We are so small brown broadcast now from Colleen power regarding the nature of squaring functions, which includes the square root of number i, and the density function of Al f naught point five. So, when we look at the number line, obviously 12345678 were all quite clear and all of that and every number has a square number. So, if we square the number two we get the number four, square them three get number nine. Obviously, we say that zero squared is not recognised by standard mathematics but in in mathematics is just as zero squared equals zero. So does one squared equal one but obviously there’s a shift in dimension when that happens, and in the zero in the perspective of zero divides infinite number space into four. And in that from the perspective of the number one, it creates a boundary around that space, encapsulating encapsulating all of the reciprocal numbers in the sense. Once we expand beyond square numbers beyond that, we’re really expanding reciprocal space, if you could think of it and it goes through a certain number pan up until we get to 100. And because we work in base 10, you could say that what the number 100 is one with two zeros, and we have a sequence now that goes from one to 100, which is one times 100, but it doesn’t flow. If you imagine them going like 1412345 We got to 2.56789 10 we get to 100. Count down the sequence. Yeah, from the start from 149 1625. That’s the 123 4/5 number. And then 3649 Six, why do you want to have 100? That’s the fifth, sixth, seventh, eighth, ninth 10th number. So once again, it’s the number 25. We’ve talked about it in a pie solution. And it’s there again, in the in the square numbers. When we go to the square roots, let’s have a little look let’s have a count through you could say after the number one that we had the number two square root of two be going the other way with name. So above the four, you know, we’re gonna put the two and we can put a square root beneath it saying hey, look, you can you can go down, go on your end, and it does it does. It kind of flows in a straight line, doesn’t it? In a sense I was able to think yeah, actually is a 45 degree offset if you think about it, because what we’re really doing is when we, when we, if you think about the the combination of the number one and the square root of two, the square root two is really a diagonal to the square of one. So that’s means let’s say we set everything off. We could put the number one we put the square root two above it. When we get to the number four, we find the square root of eight is what divides the square nine, suddenly we get to 18. Dividing the square square root of 18. And when we get to 16, it’s the square root of 32 Or is that 32 number again, isn’t it everybody? This time I’m paired with the number 16. If we imagine 16 was the seven and the five. So I’m going to let you have a little think about all that. And then the next step we move into the 2550. Which actually is if you think about it, it’s a quarter versus a half really, if you think about the number 150 is half of 125 is a quarter. So we’ve reached a very special point they’re at the square root of 50. We can say also squaring of five is a function of 10 is a function of 10. So we’d have to get 50 divided by 10. So we get square into 55 by 10 gets wearing five don’t Yeah, so that. That’s all fi stuff. And you can find out more about fi stuff from some of our other broadcasts. But for now, the follow up to to conclusion, what we’re noticing is there’s a pattern here 16 is doubling to 32. When we look at it as a square root of that function of the of the of the square. Yeah, so for example, one is doubled to do the Tuesday. What isn’t one yet? Yeah, exactly. And we’ve just put a square root in front of it. And we found that diagonal for doubled is eight. Yeah, inverse square root just a square root in front of it just to signify it’s the is changed direction. Yeah, but is this the number eight? Isn’t it just in a different direction? That’s all Yeah. And so what we find is there’s that there’s that square root function, or that sign of the square root, actually is a compression of infinity. That’s what the entry is. That’s what the square root function does, and how it compresses it. Well, it compresses it if we imagine on the one sense, we could say we’re growing through square numbers, Aren’t we here and we’re on here with the route numbers. And it’s a it’s a one to two ratio. So when we when we take that down, that’d be naught point five to one ratio. And there we have it density ratio, isn’t it? Yeah. Everything is in density ratio, then isn’t it? Yeah. So whether we look at something as being one density naught point five, and f naught point five is just an example of density. Ratio, isn’t it between the hole fractional numbers and the whole numbers. And here what we’re seeing is we’ve got the square numbers have exactly the same density ratio of naught point five to one, compared to the root of numbers one and what we’ve done is we have to do is we just have to add the root number to change the direction and in the sense by changing direction, that’s what doubles the number. Yeah. So what he has is we have here when we changed direction, we’re creating a second number line has right we’re rotating the number line Yep. And it’s creating a second number line. And that number line is double because we’ve doubled that we had one line before we’ve rotated it, we’ve doubled the number of number lines that we have now. Yeah, ending. So now infinity doesn’t end infinity ends in straight line does it ends on a two dimensional plane suddenly, and is that transformation from one dimension to two dimension, which creates that pie function? So we’re going to do they’re always going to have a little look back at the just go back a little bit and just to have a little bit of examination then of what happens then just before the screws are square root of two because we got one square root two, what about zero and doubled was 02, wouldn’t it Yeah, and so the square root function, then would be 002. Yet square root? Yeah. Okay, so that’s a little bit of a weird one for people to I know. Yeah. But you can imagine we’ve split we can split zero into two. Yeah, that’s right. We’ve got a plus zero, negative negative zero. And so once we start to understand that we can have that concept with the neutral zero, which is what we find at the centre of the atom, you know, the proton and the neutron and the neutron configuration, neutrons don’t have a charge, yet protons do. And at the same time, we have the negative electrons. So you know, it’s an attack as an atomic composite, and that’s what we’re looking at with fourth dimension. So we have a we have a negative zero, positive zero and a 00. And so that’s what we’re looking at that we can divide those numbers divide zero into two, what we get is positive zero, negative zero. We’re dividing nonpolar zero into positive, negative positive. And, and therefore what we do is when we put the square root of one above it, what we’re saying is we’re re congealing the two, aren’t we where I’m where we’re going from a squaring. If it was a squared zero, let’s say we have squared zero metre cross, or the square root of Wonder is doing is it’s collapsing the zero. It’s collapsing that number line back into a line. But as it does, so what we’re doing is we’re actually rotating, we’re opening up one’s line at 90 degrees. And when we’re collapsing, it was saying, Well, which one is collapsing into which one we don’t know. And so there’s a 50% chance it could be collapsing one way and a 50% chance it could be collapsing the other way. There’s a probabilistic chance, isn’t it? Yep. And we’ll go down to what is the number at the end of infinity when it reaches which is in causality is limited by the number three. But, but when we talk about in numerical space, we have ordinals that limit that sort of thing. And so we see that in the ordinal space, that happens in the negative first and it swings around in an anti clockwise, and therefore when we collapse that one will swing back and it will just continue collapsing in the anti clockwise direction. If we’ve labelled a number line with the plus on the right side and the negative on the negative side is swings round, and it collapses back round. And that’s where we get something called the unit circle, when we apply the square root of AI into the complex number plane. And so if you think about it, this solves the Riemann hypothesis. So this is our solution to the Riemann hypothesis, or part of it, is that as we as the square root one is a if you like an opening and collapsing of space, numerical space, it’s opening the zeros collapsing the zeros opening the zero. And as it does, it can rotate in an anti clockwise direction. And that’s why it’s every other non trivial zero in which we’re hitting these zero points. And that’s because the way that the Raymond constructed his four dimensional plane was a kind of strange, like it’s slightly strange, it’s slightly out of sync with the other numbers that are missing in the fourth dimensional mathematic that aren’t apparent. But once I put those other numbers in which you can see by the angular which you can see by the function of zero squared, actually, we get rid of the number I and what happens is number I now gets reserved for something else. We call zero to the power of three, which generates the number eyeline, which we call the Z line. You can call it the eyeline and you can also see what’s happening then if you compare the two models between the fourth dimensional model, which does accommodate for the square root of one quite happily, by balancing it through the rotational function of squaring, that we do find that the Raymond Zita plane is distinctly divided just into two halves, whereas the fourth dimensional plane that we are suggesting is divided into a quadrature, which equals a quarter pi. So therefore, we we’ve sown shown that through the pie solution, that’s how the plane is actually divided in the second dimension, not into half as as the Romans or the other solution with the number pi and because of that very nature, what we have is an offset and that offset creates all sorts of confusion. It stops also many things from happening with the Mandelbrot set, it stops the the formation of the second bowl. On the other half. You might notice that it’s famous because it got one ball shooting up in one direction and that’s, that’s just the nature of negative squaring, which we overcome with the fourth dimensional mathematic, which will return. Obviously, once we use the fourth dimension, you’ll see that you’ll see the other half returning, and also because you’re halfing of infinity there, what you will actually see is it will actually reflect equally in the four planes and what you’ll get is a perfect reflection of numerical number space. And what you’re seeing there with the bold is really just the PI function that is actually predicted in four dimensional space of the squaring of zero. And what you’re seeing in the centre function there is what we call the one inside the one so you know, Mandelbrot can actually is actually a very useful tool and from fourth dimensional mathematics. Once we overcome the number I want to reject, we just adjust the mathematics slightly to become fourth dimensional. And what we will see is it will turn into a symmetrical four way pattern. And that means we’ve got four ways symmetry, which means you will have a right angle at the centre which was which you can sort of investigate stuff, and we recenter the zero now back at the centre of the number plane. When you look at the Ryman number plane, what you see is the zeros actually offset which creates that distortion in the first place and the number one is unified. So what they’ve actually done is they’ve kind of unified the number one rather than what we’ve done is unified the number zero and spaced the zero out with a number one in four locations around the zero, which we could call the the cardinal numbers if you’d like we show that with the function, the Cardinals new ordinals offset and the minus one. So that shows you the function of of the plane of the fourth dimensional plane, and wide works extremely differently from the number II. It also solves the Riemann hypothesis. And as far as prime numbers go, we’ve got some information about some of that stuff as well, which also shows you how powerful fourth dimensional mathematics is because it gives us a new solution to primes. Okay, so that’s a little bit on the square number code and the intensity of LF naught point five and why the square root of one on the Ryman on the on the remond Zita plane, why it produces this offset. So every other non zeros they say is apparent once we apply the function. Okay. Thank you very much for listening. That’s my solution to the Roman Hotham hypothesis or some of it. There’ll be more solutions to the Riemann hypothesis coming soon. Stay tuned, and we’ll get back to you this has been into infinity column power, broadcasting the solutions to pi infinity the square root of minus one, the square root of one in fact as well and the Roman hypothesis. Thank you very much for listening.