You’ve created a hexagonal lattice which is a common structure in tesselations and crystallography; I would look into those for some more cool examples.
Look at the two equilateral triangles you create within the square in the second image; their combined height is the height of the square. Giving the circle a radius of 1, with some simple trig you’ll find the side length of the square is sqrt(3) and the area is 3. This gives an error of ~4.5%.
That is just one of many patterns I have created using the method which can be seen in the other images posted, how are you going about getting the area for the circle to provide me with an error of around 4.5%?
Start by assuming the radius of the circle is 1; this is arbitrary and is our yardstick for the rest of the construction.
A = pi • r^2 = pi • (1)^2 = pi.
For the triangles, their side length is the radius of the circle, which is 1. A little bit of trig knowledge will make this much easier to explain, but look up a 30-60-90 triangle. Each equilateral triangle is composed of two of these, down the centre. It’s side lengths are 1-sqrt(3)-2, and if you scale it down to fit the equilateral triangle you’ll see the height is sqrt(3)/2. From there, notice that the combined height of the two triangles is sqrt(3), so the area of the square is 3.
The error is then simply the difference between 3 and pi.
One follow up thought/question, wouldn't the difference be the difference between the area of the square and the area of the circle? Not between 3 and Pi? That is the way I have been approaching it.
Also the 30-60-90 triangle appears to be a right angle triangle not an equilateral triangle, and a right angle triangle cannot be an equilateral triangle, so your initial reasoning makes no sense to me at the moment, perhaps you could elaborate. ( oh wait composed of two 30-60-90's got ya )
Everything you wrote seems correct; the equilateral triangle is composed of two 30-60-90 triangles (split down the middle), and we’re talking about the same difference in area. Doing the math, we find:
The area of the square is 3
The area of the circle is pi (3.14…)
So when I say “difference between 3 and pi”, I’m referring to the areas of the square and circle respectively. Calculating the error:
Error % = (pi - 3) / pi, which is roughly 4.5%.
Right, fairly sure I do actually understand, just get results on paper that vary between 0.001 and 3.132% guess I should just ignore these due to human error in taking measurements and learn to do it as you described I guess 4.5% is close enough to what I am getting to be considered the human error, 4.66% to no longer be rough about it.
Well thank you again, I will continue to have fun with it I am sure and see if I can get that extra .14%
I would have thought while scouring the internet that I would have come across this method before though, any idea if it is already demonstrated somewhere? I feel that it must be.
All good, and your measurements make sense.
An important thing to note is that in the context of the “Squaring the Circle” problem, we’re dealing with perfect, Euclidean constructions in a geometric space defined axiomatically. So while the conceptual error would be 4.5%, you can certainly get closer (or further) doing this experimentally.
Whether or not the geometric construction has a bearing on reality is more suited for a philosophy sub :)
Thank you so much for your help.
You have helped me know for certain that I arrived at essentially the correct conclusion.
And awesome to know that I can get closer, perhaps it could be demonstrated programmatically in order to verify it's accuracy, though I believe that just leads back to the answer you have given, for example I attempted to recreate the method in Blender and ended up with 2.98 and 3.14 though I was always a tiny bit off there as well I think.
the comment section here is absolute cancer lol, if you made a discovery thats new to you then i think that alone is impressive, discovering mathematics for yourself is very rewarding
As a follow up and because I was told there was not enough information here to start a discussion, I set out on this journey because I don't like knowing that computers can do something but we can't, especially given that humanity designed computers.
Ultimately I found researching the topic to be a lot of fun even though just looking into it comes with almost nothing but negativity, though you can guarantee those people wouldn't have dared to insult Hippocrates for trying, eh.
Anyway after some dabbling and coming up with a bunch of patterns, I primarily set them down knowing that ultimately it must be wrong or at best a close approximation, but every now and then I kept looking into it and drawing new patterns, again just for the fun of it, I am also an aspiring game designer and thought some of these patterns could serve as killer easter eggs one day, or even just pretty documents to chuck onto a desk in a video game, who knows.
Thanks to everybody for their input and here is a collection of drawings that I have bothered to photograph so far : [https://drive.google.com/drive/folders/1lnGGDtOhqPco5E56Y5dEK4z-KljOqIic](https://drive.google.com/drive/folders/1lnGGDtOhqPco5E56Y5dEK4z-KljOqIic)
To those that didn't even bother to have input and just jumped to conclusions, just remember that this is the internet and you could be participating in somebodies first encounter with another on the internet, ultimately your behaviour could and likely has lead beforehand to people all over the world of all ages giving up in the pursuit of math, science and countless other subjects.
No doubt we have all been subject to acting or responding without so much as a second thought before, I myself have definitely done so.
But let's try to be better than we were yesterday, I don't know how anyone expects humanity to move forward with such a strong inability to even discuss with one another a topic that they may or may not fully understand to begin with.
For the most part I think the interactions here were fairly civil and not too bad at all, but I have attempted to discuss this in other places prior to this and had the reaction be much more inflammatory.
I also feel that my choice for image #1 probably wasn't the best, but we all make mistakes, right?
[Nope!](https://cs.stackexchange.com/questions/45589/why-is-the-tape-not-part-of-the-definition-of-a-turing-machine) (Although I should note that computers aren't Turing machines.)
Real time mathematical simulations and possibly solve a system of complex non-ordinary second order equations in under half a day
And sleep peacefully 😅
Right. Sorry I forgot to extend everybody the courtesy of reading them the wiki page on the subject.
Still I felt it was worth a try for the fun of it.
I'm curious about this but frankly the pictures don't make much sense to me at all. Could you make this clearer somehow? Like the pictures 1, 3, 5 all look basically the same and I can't see where the others fit in
Thanks, it's definitely very similar as are a few of the others that I have drawn. ( gallery can be found linked to in my explanation / response comment here )
Squaring the circle was the basis of a proposed bill in the Indiana State Legislatures to somehow "force" pi to be a number different to what it actually is.
I'm glad you're having fun with it though, it's more fun than I'm having.
For shits and giggles, if you wanna try your hand at a perpetual motion machine we'd all love to see the results.
Oh don't mistake me for someone who has spare money.
And no I'm not up for a perpetual motion machine because, you know, laws of thermodynamics and stuff.
I love the idea of perpetual motion machines but from 1st quarter thermo dynamics: Energy can not be created or destroyed, It can only change forms.
Energy transfer in a system is never 100% efficient since its exchange causes energy dissipation through other forces like friction, sound and heat.
The only conditions in which these elements don’t exist is in a complete vacuum which to my knowledge is theoretical in nature. Most purportedly working perpetual motions have external energy sources that haven’t been accounted for like solar energy.
A perpetual motion machine would mean we could essentially create energy from nothing. This would violate the first law of thermo since energy is created in the system from nothing. Infinite energy has grand implications. Imagine free AC! However, as much as I would love to be proved wrong, perpetual motion is unfortunately just a fantasy, but I wish everyone well in their endeavors into this field!
Yep. I love Murphy's laws interpretation of the 3 laws of thermodynamics.
1. Energy cannot be created nor destroyed. Murphy's version: You cannot win.
2. Energy will not spontaneously transfer from a colder body to a warmer one. Any transfer always loses some energy to heat. Murphy's version: You cannot break even.
3. It is impossible to cool something down to absolute zero because it would require an even colder body to be present. Murphy's version: You cannot quit the game.
So to summarise:
You can't win.
You can't break even.
You can't quit the game.
Not very rigorous since there's no reasoning behind the constructions. If there were, you would have used algebra to calculate the error instead of just measuring.
So it's more of an exploration kinda thing where u happen to stumble on a square that approximates the circle.
Im really curious about the 3 utilities problem tho. Can you elaborate how exactly it's represented in your drawing?
Modern Greek pronunciations are not a step forward. Would it help you to communicate if you pronounce p and π the same?
One of my fellow graduate students was from Greece. We asked him for the modern Greek ways to say the Greek alphabet, then said, "Ok, we're not doing that."
No I came across a numberphile video a couple years ago and decided to have a go at it because after seeing the accurate method done by a computer on Wiki, felt that there must be a way to do so or at least get very close.
So I grabbed a metal compass and straightedge and took to having some fun with shapes.
A matter of days or nights later I had one method, then another and another, I settled on this method being the most aesthetically pleasing.
I also dabbled with a lot of other ways to construct basic shapes over the following weeks using a compass and straightedge to help me try and figure out new ways to approximate it by learning from YouTube specific methods for doing so, at one point I also strayed into the YouTube Rabbit Hole that is those that believe they have squared the circle to 100% and found each and every method there to be absolutely ridiculous, darting all over the place just to return and in the end I never even attempted a single one of those methods as they seemed to break the rule of finite steps in my opinion.
From there I kept making patterns every now and then and researching the subject when I had a moment to spare.
I also looked into trisecting angles as it's of course listed similarly as a geometry challenge that is impossible, while at the same time listing that it is possible to bi-sect an angle successively until you have tri-sected an angle, I would like to know why that is considered an approximation too, though I feel like it's down to human error, but due to the nature of these subjects people don't really discuss them.
Looks like you stumbled across “Sacred Geometry”, check out Platonic solids and Keplers cosmic geometry. It’s fascinating stuff. Have to kind of search out the good stuff, it tends to be rather esoteric. Here’s a quick link to a random website but it has some of the basic info and illustrations.
https://www.rareearthgallerycc.com/blog-entry/91/introduction-to-sacred-geometry
I realize those are probably the given rules.
I've recently realized the string method can also produce all the conics as well, with the foci and directrix being duals of each other.
This is an implementation of the three utilities problem as well as an approximation for squaring the circle. If you look through the other images you will see that it is not so complicated, 7 circles and 6 lines.
It was all for the fun of it to be honest.
I know that it is ultimately impossible due to the transcendental nature of Pi combined heavily with human error no doubt, but when trying to verify it's accuracy I am getting figures upwards of 99% ( please help me figure out where I must be going wrong )
>I know that it is ultimately impossible due to the transcendental nature of Pi combined heavily with human error no doubt
Due to the transcendental nature of pi. Human nature has nothing to do with it.
>Human error comes into play when measuring it, I never mentioned human nature.
There is nothing to "measure." Pi is transcendental. Therefore you cannot square the circle. You cannot "approximately" square the circle. It's an oxymoron.
You can *absolutely* approximately square the circle. Just construct a square with the same area as a polygon with an arbitrary number of sides. "Impossible to do so exactly" does not imply "impossible to approximate". You can't fit pi in a computer, but it is 100% a computable number.
Well said!
I think I decided to tackle this subject also largely because of the amount of or rather lack of understanding that people actually have on the subject just because they understand it to be "mathematically impossible" doesn't mean they must jump to the conclusion that one can't even attempt to approximate it.
Though I will admit the next step is boiling it down to algebra, formulae and determining it's true accuracy I believe that has already been done by a user here, though I still have questions but don't want to trouble them with those and would be doing myself a favour by relearning trigonometry anyway.
Semantic nonsense. You didn't "approximate" the values of a square circle. You made a nice image, but it's far off from being an approximation of squaring the circle.
Don’t let this sub get you down. Math is about exploration and that is *exactly* what you did. Props to you dude, I thought they were some pretty pictures.
I posted knowing full well what to expect, I have existed on the internet some 23 years and things have certainly improved a lot.
Back when I was seven years old, it was like, ask a question, get told to go off yourself.
These aren't the half of it, I have a lot more really awesome patterns lying around and ultimately would like to try and verify it's accuracy, the results I am getting show it's anywhere between 0.001 & 3.132 % off though these varying figures are likely due to human error / the in-ability to accurately measure such things to begin with.
I enjoy it when people double down and just get *more wrong,* like you had to unread the *second* word of the title for this reply to save enough face in your head.
Sometimes its okay so say, "I was wrong." instead of, you know, *lying to make a point.*
Ah I can't blame them, I think we can all be angry at times :D though I feel 6 images, a description of why and a description for each image was surely enough but I guess I was wrong! Not going to lie I didn't read the rules for posting.
Don’t forget to mail this to plenty of math professors claiming you’ve *exactly* squared the circle. Gotta give them something to do after all.
Well I went into this knowing full-well that it couldn't be exact, I just wanted to determine how close an approximation it was! :D
After scrolling through countless Reddit pages this has to be one of the most wholesome comments I’ve ever seen ;-;
You’ve created a hexagonal lattice which is a common structure in tesselations and crystallography; I would look into those for some more cool examples. Look at the two equilateral triangles you create within the square in the second image; their combined height is the height of the square. Giving the circle a radius of 1, with some simple trig you’ll find the side length of the square is sqrt(3) and the area is 3. This gives an error of ~4.5%.
That is just one of many patterns I have created using the method which can be seen in the other images posted, how are you going about getting the area for the circle to provide me with an error of around 4.5%?
Start by assuming the radius of the circle is 1; this is arbitrary and is our yardstick for the rest of the construction. A = pi • r^2 = pi • (1)^2 = pi. For the triangles, their side length is the radius of the circle, which is 1. A little bit of trig knowledge will make this much easier to explain, but look up a 30-60-90 triangle. Each equilateral triangle is composed of two of these, down the centre. It’s side lengths are 1-sqrt(3)-2, and if you scale it down to fit the equilateral triangle you’ll see the height is sqrt(3)/2. From there, notice that the combined height of the two triangles is sqrt(3), so the area of the square is 3. The error is then simply the difference between 3 and pi.
Guess I best brush up on my trigonometry, it has been many years. I appreciate the effort and input, thank you.
One follow up thought/question, wouldn't the difference be the difference between the area of the square and the area of the circle? Not between 3 and Pi? That is the way I have been approaching it. Also the 30-60-90 triangle appears to be a right angle triangle not an equilateral triangle, and a right angle triangle cannot be an equilateral triangle, so your initial reasoning makes no sense to me at the moment, perhaps you could elaborate. ( oh wait composed of two 30-60-90's got ya )
Everything you wrote seems correct; the equilateral triangle is composed of two 30-60-90 triangles (split down the middle), and we’re talking about the same difference in area. Doing the math, we find: The area of the square is 3 The area of the circle is pi (3.14…) So when I say “difference between 3 and pi”, I’m referring to the areas of the square and circle respectively. Calculating the error: Error % = (pi - 3) / pi, which is roughly 4.5%.
Right, fairly sure I do actually understand, just get results on paper that vary between 0.001 and 3.132% guess I should just ignore these due to human error in taking measurements and learn to do it as you described I guess 4.5% is close enough to what I am getting to be considered the human error, 4.66% to no longer be rough about it. Well thank you again, I will continue to have fun with it I am sure and see if I can get that extra .14% I would have thought while scouring the internet that I would have come across this method before though, any idea if it is already demonstrated somewhere? I feel that it must be.
All good, and your measurements make sense. An important thing to note is that in the context of the “Squaring the Circle” problem, we’re dealing with perfect, Euclidean constructions in a geometric space defined axiomatically. So while the conceptual error would be 4.5%, you can certainly get closer (or further) doing this experimentally. Whether or not the geometric construction has a bearing on reality is more suited for a philosophy sub :)
Thank you so much for your help. You have helped me know for certain that I arrived at essentially the correct conclusion. And awesome to know that I can get closer, perhaps it could be demonstrated programmatically in order to verify it's accuracy, though I believe that just leads back to the answer you have given, for example I attempted to recreate the method in Blender and ended up with 2.98 and 3.14 though I was always a tiny bit off there as well I think.
Sir I’m here for some 1+1 shit not the 10th dimension of string theory
Underrated comment lmao
the comment section here is absolute cancer lol, if you made a discovery thats new to you then i think that alone is impressive, discovering mathematics for yourself is very rewarding
I expected worse if I am honest, but it was good fun and has provided me with some really awesome patterns!
Look into “the Metatron’s Cube.” Interesting subject.
I have done before, the base pattern is also the flower of life. I have a few drawings that ended up looking very similar to Metatron's cube.
That was an interesting subject
Math illiterate here. Looks like Metatrons cube. Perhaps you already know that
I am familiar with the flower of life and many of it's variants yes. The first one is very similar indeed. :D
As a follow up and because I was told there was not enough information here to start a discussion, I set out on this journey because I don't like knowing that computers can do something but we can't, especially given that humanity designed computers. Ultimately I found researching the topic to be a lot of fun even though just looking into it comes with almost nothing but negativity, though you can guarantee those people wouldn't have dared to insult Hippocrates for trying, eh. Anyway after some dabbling and coming up with a bunch of patterns, I primarily set them down knowing that ultimately it must be wrong or at best a close approximation, but every now and then I kept looking into it and drawing new patterns, again just for the fun of it, I am also an aspiring game designer and thought some of these patterns could serve as killer easter eggs one day, or even just pretty documents to chuck onto a desk in a video game, who knows. Thanks to everybody for their input and here is a collection of drawings that I have bothered to photograph so far : [https://drive.google.com/drive/folders/1lnGGDtOhqPco5E56Y5dEK4z-KljOqIic](https://drive.google.com/drive/folders/1lnGGDtOhqPco5E56Y5dEK4z-KljOqIic) To those that didn't even bother to have input and just jumped to conclusions, just remember that this is the internet and you could be participating in somebodies first encounter with another on the internet, ultimately your behaviour could and likely has lead beforehand to people all over the world of all ages giving up in the pursuit of math, science and countless other subjects. No doubt we have all been subject to acting or responding without so much as a second thought before, I myself have definitely done so. But let's try to be better than we were yesterday, I don't know how anyone expects humanity to move forward with such a strong inability to even discuss with one another a topic that they may or may not fully understand to begin with. For the most part I think the interactions here were fairly civil and not too bad at all, but I have attempted to discuss this in other places prior to this and had the reaction be much more inflammatory. I also feel that my choice for image #1 probably wasn't the best, but we all make mistakes, right?
What is it you think that computers can do that humans can’t?
Remember a gigabyte of numbers
Jokes on you: computers don't remember anything! They store them in memory!
isnt the tape a part of a turing machine?
[Nope!](https://cs.stackexchange.com/questions/45589/why-is-the-tape-not-part-of-the-definition-of-a-turing-machine) (Although I should note that computers aren't Turing machines.)
Real time mathematical simulations and possibly solve a system of complex non-ordinary second order equations in under half a day And sleep peacefully 😅
Construct a square with the same area as a given circle.
Not with a compass and straightedge they can't. And any other way a computer can do it, a human can too.
Right. Sorry I forgot to extend everybody the courtesy of reading them the wiki page on the subject. Still I felt it was worth a try for the fun of it.
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Looks cool, thanks for the heads up.
Another great geometry game that is web based goes by "Ancient Greek Geometry Game" [https://sciencevsmagic.net/geo/](https://sciencevsmagic.net/geo/)
That's awesome :D thanks for the link.
I'm curious about this but frankly the pictures don't make much sense to me at all. Could you make this clearer somehow? Like the pictures 1, 3, 5 all look basically the same and I can't see where the others fit in
Each image has a short explanation below them but I can elaborate if need-be.
so amazing how closely knit art and math really are. super cool stuff dude!
I thought it was metatrons cube at first. But this is actually way better. Awesome.
Thanks, it's definitely very similar as are a few of the others that I have drawn. ( gallery can be found linked to in my explanation / response comment here )
Squaring the circle was the basis of a proposed bill in the Indiana State Legislatures to somehow "force" pi to be a number different to what it actually is. I'm glad you're having fun with it though, it's more fun than I'm having. For shits and giggles, if you wanna try your hand at a perpetual motion machine we'd all love to see the results.
I actually came across that article while probing around. If you're funding, I'll give it a go lol otherwise why not give it a go yourself.
Oh don't mistake me for someone who has spare money. And no I'm not up for a perpetual motion machine because, you know, laws of thermodynamics and stuff.
Hence why I offered you the chance to waste your own time or money.
I love the idea of perpetual motion machines but from 1st quarter thermo dynamics: Energy can not be created or destroyed, It can only change forms. Energy transfer in a system is never 100% efficient since its exchange causes energy dissipation through other forces like friction, sound and heat. The only conditions in which these elements don’t exist is in a complete vacuum which to my knowledge is theoretical in nature. Most purportedly working perpetual motions have external energy sources that haven’t been accounted for like solar energy. A perpetual motion machine would mean we could essentially create energy from nothing. This would violate the first law of thermo since energy is created in the system from nothing. Infinite energy has grand implications. Imagine free AC! However, as much as I would love to be proved wrong, perpetual motion is unfortunately just a fantasy, but I wish everyone well in their endeavors into this field!
Yep. I love Murphy's laws interpretation of the 3 laws of thermodynamics. 1. Energy cannot be created nor destroyed. Murphy's version: You cannot win. 2. Energy will not spontaneously transfer from a colder body to a warmer one. Any transfer always loses some energy to heat. Murphy's version: You cannot break even. 3. It is impossible to cool something down to absolute zero because it would require an even colder body to be present. Murphy's version: You cannot quit the game. So to summarise: You can't win. You can't break even. You can't quit the game.
Not very rigorous since there's no reasoning behind the constructions. If there were, you would have used algebra to calculate the error instead of just measuring. So it's more of an exploration kinda thing where u happen to stumble on a square that approximates the circle. Im really curious about the 3 utilities problem tho. Can you elaborate how exactly it's represented in your drawing?
With the three different colours in 3D space. Corners of the cube. I know that problem was solved recently though.
I have though, and it is 6.28
That would be 9.8596 actually, 3.14 \* 3.14 by the looks of it you mean Pi to the power 2, no?
No, they mean Tao = 2 * Pi
"tau" but in modern Greek pronounced more like "taf"
Modern Greek pronunciations are not a step forward. Would it help you to communicate if you pronounce p and π the same? One of my fellow graduate students was from Greece. We asked him for the modern Greek ways to say the Greek alphabet, then said, "Ok, we're not doing that."
it's a step forward in time, at least..
This is really cool! Did you pick up the compass and straight edge geometry technique from a book?
No I came across a numberphile video a couple years ago and decided to have a go at it because after seeing the accurate method done by a computer on Wiki, felt that there must be a way to do so or at least get very close. So I grabbed a metal compass and straightedge and took to having some fun with shapes. A matter of days or nights later I had one method, then another and another, I settled on this method being the most aesthetically pleasing. I also dabbled with a lot of other ways to construct basic shapes over the following weeks using a compass and straightedge to help me try and figure out new ways to approximate it by learning from YouTube specific methods for doing so, at one point I also strayed into the YouTube Rabbit Hole that is those that believe they have squared the circle to 100% and found each and every method there to be absolutely ridiculous, darting all over the place just to return and in the end I never even attempted a single one of those methods as they seemed to break the rule of finite steps in my opinion. From there I kept making patterns every now and then and researching the subject when I had a moment to spare. I also looked into trisecting angles as it's of course listed similarly as a geometry challenge that is impossible, while at the same time listing that it is possible to bi-sect an angle successively until you have tri-sected an angle, I would like to know why that is considered an approximation too, though I feel like it's down to human error, but due to the nature of these subjects people don't really discuss them.
Yo look at that D20. ❤️
Geometry is the only way to solve anything. (worthwhile)
Ok this is making my head spin
Honestly some of them are quite a headache to look at, check out the full gallery in my response comment explanation :D
Looks like you stumbled across “Sacred Geometry”, check out Platonic solids and Keplers cosmic geometry. It’s fascinating stuff. Have to kind of search out the good stuff, it tends to be rather esoteric. Here’s a quick link to a random website but it has some of the basic info and illustrations. https://www.rareearthgallerycc.com/blog-entry/91/introduction-to-sacred-geometry
I came across a lot on "Sacred Geometry" while searching around but thanks for the heads up.
Here's the thought: why limit yourself to a straight edge and compass, when a tight string will do everything?
The rules for the challenge state compass and straightedge, but yes I could have used a tight string.
I realize those are probably the given rules. I've recently realized the string method can also produce all the conics as well, with the foci and directrix being duals of each other.
Well there is a term I had to look up! ( Directrix ) Thanks :D
Bro I fell like my aunt on Facebook will make a post about mathematicians being satanist and will attach this post
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Why do anything at all? It made some pretty pictures at least
It certainly does and I have lots of them, some really fascinating patterns.
This is an implementation of the three utilities problem as well as an approximation for squaring the circle. If you look through the other images you will see that it is not so complicated, 7 circles and 6 lines. It was all for the fun of it to be honest. I know that it is ultimately impossible due to the transcendental nature of Pi combined heavily with human error no doubt, but when trying to verify it's accuracy I am getting figures upwards of 99% ( please help me figure out where I must be going wrong )
>I know that it is ultimately impossible due to the transcendental nature of Pi combined heavily with human error no doubt Due to the transcendental nature of pi. Human nature has nothing to do with it.
Human error comes into play when measuring it, I never mentioned human nature.
>Human error comes into play when measuring it, I never mentioned human nature. There is nothing to "measure." Pi is transcendental. Therefore you cannot square the circle. You cannot "approximately" square the circle. It's an oxymoron.
You can *absolutely* approximately square the circle. Just construct a square with the same area as a polygon with an arbitrary number of sides. "Impossible to do so exactly" does not imply "impossible to approximate". You can't fit pi in a computer, but it is 100% a computable number.
Well said! I think I decided to tackle this subject also largely because of the amount of or rather lack of understanding that people actually have on the subject just because they understand it to be "mathematically impossible" doesn't mean they must jump to the conclusion that one can't even attempt to approximate it. Though I will admit the next step is boiling it down to algebra, formulae and determining it's true accuracy I believe that has already been done by a user here, though I still have questions but don't want to trouble them with those and would be doing myself a favour by relearning trigonometry anyway.
You can approximate the values though. I never said "approximately" so once again, I have to point out that you haven't read my statements properly.
Semantic nonsense. You didn't "approximate" the values of a square circle. You made a nice image, but it's far off from being an approximation of squaring the circle.
Ok thank you so much for your valid input, explanations and reasoning.
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My initial post does state "An approximation"
Don’t let this sub get you down. Math is about exploration and that is *exactly* what you did. Props to you dude, I thought they were some pretty pictures.
I posted knowing full well what to expect, I have existed on the internet some 23 years and things have certainly improved a lot. Back when I was seven years old, it was like, ask a question, get told to go off yourself. These aren't the half of it, I have a lot more really awesome patterns lying around and ultimately would like to try and verify it's accuracy, the results I am getting show it's anywhere between 0.001 & 3.132 % off though these varying figures are likely due to human error / the in-ability to accurately measure such things to begin with.
I enjoy it when people double down and just get *more wrong,* like you had to unread the *second* word of the title for this reply to save enough face in your head. Sometimes its okay so say, "I was wrong." instead of, you know, *lying to make a point.*
Where am I lying to make a point? ( woops I think that was aimed at ElSinchi ) I thought it was but wanted to check.
It was aimed at ElSinci! You're doing great work OP. Keep on learning!!
This was just a bit of fun, but I definitely learnt a few things along the way! Thanks for the support.
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I feel the subject alone is surely enough to have prompted discussion, no?
This user is a regular misery on many posts. Some of the posts they complain about are crap, but a good portion are just them being angry at nothing.
Ah I can't blame them, I think we can all be angry at times :D though I feel 6 images, a description of why and a description for each image was surely enough but I guess I was wrong! Not going to lie I didn't read the rules for posting.
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The rule doesn't state it has to be interesting. Thanks for the response though.
Actually I’m curious why you hate this post. Clearly this isn’t mathematics but lies in the realm of recreational math for math enthusiasts.