematics: Increments in Series and Derivative Calculations

increments in series and derivative calculations:

ratios, fractional odds and probabilities

4:3 and 5:4
57% and 56%
57:43 and 56:44

7:4 and 9:5
64% and 64%
64:36 and 64:36

around the middle of the decimal series 0,1,2,3,4,5,6,7,8,9 and its derivative series and fractional odds and probabilities, commonly used in gaming and associated betting, something in the pattern of numbers is significant in various series and derivative calculations. when used in predictive mathematical models and algorithms, it reduces unnecessary calculation in the best instances.

although the difference between 57% and 56% is tiny, the difference between 57% and 64%, for example, is significant. in the case of:

3:2
60%
60:40

5:3
63%
63:37

the difference between 60% and 63% is tiny.

numerical algorithms are patterns of numbers that can benefit mathematical models, used in programming and other applied sciences.

CLEARCHARGE

Some Examples of Mathematical Series:

some examples of mathematical series:

let us examine some mathematical series, which seem to be random combinations of the first four numbers in the decimal number system:

4,3,1,2
leads to 43-12=31

4,3,2,1
leads to 43-21=22

3,4,2,1
leads to 34-21=13

3,4,1,2
leads to 34-12=22

note 21-12=9 and 32-23=9 and 43-34=9

CLEARCHARGE

Mathematics: Algebraic Complexity Examples

Algebraic Complexity Examples:

Example a
2x+3+0=6
2x=3
x=3/2

Example b
2x+3+1=6
2x=2
x=1

Example c
2x+3+2=6
2x=1
x=1/2

Series a,b,c: x=3/2,x=1,x=1/2
What is the next number in this series?

2x+3+3=6
2x=0
x=0

the next number is 0

More examples:
2x+3=(1/2)+5
2x+3=11/2
2(2x+3)=11
4x+6=11
4x=5
x=5/4

2x+3=1+5
2x+3=6
2x=3
x=3/2

CLEARCHARGE