in mathematics there is no exact definition of a circle.

as well as accurate determination of the radius.

A circle is a lot of a square - where there are 35 thousand angles. And it can be complicated endlessly. But what if we simplify the circle and radius? There will be just 3 sides.

Here, see for yourself, the circle can complicate the infinite a lot. By adding facets. But the simplest circle model is the triangle.

I want to assume that the stable radii of atoms are also triangular. A visible radius (an atom is a bluff and a mirage)

I also made a simple 2D triangle folding simulation. And I related them to round radii that do not affect each other, and interesting images turned out.

Here, see for yourself

My suggestion is that this could simplify molecular modeling and solve the problem. After all, the simplest model of a circle is a triangle.

Previously, in the era of optical tubes, scientists saw channels on Mars. But with the creation of an exact technique, these channels turned out to be mirages and optical distortion. as well as all the long-term observed radiation of an atom, can be mirages.

Why then can not we create accurate simulators of the physics of atomic and elementary particles?

Is this a quantum problem? Or are ordinary computers not capable of this?

We can not create accurate simulators of the physics of atomic and elementary particles yet so far, because, for one reason, it seems that it will take too many advanced calculations running at a time. Like you have to monitor the speed of light, the splitting of electron/positron groups, and any other quantum fluctuations and probabilities (ex. I saw a video where there is an extremely small chance that something will spawn out of nowhere (e.g. a Boltzmann Brain - if a Boltzmann Brain pops up out of nowhere we have to simulate it - too much strain on the supercomputers), or disappear, due to quantum fluctuations), and every subtle decimal place. Plus it has to be accurate with time too, so there can't be any error in the time too, but even atomic clocks build up noticeable errors over time.

Well technically, this is also a quantum problem too.

However, I am not that wholly against your idea of using intrinsic triangles in circles too. It somewhat looks like when circles are stacked on top of one another on a plane, as shown in this image:

It's a picture of 6 unfilled circles stacked on top of each other on a plane against a white background. There's a red, unfilled triangle that's drawn on top of those black circles, and a green line that divides the red triangle into two, with a green right angle that shows that the green line is perpendicular to one of the red sides.

The circles do form a sort of triangle pattern just like I see in your simulation image, so I think it has some potential. I think I kind of understand what you're saying where the circles form triangular patterns, just like normal triangles would. It would be helpful if you could explain more.

From, donuts554.

I was reading this over and decided offer what I hope will help explain some of what you are talking about, as well as ask some questions that I had regarding what you all have written.

But first off, a quick disclaimer: **I am not an expert on any of this, just someone who ends up spending way too much time on tons of websites learning about random stuff, this included. **

I am going to separate my thoughts and comments by the post that brought them up, and I will quote the post to serve as an example.

## 01010011111's first post

in mathematics there is no exact definition of a circle.

as well as accurate determination of the radius.

I agree with Donuts on this. There is actually an accurate definition of a circle, and of its radius. Are you confusing the fact that π is an irrational number? I do agree that we cannot product a perfect number. But why should we bother worrying about that? Only a few digits of π gets us really close. See How Much Pi Do You Need? from Scientific American

A circle is a lot of a square - where there are 35 thousand angles

A computer might approximate a square that way, but as Donuts said, there is a definition of a circle.

It is a great way to approximate a circle is with a many sided polygon, but 35 thousand might be a bit much. I do 3d modeling as a hobby, and have never really needed to go above maybe 150 sides, though the movie industry might go higher

I want to assume that the stable radii of atoms are also triangular

Why? A computer could handle 15 sides pretty fast, and it is much closer to a circle.

I also made a simple 2D triangle folding simulation. And I related them to round radii that do not affect each other, and interesting images turned out.

I am not 100% sure what you are trying to point out here? Could you elaborate on the triangle a little bit further?

Previously, in the era of optical tubes, scientists saw channels on Mars. But with the creation of an exact technique, these channels turned out to be mirages and optical distortion. as well as all the long-term observed radiation of an atom, can be mirages.

While I agree that our understanding might change, I also agree with donuts that your comparison might not be the best.

Also, what do you mean by the long-term radiation of an atom?

## Donuts First Reply

Channels on Mars themselves haven't been proven by Mathematics to be channels on Mars, but shape of the orbits of the electrons of atoms of the periodic table of elements has been proven by Mathematics.

Calling them orbits is not entirely accurate. They do not orbit the way drawings commonly illustrates (almost like planets around a star), but actually exist within a cloud of probability, they exist somewhere within said cloud. This gets into weird quantum mechanics stuff that I cannot really explain as I do not fully understand it myself.

## 01010011111's second post

Why then can not we create accurate simulators of the physics of atomic and elementary particles?0

Is this a quantum problem? Or are ordinary computers not capable of this?

Its for a combination of reasons. Part of it is what donuts said. Since this stuff is so small, a lot of them exist in a very small area, which means that it is harder to simulate, just because of how many of them there are.

Additionally, the electron density clouds I mentioned makes it even more complicated. Since the electrons are in a weird probability cloud thing, we cant just drop a few electrons in and call it good, we would have to simulate the probability cloud.

Protein folding is done at different scales by other projects, like Folding@home, which models proteins by atom, instead of by sidechain segment, while DMPfold runs at a similar level as foldit, but uses deep-learning to try to work out how proteins fold.

But foldit does have a different interesting aspect, in that it is not entirely reliant on computers. Instead, humans looking at it add some interesting intuition and pattern recognition that computers don't have, might work out interesting designs that a computer cannot. Furthermore, analysis of designs that humans figure out can be used to make better computer simulations in the future.

I think that the radii of atoms is assumed to be triangular, because according to what the first post says, theoretically, the triangle is a simplification of a circle in terms of the number of sides, and also since a stack of circles forms a triangular pattern, such as the cross-section of a pile of straight steel pipes.

I also think that what is meant by "*related them to round radii that do not affect each other*" is that in the 2D triangle folding simulation, the side of the atom that isn't touching or affecting other atoms is shown to have a spherical rounded surface. It is just like the shape that is formed when 3 soap bubbles are clustered together, as shown in this image:

See how in this image, it seems that there are straight lines that are formed when the bubbles are touching, or affecting, each other, as if the atoms were triangular polygons when they are affect each other, and that when the part of the bubble is not affecting other bubbles, it is shown to be rounded.

I also think that what is meant by "the long-term observed radiation of an atom", is the spectroscopy of an atom, which shows the different frequencies and wavelengths of light radiation that are emitted when white light is shined at an atom. What may be meant by this is that this spectrum that is formed may be a mirage, that may be possibly formed by a combination of small factors and imperfections that are outside of the atom, instead of inside the atom.

I think that there is an exact definition of a circle.

According to a Wikipedia article that is talking about the circle, "

A circle is a shape consisting of all points in a plane that are a given distance from a given point, the center;".The article also says, "

The distance between any point of the circle and the center is called the radius.". I also don't think a circle has 35,000 angles.I also think that in the first image, in https://imgur.com/ina6c5b, I think the designs in between the triangle shape and the most circular shape make it

seemcomplicated, but not the circle itself. Also, I don't think a triangle is necessarily the simplest model of a circle. It's because you are thinking of a "circle" in terms of its number of sides,when essentially a circle just consists of a points that are all the same distance from the circle's center.About your second image, https://imgur.com/a/LGpQm1t, it is very interesting, and I would like to share my thoughts on that image.

What is shown in the image is similar to the tessellating hexagonal pattern on a honeycomb, and the arrangement of when multiple circles are stacked in 2-D.

However, a triangle that is in the position as shown on the image

seemsvery unstable, because the set of points on the triangle have varying distances to the center of the atom. The electrons can't be constrained in a triangular shape, so they have to orbit in an elliptical shaped orbit.Although a triangle is unstable itself internally, a triangle is a very stable shape externally, even with pressure, as seen on wires and arches on constructed road bridges. Also, the pattern formed by clusters of bubbles is hexagonal, which is similar to the pattern formed in your second image. The shape formed is similar to the image in https://www.researchgate.net/figure/a-At-b-p-2-the-reference-describes-a-cluster-of-3-identical-bubbles-b-Three-bubble_fig1_6429034 , which shows the 120 degree angle formed when 3 bubbles cluster together, as if the bubbles were

hexagons.I also think that your comment about

channels on Mars being Miragesdoesn't look that related to your topic aboutatoms as mirages. Those are twocompletely different things, on completely different scales, on completely different subjects, in completely different contexts.Channels on Mars themselves haven't been proven by Mathematics to be channels on Mars, but shape of the orbits of the electrons of atoms of the periodic table of elements has been proven by Mathematics. Mathematics is a very important and necessary thing that you have to try to incorporate into your assumptions on science to prove them as that they are logical, of course.

According a book written by Theodore Gray, co-founder of Wolfram Research,

.I see that what you say doesn't agree with what has been described and theoretically proved in mathematics, and since mathematics is factual, it seems that your assumption is not consistent with the rules of reasoning that is assessed according to strict principles of validity, which can include evidence. But I do believe part of your assumption though, where your simulation could simplify molecular modeling.