In2infinity Podcasts

Infinite Density of the Number e

In2infinity - 4D Maths
In2infinity - 4D Maths
Infinite Density of the Number e

Good day everybody it’s Colin Power from in2infinity with another podcast about some of the infinite mathematics we’re dealing with. Today we’re going to be talking about the density of number E and why does a number he have that rather particular number? We’re going to try and solve this in a sense by looking at the square and the triangle. As you know, as you remember, what we said before is that an F naught point five if you remember that was a half of the density of the normal numbers or was it is twice as much numbers as there are normal numbers and LF naught point five and we find that by just dividing the reciprocal space of a line between zero and one and adding the totals up together as you go through, and you can find out more about that. But if you think about the number you what it’s kind of doing as a function, it’s like taking one then it’s taking one plus two. Yeah, there’s a cool factor also taking one plus two plus three, and it’s adding all of those reciprocals together from a triangle and really trying to compress it all into a single number, a dot you know, that’s, that’s what you can see the number is doing. Yeah. So it’s, it’s compressing a triangle. And when you come to rotate the number or something like that, we see the number appearing in pi. And that’s because the density function in a sense of what we’re looking at. So you can imagine, if you look at something called inverse geometry, and what we show you is actually there’s a triangle will turn into a hexagon and that’s a process of inverse geometry. You can check that out, and that will double it surface area is doubling factor. And we have inverse geometry that turns a diamond shape into a square. And so what you’re seeing there is you can put a circle around the outside and you can see that PI will fit around a hexagon perfectly and then we’ll divide pi into six. And you can put a circle inside the square in the what we call the route to fractal or the inverse geometry of the circle. You can put one inside the fractal and you can also put one outside Yeah. Whereas the triangle, you just gonna put one circle. So that’s the difference. There. We’ve got two circles and verses one. And they both pan out into the hexagon plane and the which we call zero to the power three, and the square plane which we call zero to the power two. So there’s difference there’s a discrepancy between remember number II is a triangle and when it wants to try and rotate on the on the square axis, suddenly, you know, there’s a lot more space that needs to be accumulated, accommodated. And so what we could look at them is that we can start to examine the dimensions of a triangle. And what you find is, if you stick two triangles on top of each other, you get square root three divided by two. So if you take one train running from tip to tip, so if you cut that in half, you find it from tip to tip will be square root of three divided by two. And that will divide the one of the lines which we’re gonna have lines of one, so one of the lines will be divided nought point five. So the square root of three by naught point five can split a triangle in half, and we can flip that it becomes the dimensions of a rectangle square root of three divided by two, hi, and not point five across. Yep. And so in order to make that one, what we can do is we can take two of those rectangles, and we can glue them together two of those rectangles. Yeah. So in other words, we’ve gone into the two triangles, there’s two halves and we’ve got double density on the whole triangle now Yeah, and we made a square. That’s that double density of infinity. And on the on the square, let’s just move on to the square a second. We’re going to just divide the square with a single diagonal and cut it into two and we can create a square of one so you can see what’s happening two triangles, making a square and a square being formed of two other triangles. Yep. So A to E collateral triangles make being cut in half making a square and we got two right angled triangles. They but there’s a slight difference. There’s a discrepancy between the size of the square the overall size of the square because it’s not a square the triangle when it’s a rectangle, it only goes to the square root of three divided by two Hi, not one. So got a slight discrepancy that and when we look at that discrepancy, what we can say is you know, the square root of three divided by one minus the square root of three over two, it gives you a certain number, doesn’t it? And that’s the number we’re going to look at. But But first, what we’re gonna do is just have a look at the density ratio. So you can imagine let’s draw a diagonal across the rectangle, it will be the square root of two. If it’s the square, yeah, going across the diagonal. But if it’s the diagonal on the triangle, it’ll be the square root of 1.75. And what that’s done is it’s reduced it by the square root of seven over eight, which is a funky pie number, isn’t it? Yeah, seven over eight. Yep. Yeah. Sort of gets in that seven zone. You can see actually, very close to 20 to over seven minus two. Anyway, you get the idea. Yep. The square root of that.

So let’s Haftar thing again. So we get a kind of idea of where things are going. And the ratio remains the same. But at naught point five, a square of naught point five. We get the square root of 4375. So that that gap, you know, it seems to sort of get different, it’s still a square of A over seven, but the numbers start to change quite dramatically. Can you see from 175 to naught point 4375. So the numbers are changing, whereas on the other side is just going to number just moving across. We’re going to five is that 25? Isn’t it 2.5? Is that is that ratio, isn’t it? Yeah, movement of numbers. I get that’s a bit much for you not to worry. What we’ll do is we’re going to take it now from the beginning and the basics. Yeah. So we’re going to take one, and we’re going to minus the square root of three divided by two and we get a number it’s like naught point. 13397, something like that. It’s pretty close, actually, to 1.34. Yeah. But it’s just a little bit over, you know, and so what we can do is, well, maybe what we should do is we should times that value by, you know, the square root of eight over seven. That’s the compression value, isn’t it? Yeah. And we got a new value is actually naught point naught naught 5413391. Okay, so we’ve got the five and the four for those people who know a little bit about infinite mathematics, five fours. Interesting number splits the nine, doesn’t it? Yeah. So we’re looking at a number here. And what happens is if we take the number e, we minus that number of the number A will get the number like 266414791. Now it’s quite interesting when I saw that number, because obviously the number 414 is a square of two number, isn’t it? Yeah. And you can see there can’t Yep, that actually, if I took you see, I’m saying it’s 20 if i times it by 100, that number, I can actually minus the square root of two of it, and I get a number very close to 265. Because minus the square root two of that six and the 414 went and left us with 26. That went down to a five Yep, and obviously, that’s just 15 more points, if you imagine more than are two to 250, which is three times five. Yeah. So I’m just trying to show in the workings of a little bit, some of the stuff that you can start to observe when you start to look at the number in ratio from the perspective of ratio. So that was, let’s say that’s going from the square to the triangle, and we want to go triangle square. And we can do that because we can take the same number, and this time, we’ll divide it by the ratio, seven over ATM, and we get another number 3315 Not point 33157020 is a double three good Yeah. So we’re getting a double three there. And what we want to do then is what we can do is we can start to sort of work with these numbers in a certain kind of way. So let’s take for example, our first number naught point naught 541359, which we derived from the number minus for me earlier in the last equation. And what we’re going to do is we’re going to times that by actually the function, the one naught point 13397459. We’re going to times that by the function. So we’re going to go into the square if you think of it like that, and the result that we actually get there is a very small discrepancy now we’ve got a little bit smaller is 00072525. All right, we’ve got the two fives and two fives back. It goes on. Obviously, there’s an infinite number. But, but we could divide that number by the one point, the ratio of 1.81 Sorry, the ratio of square root of eight over seven. Yeah, we’ll get we’ll get another number actually goes up in value, it goes to 0.01794919. And it was those nines that were popping up that I thought was quite interesting because we see a lot of that in the number is eight, isn’t it? That swapping them? So I thought okay, well, that looks like quite interesting number. Let’s subtract it from the number e and what do we get? Well, actually what we get is we get the number 2.7. Then we get 00. And then it’s like 33263. And what we’re going to say is we think that 333 is actually a 333 is actually carried on to infinity. And then what we’ve got here then is 27.

And the number 27 is actually three squared. So if you like what we’ve done is we’ve tried to prise apart the function v a little bit before the base 10 kicks in and gets a little bit too messy. And what we can kind of see here on the one side, the triangle side, you can start to imagine you’ve got the 25, the 15 and everything like that on the triangle density yet, which is one of our solutions to pi. And then we’ve got the threes on the square side, which kind of makes sense, doesn’t it? Yeah. naught point two five of the square going into a three of the triangle you know what I mean? Then that kind of makes sense. So on the square side, they see it as like more like that number three, the 27 three squared, followed by the infinity of threes, when we minus e when we might as naught point naught 1794919, or V. Yeah, we’re getting that sort of number we understand. And when we’re on the other side, when we’re minuses of a V on the triangle skyed side we’re getting you know, we’re getting to six five, yeah. Which is very close to 250. It’s just plus 15. Three times five. That’s right. And, and so, so basically what we’re saying is there you can start to mess with these densities. Now that you know, that pi ratio, and you can start to get across when a feel free like a more of an intuitive grasp through the base 10 distortion. So anyway, that’s, that’s just a little bit on the number in the density function. And you can see that the number eight over seven is a quite an important number when it comes to the number pi when we do the, you know, when we start to work out what the number pi is, and we find that number seven does create quite a distortion in the wave. So that’s probably why we’re seeing the number two there in that one because it drops to two on the 2.70033 to six. Yeah, so it’d be seven interfering with that which pumps pumps out from three. And on the other side, the 265 point 00057. Once you go to five, it’s a midway split in the infinity and then it’s seven, eight. So there we are. So you can see what we’re sort of saying it’s all there if you just look at some of the numbers. Yeah. So if you’re into the mathematics, get your calculator out and have a little play with E and just see what you can make out and put your post up in the comments anything interesting that you find. Anyway, that’s all for me today. This has been Colin Powell and a little broadcast on the density of E in accordance with LF naught point five. And, and you’ll see there that basically we’ve we’ve created a few functions and there’s more to explore. We’re just done a little bit of an outline for you. Thank you very much, and this economy from into infinity and whatever you do, have a great day to day do come to our website into infinity calm and check out all the great stuff that we’ve got going on there. There’s loads more information about fourth dimensional mathematics and all the other stuff. In the meantime, we’ll see you shortly. do tune in again and bye bye and God bless.

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