Sure, Let's try together.
pi is not exactly equals to 22/7, It just closed to that rational numnerSquare with a 22/7 long side.
Note that: pi is an irrational number that can not be written as a ratio.
------ Post added on Aug 13, 2022 at 9:53 AM
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What is π squared
- Thread starter imhotep
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Note that: pi is an irrational number that can not be written as a ratio.
------ Post added on Aug 13, 2022 at 9:53 AM
පයි වර්ගේ කියන්නේ unit 1ක රවුම් දෙකක් ගලවල හදන්න පුලුවන් ස්මචතුරශ්රයේ වර්ගපලය කියලා නම් එනවා. 
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If you draw a circle of diameter pi, then it's circumference will be pi squared.
yes pi is not a ratio,
you mean like pi is equals to "circumference/2*redius" ,
I'm not talking about that ratio, actually a ratio of two integers
it is an irrational number (Non recurring infinity decimal number)
yeabro, point is made. I may be completely wrong or may stupid. I think pi is just a ratio and it is not a constant(a permanent value does not change). it doesn't have a specified value yet. Pi ratio is made, of a any circle circumference is divided by its radius. how many faces have a geometric circle? some would say 1 face only. but I would say infinite.What? Isn't the area of a circle πr^2 ? If we let r=1 then the area is π. The ratio of circumference to diameter is correct too. But in the context of this problem the area version suits better.
because if you take a triangle as an example it has 3 faces and if you apply another face(edge) it will be a 4 sided polygon(squre, rectangle, Rhombus, parallelogram). and if you apply more and more edges to it it will be pentagon>hexagon>heptagon>octagon>nonagon>decagon....etc until it is Infinite(a circle). that's why pi doesn't have a specific value. so I would say none of a polygon has a one face or two face. so in this case circle is also a polygon with infinite faces. but a ordinary line has just a one face which is not a polygon at all. sorry my english is bad. buut I think you have got my point.
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මේක හාරි නේද.පයි වර්ගේ කියන්නේ unit 1ක රවුම් දෙකක් ගලවල හදන්න පුලුවන් ස්මචතුරශ්රයේ වර්ගපලය කියලා නම් එනවා.
Idiot, next time be more precise. There are hundreds of equations for pi^2, you should have just mentioned you wanted a surface area with pi^2 in it. lol. Stop asking dumb questions here moron
Interesting question..
ප්රශ්නේ හරියට තේරුනාද කියල ෂුවර් නැහැ.
අපි දන්න දේම කරකවල මෙහෙම ලියන්න පුළුවන් ඕනමනම් අර exam වලදී උත්තරේ දන්නේ නැති උනාම වගේ
C = πD
π^2 = C^2 / D^2
here C^2 is the square of the circumference of the circle .
D^2 is Area of the square drawn on that circle's diameter
So the denominator is an Area of a square.
The numerator is a square of a curved line. So it seems to be a surface area of a curved surface. I don't know. just thinking..
ප්රශ්නේ හරියට තේරුනාද කියල ෂුවර් නැහැ.
අපි දන්න දේම කරකවල මෙහෙම ලියන්න පුළුවන් ඕනමනම්
අර exam වලදී උත්තරේ දන්නේ නැති උනාම වගේC = πD
π^2 = C^2 / D^2
here C^2 is the square of the circumference of the circle .
D^2 is Area of the square drawn on that circle's diameter
So the denominator is an Area of a square.
The numerator is a square of a curved line. So it seems to be a surface area of a curved surface. I don't know. just thinking..
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Yes ... It's the surface area of a Horn Torus with an outer radius of one unit and a inner radius of 0.Interesting question..
ප්රශ්නේ හරියට තේරුනාද කියල ෂුවර් නැහැ.
අපි දන්න දේම කරකවල මෙහෙම ලියන්න පුළුවන් ඕනමනම්
C = πD
π^2 = C^2 / D^2
here C^2 is the square of the circumference of the circle .
D^2 is Area of the square drawn on that circle's diameter
View attachment 181598
So the denominator is an Area of a square.
The numerator is a square of a curved line. So it seems to be a surface area of a curved surface. I don't know. just thinking..
https://www.horntorus.com/image0index.html#dyn
You can clearly tell this is a question by a non math person. Asking stupid questions. I’m sure next time you’ll ask what’s the next number of a sequence 
TFS. didn't expect that to be such a unique shape. (On the other hand, π is special, then why wouldn't be π^2?
)Hello @imhotep, perhaps remember to mention me when you're posting such math/philosophy questions. I guarantee that you will have a stimulating answer. (You'll be amazed that I'm well versed in more things than ජංගි) 
Pi squared is the surface area of a point hole, unit radius 3D Torus. You can think of it as an උළුදු වඩේ with a middle hole that is infinitesimally small. The surface area of one such shape is Pi squared.
You can get this by thinking exactly as in the definition. The area of a unit radius circle is Pi. Think how that happens. You take a unit length, hold it from one end point and rotate it from that end.
Thinking along that definition, you can understand the Pi squared quite easily. A circle (2D) develops when a unit length line (1D) is rotated about its end. Similarly, a point hole Torus (3D) is a unit circle (2D) rotated from a point in its perimeter.
From the definition of Pi, the area of a unit radius circle is Pi. Similarly, the surface area of a unit radius, point hole Torus is Pi x Pi. We rotate once to get the circle (Pi), we rotate it again to get the Torus (Pi x Pi).
If you like, you can think about the shape of Pi^3. You might think that's stupid, but the f electron shell of large atoms in Lanthenide series (electron shells are named s, p, d, f, if you remember some chemistry) have a 95% probability of being in the 3D emulation of such shaped area.
සරලව සිංහලෙන් කිව්වොත් unit දෙකක් පළල, මැද හිල ලක්ෂ්යයක් වන උළුඳු වඩේ එකක පිටත පෘෂ්ඨ වර්ගඵලය Pi වර්ගයට සමානයි. අාස නම් Pi^3 හැඩය හිතලා බලන්න ඔය විදිහටම. Lanthenide series එකේ පරමාණුවල f ඉලෙක්ට්රෝන කවචයෙ 3d හැඩය එ් වගේමයි (95% සම්භාවිතාව).
------ Post added on Aug 13, 2022 at 7:47 PM
Pi squared is the surface area of a point hole, unit radius 3D Torus. You can think of it as an උළුදු වඩේ with a middle hole that is infinitesimally small. The surface area of one such shape is Pi squared.
You can get this by thinking exactly as in the definition. The area of a unit radius circle is Pi. Think how that happens. You take a unit length, hold it from one end point and rotate it from that end.
Thinking along that definition, you can understand the Pi squared quite easily. A circle (2D) develops when a unit length line (1D) is rotated about its end. Similarly, a point hole Torus (3D) is a unit circle (2D) rotated from a point in its perimeter.
From the definition of Pi, the area of a unit radius circle is Pi. Similarly, the surface area of a unit radius, point hole Torus is Pi x Pi. We rotate once to get the circle (Pi), we rotate it again to get the Torus (Pi x Pi).
If you like, you can think about the shape of Pi^3. You might think that's stupid, but the f electron shell of large atoms in Lanthenide series (electron shells are named s, p, d, f, if you remember some chemistry) have a 95% probability of being in the 3D emulation of such shaped area.
සරලව සිංහලෙන් කිව්වොත් unit දෙකක් පළල, මැද හිල ලක්ෂ්යයක් වන උළුඳු වඩේ එකක පිටත පෘෂ්ඨ වර්ගඵලය Pi වර්ගයට සමානයි. අාස නම් Pi^3 හැඩය හිතලා බලන්න ඔය විදිහටම. Lanthenide series එකේ පරමාණුවල f ඉලෙක්ට්රෝන කවචයෙ 3d හැඩය එ් වගේමයි (95% සම්භාවිතාව).
Pi^2 is special. Read the explanation.TFS. didn't expect that to be such a unique shape. (On the other hand, π is special, then why wouldn't be π^2?
------ Post added on Aug 13, 2022 at 7:47 PM
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එ්ක කියවල පිස්සු වගෙ. හැබැයි උබ කියන කතාව ගැන සාමානයෙන් අයිඩියා එකක් අාව. 1d ඉරක් කැරකුවම 2d රවුමක්. 2d රවුම කැරකුවම 3d torus එක. හරි නේද.Hello @imhotep, perhaps remember to mention me when you're posting such math/philosophy questions. I guarantee that you will have a stimulating answer. (You'll be amazed that I'm well versed in more things than ජංගි)
Pi squared is the surface area of a point hole, unit radius 3D Torus. You can think of it as an උළුදු වඩේ with a middle hole that is infinitesimally small. The surface area of one such shape is Pi squared.
You can get this by thinking exactly as in the definition. The area of a unit radius circle is Pi. Think how that happens. You take a unit length, hold it from one end point and rotate it from that end.
Thinking along that definition, you can understand the Pi squared quite easily. A circle (2D) develops when a unit length line (1D) is rotated about its end. Similarly, a point hole Torus (3D) is a unit circle (2D) rotated from a point in its perimeter.
From the definition of Pi, the area of a unit radius circle is Pi. Similarly, the surface area of a unit radius, point hole Torus is Pi x Pi. We rotate once to get the circle (Pi), we rotate it again to get the Torus (Pi x Pi).
If you like, you can think about the shape of Pi^3. You might think that's stupid, but the f electron shell of large atoms in Lanthenide series (electron shells are named s, p, d, f, if you remember some chemistry) have a 95% being in the 3D emulation of such shaped area.
සරලව සිංහලෙන් කිව්වොත් unit දෙකක් පළල, මැද හිල ලක්ෂ්යයක් වන උළුඳු වඩේ එකක පිටත පෘෂ්ඨ වර්ගඵලය Pi වර්ගයට සමානයි. අාස නම් Pi^3 හැඩය හිතලා බලන්න ඔය විදිහටම. Lanthenide series එකේ පරමාණුවල f ඉලෙක්ට්රෝන කවචයෙ 3d හැඩය එ් වගේමයි (95% සම්භාවිතාව).
Pi^2 is special. Read the explanation.
------ Post added on Aug 13, 2022 at 7:47 PM
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ඔව් බං. උඩ එවුනුත් උත්තරේ දාලා තියෙනවා. හැබැයි දැන් එහෙම වෙන්නෙ අැයි කියලා උඹලටත් තේරෙනවා අැති.එ්ක කියවල පිස්සු වගෙ. හැබැයි උබ කියන කතාව ගැන සාමානයෙන් අයිඩියා එකක් අාව. 1d ඉරක් කැරකුවම 2d රවුමක්. 2d රවුම කැරකුවම 3d torus එක. හරි නේද.
සිරාවටම කියන්නෙ ටිකක් හිතලා බලහන් Pi^3 හැඩය ගැන. ඔය වගේ Torus එකක් එක කෙළවරකින් අල්ලලා 4th dimension එකේ කරකවන්න ඕන.
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You are mostly on the forum. I was wondering why you haven't responded.. @pdn.ac.lk did. Thanks for the write up.Hello @imhotep, perhaps remember to mention me when you're posting such math/philosophy questions. I guarantee that you will have a stimulating answer. (You'll be amazed that I'm well versed in more things than ජංගි)
Pi squared is the surface area of a point hole, unit radius 3D Torus. You can think of it as an උළුදු වඩේ with a middle hole that is infinitesimally small. The surface area of one such shape is Pi squared.
You can get this by thinking exactly as in the definition. The area of a unit radius circle is Pi. Think how that happens. You take a unit length, hold it from one end point and rotate it from that end.
Thinking along that definition, you can understand the Pi squared quite easily. A circle (2D) develops when a unit length line (1D) is rotated about its end. Similarly, a point hole Torus (3D) is a unit circle (2D) rotated from a point in its perimeter.
From the definition of Pi, the area of a unit radius circle is Pi. Similarly, the surface area of a unit radius, point hole Torus is Pi x Pi. We rotate once to get the circle (Pi), we rotate it again to get the Torus (Pi x Pi).
If you like, you can think about the shape of Pi^3. You might think that's stupid, but the f electron shell of large atoms in Lanthenide series (electron shells are named s, p, d, f, if you remember some chemistry) have a 95% probability of being in the 3D emulation of such shaped area.
සරලව සිංහලෙන් කිව්වොත් unit දෙකක් පළල, මැද හිල ලක්ෂ්යයක් වන උළුඳු වඩේ එකක පිටත පෘෂ්ඨ වර්ගඵලය Pi වර්ගයට සමානයි. අාස නම් Pi^3 හැඩය හිතලා බලන්න ඔය විදිහටම. Lanthenide series එකේ පරමාණුවල f ඉලෙක්ට්රෝන කවචයෙ 3d හැඩය එ් වගේමයි (95% සම්භාවිතාව).
Pi^2 is special. Read the explanation.
------ Post added on Aug 13, 2022 at 7:47 PM
Another instance where π^2 appears is with the 3-sphere.
The 3-dimensional surface volume of a 3-sphere of radius r is 2.π^2.r^3 while while the 4-dimensional hypervolume (the content of the 4-dimensional region bounded by the 3-sphere) is (1/2).π^2.r^4
Ref: https://en.wikipedia.org/wiki/3-sphere
PS: Thanks for eveyone who ressponded. As @pdn.ac.lk mentioned it is an interesting question. Many came up with interesting solutions too. Only one certified moron who seem to think he's Einstein was far too retarded even to comprehend the sentence "Just like π is the area of a unit circle, what could be a similar instance for π^2?" - this nincompoop went on ranting claiming to provide hundreds of formulae with π^2. At least he bumped the thread. Thanks for that.
(I have never claimed that I am a mathematician. I am not. However, it's one of my hobbies. )
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