Anything is possible if you approximate it. But, since π has no end, √π also has no end. Theoretically, it's possible, without approximation, within a certain percentage of error. But, that just means that, in practice, no.
By that standard, you also cannot have a square with an area of exactly 1. You cannot measure a side length of exactly 1, it's always only an approximate with only a finite amount of precision.
@@jameskuyper That's why humans cheated and got around that problem with units. Which was improved further by standard units. So you have kilos, meters, liters, atmospheres, bars of pressure, as examples. Clear units, clear definitions, clear calculations. We know what a gram is and we know what a joule of energy is. Even Euler's number is more friendly than π as we know how it recurs after the decimal point. Which means that we know what to do with it up to infinity, in theory, to use it for what it needs to be used for. But, with π didn't people stop working out the next digit until after it reached over a million decimal places. Which is crazy, but it also means π is an unfinished number as there are still an unknown number of calculations to go. 1 is definitive. There is 1 of you, 1 of me. You cannot measure one of something, but if you see a person, that is 1 singular person. The problem with anything to do with π is that it is never finished. It is an irrational number. Like √2 or √3, which pi is built upon, there is no definitive end. We don't even know which number it ends on. There's also the small issue that not even the super delicate paintbrushes that toy makers of old used to get fine details on their toys will ever be accurate enough to draw something so precise. Anyway, sorry for the lecture. Just an idiot who likes numbers.
There is a difference between tolerances and approximations. When you say we want a square of area 1.0 - that is not an approximation. We can calculate out exactly the lenghts of sides. If we try to make this item in reality, we will be subject to tolerances of machining or any other process. The goal is to get as close to 1.00 as possible. However, the value of Pi is an irrational number meaning it does not have a final decimal calculated out. Similarly the root of Pi will have the same irrational property. So we wil compound the 2 problems - not having a fixed theoretical value (where we use approximations) and the second problem of having tolerances if we try to build it. So it really means we cannot even theoretically make a perfect square with area of Pi. With approximations and tolerances we would get kind of close.
@@johnklen2991 The irrationality of pi is infinitely less important a problem than the issue of tolerances. We can calculate pi with far more precision than we could ever hope to measure, by many orders of magnitude . And, in some alternate reality where tolerances were never an issue, no matter how much precision you needed, even if the desired precision were literally infinite, a distance of pi units could be laid out exactly by rolling a cylinder with a diameter of 0.5 units by along a flat surface. Such a reality could not be quantized, so it's laws of physics would have to be very different from those of our world. Perfectly circular cylinders and perfectly flat surfaces should be naturally occurring things in such an alternate reality.
I think this is like "Quadratur des Kreises" ... "squaring a circle". Meaning: *geometrically* constructing the square with the same area with a circle. Here you did it using algebra. But just with geometrical tools I haven't seen it done yet.
The hilarious but true thing that you said was you did it using algebra which is still true but pi can't be contained by algebra since it is a transcendental number
If you can have a side of a square (ie, a line) be exactly 1 down to the last ink molecule, so can you have a side of exactly √π down to its last ink molecule... but that maximum resolution is down to the width of a single ink molecule. But in reality, you can't, because that ink-molecule-width is the maximum resolution of the length of that side, so it'll likely never be exactly 1.0000000... either. So if you can get 58 decimal places of resolution for 1.00000... then you'll similarly get that same resolution of 58 places of √π, too.
Negative number can not be considered in geometry. Not measurable numbers can be considered, why? sqrt(PI) is not measurable - it means you can not point (or draw) it on the axis.
Pi and squares, two concepts you’d think wouldn’t mix, but that’s the beauty of math! A square with an area of π just means each side has a length of √π. It’s a fun reminder that numbers we think of as ‘abstract’ can still fit into geometric shapes. Tools like SolutionInn make exploring these ideas way easier! This video me appreciate how math stretches our imagination. Honestly, this is the kind of question that makes you want to dive back into geometry.
I have not (yet) watched the video, but it seems theoretically possible… Imagine a circle with a radius of 0.5 units - the circle has a radius of Pi units. Cut the circle and stretch out to a straight line - you now have a line with length Pi units. A straight line with finite length x suggests the possibility of Sqrt(x) - thus Sqrt(Pi) seems theoretically possible (of course without being precisely measurable). So, if you can have a straight line with length Sqrt(Pi) units, you can indeed (theoretically) have a square with an area of Pi square units.
I actually wonder what motivated this question in the first place. Maybe they were trying to ask if it is possible for a square to have an area of pi while simultaneously having a rational side length? *shrug*
I know this is the "math basics" bprp channel, but this is incorrect at a bit higher level. The number π is not constructible (with straightedge and compass), so you cannot have a square with π as its side -- even less with √π -- so from that point of view the answer is a definite NO.
It's possible theoretically, but it can't physically exist, in my opinion. I think the probability of 4 right angles in a plane with sides of the same transcendental length is zero.
OK, I need to go back to skool! It’s possible, a circle with R=1 will have an area of pi so anything with the same circumference will have an area of pi. As long as you can accept that the length of a side will be a transcendental. So it can only be solved mathematically, not physically.
It's not because two objects have the same circumference that their area will be the same. Take a 1*1square (c=4 and A=1) and a 0.5*1.5 rectangle (c=4 and A=3/4
Teacher:- Can a square have an area of pi?? Me:- Yes, root of pi * root of pi = pi This guy:- Take a whole 3 mins to explain the same Teacher:- I prefer this guy's answer, you should learn something from him Me:- WTF
Can the area and the perimeter of a rectangle both equal 1 (numerically)?
Answer: ruclips.net/video/-lTw4tRPRV4/видео.html
I have a question I got in olympiadic test
a,b,c are positive integers show that if:
(a/b)+(b/c)+(c/a) is an integer
then a*b*c is a cube
I don't like the digital screen. I like the white board. It's disconnected if you use the digital one, as we can't see you point or make motions.
Yeah i thought i was the only one. His name is black pen red pen but now there is no white board for it
Ya, but now we don't know whether he's in his PJs. Do you want to know when he's wearing his PJs with these?
For once, a video on this channel that doesn't require more than one second of thinking.
Anything is possible if you approximate it. But, since π has no end, √π also has no end.
Theoretically, it's possible, without approximation, within a certain percentage of error. But, that just means that, in practice, no.
By that standard, you also cannot have a square with an area of exactly 1. You cannot measure a side length of exactly 1, it's always only an approximate with only a finite amount of precision.
@@jameskuyper That's why humans cheated and got around that problem with units. Which was improved further by standard units. So you have kilos, meters, liters, atmospheres, bars of pressure, as examples. Clear units, clear definitions, clear calculations. We know what a gram is and we know what a joule of energy is. Even Euler's number is more friendly than π as we know how it recurs after the decimal point. Which means that we know what to do with it up to infinity, in theory, to use it for what it needs to be used for.
But, with π didn't people stop working out the next digit until after it reached over a million decimal places. Which is crazy, but it also means π is an unfinished number as there are still an unknown number of calculations to go. 1 is definitive. There is 1 of you, 1 of me. You cannot measure one of something, but if you see a person, that is 1 singular person.
The problem with anything to do with π is that it is never finished. It is an irrational number. Like √2 or √3, which pi is built upon, there is no definitive end. We don't even know which number it ends on.
There's also the small issue that not even the super delicate paintbrushes that toy makers of old used to get fine details on their toys will ever be accurate enough to draw something so precise.
Anyway, sorry for the lecture. Just an idiot who likes numbers.
There is a difference between tolerances and approximations. When you say we want a square of area 1.0 - that is not an approximation. We can calculate out exactly the lenghts of sides. If we try to make this item in reality, we will be subject to tolerances of machining or any other process. The goal is to get as close to 1.00 as possible. However, the value of Pi is an irrational number meaning it does not have a final decimal calculated out. Similarly the root of Pi will have the same irrational property. So we wil compound the 2 problems - not having a fixed theoretical value (where we use approximations) and the second problem of having tolerances if we try to build it. So it really means we cannot even theoretically make a perfect square with area of Pi. With approximations and tolerances we would get kind of close.
@@johnklen2991 The irrationality of pi is infinitely less important a problem than the issue of tolerances. We can calculate pi with far more precision than we could ever hope to measure, by many orders of magnitude . And, in some alternate reality where tolerances were never an issue, no matter how much precision you needed, even if the desired precision were literally infinite, a distance of pi units could be laid out exactly by rolling a cylinder with a diameter of 0.5 units by along a flat surface. Such a reality could not be quantized, so it's laws of physics would have to be very different from those of our world. Perfectly circular cylinders and perfectly flat surfaces should be naturally occurring things in such an alternate reality.
Not if you have to construct such a square with compass and straightedge.
Right, I think one cannot construct a line segment having length sqrt(pi).
By having side lengths of sqrt(pi)
Ofc
I think the question was more about how can you have a non-algebraic number of an actual length.
Can you prove the limit rules with epsilon delta ?
Here’s the product one ruclips.net/video/x_CV33zll1s/видео.htmlsi=f-YRxWNyYH286L8o
@ thanks
Can you prove the rule that states
If f is a continuous function
lim x-> a f(g(x)) = f(lim x-> a (g(x)))
You can, but you cant construct it with compass and straightedge alone. But it is easy to construct with other means.
I think this is like "Quadratur des Kreises" ... "squaring a circle".
Meaning: *geometrically* constructing the square with the same area with a circle.
Here you did it using algebra.
But just with geometrical tools I haven't seen it done yet.
The hilarious but true thing that you said was you did it using algebra which is still true but pi can't be contained by algebra since it is a transcendental number
If you can have a side of a square (ie, a line) be exactly 1 down to the last ink molecule, so can you have a side of exactly √π down to its last ink molecule... but that maximum resolution is down to the width of a single ink molecule. But in reality, you can't, because that ink-molecule-width is the maximum resolution of the length of that side, so it'll likely never be exactly 1.0000000... either. So if you can get 58 decimal places of resolution for 1.00000... then you'll similarly get that same resolution of 58 places of √π, too.
Negative number can not be considered in geometry. Not measurable numbers can be considered, why? sqrt(PI) is not measurable - it means you can not point (or draw) it on the axis.
Some people in the comment section believing that irrational numbers can't actually exist make me sad for the future of the human race
Also, the length of the squares diagonal is √(2π), which is even more irrational.
Pi and squares, two concepts you’d think wouldn’t mix, but that’s the beauty of math! A square with an area of π just means each side has a length of √π. It’s a fun reminder that numbers we think of as ‘abstract’ can still fit into geometric shapes. Tools like SolutionInn make exploring these ideas way easier! This video me appreciate how math stretches our imagination. Honestly, this is the kind of question that makes you want to dive back into geometry.
This one is so obvious, I feel like you're running out of material
ok
Next video: prove that 1+1= a window
That's why this account is called math basics
It needs to complemented by showing how to use a Lax pair to solve a nonlinear partial differential equation.
So true
but the area cannot be exactly equal to pie bcz it is irrational number the side length 1.772 is an approximation
This feels off due to squaring the circle but it is still an appropriate answer
I have not (yet) watched the video, but it seems theoretically possible…
Imagine a circle with a radius of 0.5 units - the circle has a radius of Pi units.
Cut the circle and stretch out to a straight line - you now have a line with length Pi units.
A straight line with finite length x suggests the possibility of Sqrt(x) - thus Sqrt(Pi) seems theoretically possible (of course without being precisely measurable).
So, if you can have a straight line with length Sqrt(Pi) units, you can indeed (theoretically) have a square with an area of Pi square units.
How to build a segment with the length of the root of pi? 🤔
Please can you tell me what is the name of the app,website etc that you are using I would be very grateful
I hate that an infinitely long number has a definite area
Infinitely long after the decimal doesnt make it an infinite number it's just adding tenths and hundredths and so on
@momo-gl1zm I didn't say it was an infinite number
@localblackman427 my bad i misunderstood "infinitely long" haha
Yes. Pi is a positive number between 3 and 4. While they are squares, they aren't total squares about having irrational amount of area.
I actually wonder what motivated this question in the first place. Maybe they were trying to ask if it is possible for a square to have an area of pi while simultaneously having a rational side length? *shrug*
I know this is the "math basics" bprp channel, but this is incorrect at a bit higher level. The number π is not constructible (with straightedge and compass), so you cannot have a square with π as its side -- even less with √π -- so from that point of view the answer is a definite NO.
I suppose it's possible if you don't use actual numbers e.g. the square's sides are sqrt(pi)
In real life it is impossible
I can only cry by hearing such question If it were asked by anyone older than 15-16.
Kids like 10yop or younger, are accepted to ask this.
You can have a square with an area of e.
I have a question I got in olympiadic test
a,b,c are positive integers show that if:
(a/b)+(b/c)+(c/a) is an integer
then a*b*c is a cube
Possible? In theory. In practice? Unlikely.
in practice its ultimately impossible to have a shape with any given area since you cannot measure things that precisely
@sithems13 Yeah, NDT has covered the topic of measurement precision.
Of course, that is possible. A square with side length √π has an area of π.
Do you see what happend, no.?
Haii can you do an epsilon delta proof for one sided limits instead of two..
It's possible theoretically, but it can't physically exist, in my opinion.
I think the probability of 4 right angles in a plane with sides of the same transcendental length is zero.
One could argue that even a square whose area is *exactly* 1 cannot physically exist either.
OK, I need to go back to skool!
It’s possible, a circle with R=1 will have an area of pi so anything with the same circumference will have an area of pi. As long as you can accept that the length of a side will be a transcendental. So it can only be solved mathematically, not physically.
It's not because two objects have the same circumference that their area will be the same. Take a 1*1square (c=4 and A=1) and a 0.5*1.5 rectangle (c=4 and A=3/4
@ Doh! I’m so used to measuring the circumference of odd-shaped curved objects to get circumference and area that I never considered rectangles LOL
What is the Area If side length equals the integral 2e^(x^2) dx 🌚
Can a pi be square?
a sicilian pi is square
No
Teacher:- Can a square have an area of pi??
Me:- Yes, root of pi * root of pi = pi
This guy:- Take a whole 3 mins to explain the same
Teacher:- I prefer this guy's answer, you should learn something from him
Me:- WTF
I love your channel but I don’t like your new screen. The old one, with you in front of a white board was much better.
❤
😂 good joke .. better u serch on how π = 22/ 7 r 3.14..
Prove it here practically ....
derch?
@@alexandergutfeldt1144 apply some sense ..
@@Quest3669 Thanks for editing ...
I don't live in the US and am not up to date with local slang and abbreviations.
@@alexandergutfeldt1144 beg ur pardon ... U from ??
@@Quest3669 a civilised country populated with polite decent people...
I have a question I got in olympiadic test
a,b,c are positive integers show that if:
(a/b)+(b/c)+(c/a) is an integer
then a*b*c is a cube
I have a question I got in olympiadic test
a,b,c are positive integers show that if:
(a/b)+(b/c)+(c/a) is an integer
then a*b*c is a cube
I have a question I got in olympiadic test
a,b,c are positive integers show that if:
(a/b)+(b/c)+(c/a) is an integer
then a*b*c is a cube