# Quadrature of a circle solved

Discussion in 'Pseudoscience' started by Jason.Marshall, Jan 7, 2015.

1. ### rpennerFully WiredStaff Member

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4,833
You were wrong when you said "better". One is not better than the other. This was addressed above.

You were wrong when you said "calculate the square root of 2". You didn't obtain √2 by your manipulations, but a different number, 2.

The thought you expressed would be better written as: π/H² = 2 = 3.125/‭ה² which is a trivial rearrangement of the definitions of H and ה. Since the definitions use 2, this is not even calculating 2. This is recovering 2 from the definitions.

For x ≠ 0, y ≠ 0 the definition z = √(y/x) means y/z² = x and x z² = y, even if x and y are a complex numbers. It's not a mathematical mystery.

3. ### Jason.MarshallBannedBanned

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The thought you expressed would be better written as: π/H² = 2 = 3.125/‭ה² which is a trivial rearrangement of the definitions of H and ה. Since the definitions use 2, this is not even calculating 2. This is recovering 2 from the definitions.

You do realise that you have just confirmed my work as correct with that statement above?? and explain to me how 2 can have more than one quantity defining its position?? I was trying to express this above statement to you days ago hence the creation of my proof?? pi(1)^2= pi = 3.125(1)= 3.125.... π/H² = 2 = 3.125/‭ה².....π/H²*2 = 1 = 3.125/‭ה²*2...area = 2 for both equations Pi(1/H)^2=2=3.125(1/1.25)^2=π/H² = 2 = 3.125/‭ה²... so my question to you if they were not the exact same one defined rationally the other irrationally then how did the two different equations arrive at the area of a circle r=(1/H)...and r = (1/1.25)...the first area calculated by pi and the second area calculated by 3.125?? but the both areas = 2 ???‭

5. ### Jason.MarshallBannedBanned

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654
The thought you expressed would be better written as: π/H² = 2 = 3.125/‭ה² which is a trivial rearrangement of the definitions of H and ה. Since the definitions use 2, this is not even calculating 2. This is recovering 2 from the definitions.

You do realise that you have just confirmed my work as correct with that statement above?? and explain to me how 2 can have more than one quantity defining its position?? I was trying to express this above statement to you days ago hence the creation of my proof?? pi(1)^2= pi = 3.125(1)= 3.125.... π/H² = 2 = 3.125/‭ה².....π/H²*2 = 1 = 3.125/‭ה²*2...area = 2 for both equations Pi(1/H)^2=2=3.125(1/1.25)^2=π/H² = 2 = 3.125/‭ה²... so my question to you if they were not the exact same one defined rationally the other irrationally then how did the two different equations arrive at the exact same area of a circle r=(1/H)...and r = (1/1.25)...the first area calculated by pi and the second area calculated by 3.125?? but the both areas = 2 ??? and the sides are equal to "sqrt{2}" for 3.125 area was equal to exactly 2 without calculating to infinite irrational pi???
sqrt{pi}/sqrt{2}=H ....and sqrt{3.125}/sqrt{2}= 1.25...This is because 1.25 is the universal growth ratio identifiying the relationship between pi and 2‭

Last edited: Jan 11, 2015

7. ### Jason.MarshallBannedBanned

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[3.125(H/1.25)] (H/1.25)= pi

8. ### James RJust this guy, you know?Staff Member

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30,015
Jason.Marshall,

It's a pity that you ignored most of what rpenner told you. Probably you skimmed over most of it because you couldn't follow the mathematics.

Perhaps the most important point you need to take away about your algebra is that it is circular. You start by defining certain things, like H, in a particular way. Then, you manipulate expressions until to get a result that is, in the end, just a rearrangement of your initial definition. This kind of process doesn't prove anything. It's just shuffling around of terms in an equation.

Look. Suppose I define J = 2/17.5. Now watch some amazing arithmetic:

$(8 + 9.5)\times J = 2$, exactly!

Wow! Look! That J thing must be really important, like pi. Because I can make the number 2 using J.

Do you see what happened there?

Now look what you did. You say the result $\pi \times (1/H)^2 = 2$ is incredible. But look at your definition of H:

$H=\sqrt{\frac{\pi}{2}}$

Therefore
$\frac{1}{H} =\sqrt{\frac{2}{\pi}}$

Therefore
$\left(\frac{1}{H}\right)^2 =\frac{2}{\pi}$

Therefore
$\pi \times \left(\frac{1}{H}\right)^2 = \pi \times \frac{2}{\pi} = 2$

There's nothing amazing about that. It's just a rearrangement of your original definition of H.

Notice also that it doesn't matter whether, in that definition of H, you use $\pi$ or 3.125. Suppose you define
$H = \sqrt{\frac{3.125}{2}}$

Then it follows that
$3.125 \times (1/H)^2 = 2$ exactly - just as before.

Instead of 3.125 in the definition, you could use 163.7 or 14.356 or -83 and the result would still hold.

9. ### Jason.MarshallBannedBanned

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654
James H is not a variable and pi is not a variable but the incorrect quantities in between pi and 3.125 are variables only to be desribed by infinite sets because it is not a rational number it is undefined in a rational way that is the reason, I am not just using arbituary number I just slotted in. These are the solutions for pi*r^2 - a^2+b^2= 0
If a circle is defined as 360 degrees 360 is a constant and does not change so then this follows that the variable that must change is diameter which is 360/pi so I define this by doing this [(360/pi) (H/1.25)] (H/1.25) = 115.2 therefore this follows 3.125 * 115.2 = 360 exactly so tell me is there some random number you can substitute that will solve for this equation your thinking about it the wrong way you cannot focus on pi because that quatity is arbituary until its defined what you need to focus on is 360 divided by some number and that number must also be a factor of 180/pi for which is the variables number. Yo must think logically if 360 doesnot change then only the diameter can change that is why it's defined by 360/pi here in this definition 360 was used as a constant divided by and irrational number will give you another irrational number. So now this number is approximately 114...... So logic would dictate if you add an infinite sum of numbers to that quantity you will eventually arrive at some rational number. you can not just keep adding infinitely small sums to a finite number and not expect it to increase that is not logical. So this follows that the next important equivalent factor in line next starting from 180/pi...114....... Will be equal 115.2. Is that so hard to believe, thus it makes complete logical sense why do you think when you use 3.14 as a substitute for pi the accuracy will be very dim? That is because the more space is added to the diameter then pi must decrease to compensate, but doesn't mean it's a variable because the variable quantities are insignificant. so this is why the computer can never produce a rational pi because a computer operates in binary code similar to a one dimensional point constructing two dimensional constructs by traveling in with only one direction 1+1+1.... And so on an infinite set of natural numbers arithmetic it will need an eternity to solve that equation which is a contradiction because time is not infinite. So this is why humans exist to help the machine along and guide it because it is blind to our realm of existence the machine conscience can not comprehend our 3 dimensional reality because it was created to comprehend a maximum of 2,... +1, and -1 am speaking metaphorically here so you will have use your imagination until I complete my full mathematical theorems and desribe all of this mathematically. But if the machine was to define pi it would arrive at 3.125 there would be no infinite set of digits after .14.......... Likewise. The real problem here is a true understanding of a dimensions and how they correctly relate to each other because things that may appear as separate on a lower dimension is unified on a higher dimension explaining the paradox of quantum entanglement and probability.

Last edited: Jan 12, 2015
10. ### Jason.MarshallBannedBanned

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and one more thing James I am here to formulate a correct proof so I was not intentionally expressing myself with circular logic since I am not a formal mathematician I need to discover a formal way to express and show my discovery is correct, I have my own methods of confirming my findings in reality and I already confirmed them correct its amazing what I discovered this appears to connect to our very tools we use to measure reality itself there seems to be a universal gap in all real quantities versus our measuring instruments this is inconclusive until further investigation so am not giving a conclusive statement at the moment. but these ratios of great interest... 1.38 ...1.038... and 1.25....1.02497. So this discussion is very important to me here I can determine how to actually prove I am correct beyond the shadow of a doubt illuminated in light. another thing I found interesting but its not really mathematical just an arbituary fact 322 the number of skull and bones correlates exactly to sqrt{3.125} which is 101.8 ...or nov 18 10,18 322 is the 322 day of the year, just something interesting I noticed not sure what to conclude about it though just saying.

11. ### Jason.MarshallBannedBanned

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So I guess this is what needs to be solved 360/360/pi = pi = 360/115.2... solve for 360/pi this here I guess you can say is circular logic but I guess my proof is not strong enough so I will have to keep thinking of the best way to present it because with my own methods I already confirmed this and it true correct and 100% accurate again circular logic of words but it gets trickier because it would seem that our measuring instruments may not represent reality in its exact nature as well so this calls for further investigation boy does it seem to have many bad alignments on this planet.

12. ### DywyddyrPenguinaciously duckalicious.Valued Senior Member

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18,474
Nonsense.

You don't have any "proof" and if "your methods have confirmed it" then your methods are deeply flawed.

Unmitigated drivel.

13. ### Jason.MarshallBannedBanned

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So Rpenner if the sqrt{2} = c and c^2 = 2 and r = 1/2 diameter of a circle = 1 radian then ..... 3.125 (1/1.25)^2 = 2 so then should this follows r^2+r^2= L^2...L= hypotenuse so then this follows (L*1.25)^2= 2... did I not show that c= L*1.25??? what is wrong with this proof if you can represent "c" as equal to "sqrt{2}"?? 3.125 (r/1.25)^2= Area so if I am able to derive the sqrt{2} from 3.125 (r/1.25)^2 when r = 1...what is wrong with this proof? I don't think this is any different from comparing g(x) = f(x) its the same concept am just comparing c^2= sqrt{2} these are two different formulas and I showed they are exactly equal and I never even used pi or H and reach an exact quantity? my first attempt I think I confused you when I said the sqrt{2} I meant 2. Area of a circle = 2 =3.125 (1/1.25)^2 ...
and area of square =2=(L*1.25)^2....and the can arrive at L by this r^2+r^2= L^2...sqrt {L^2}= L...(L*1.25)^2=c^2... a^2+b^2=c^2...
c= L*1.25 I know there is a function f(x) this is equal to I just cant remember which one??

So in conclusion what am saying is sqrt{2}=sqrt{pi}=sqrt{3.125} when r=1 is this not correct?
this proof may be weak it still may be circular logic I know there is a way this could be equal to a specific function of f(x) its not going to be straight forward because of sine(x)

Last edited: Jan 12, 2015
14. ### rpennerFully WiredStaff Member

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4,833
Mathematics on a Distant Planet”, American Math Monthly, vol 105 no 7​
In standard real algebra, you are free to define whatever terms you like as long as you take responsibility to be consistent with the rules of algebra. More generally, you are free to define new types of math as long as you take responsibility to be logically consistent and honest enough not to pass them off as standard math. But you are not doing either, so you doomed your thread and maybe the remainder of your existence to reside in pseudo-mathematics.

All the real numbers already are contained in standard algebra, so the most you can do is introduce new names for real numbers. An equals sign just says the name for the number on the left side refers to the same number as the name for the number on the right side, no matter how complicated the (legal) expression is.

You have defined $H \equiv \sqrt{\frac{\pi}{2}}, \; ה \equiv \frac{5}{4}$ which means both of these are just new names for real numbers that follow all the laws of algebra. So it follows that:
$1 = 1^2 = \frac{25}{16 ‭ה^2} = \frac{16 ‭ה^2}{25} = \frac{\pi}{2 H^2} = \frac{2 H^2}{\pi} = \frac{25 \pi}{32 H^2 ‭ה^2} = \frac{25 H^2}{8 \pi ‭ה^2} = \frac{32 H^2 ‭ה^2}{25 \pi} = \frac{8 \pi ‭ה^2}{25 H^2} \\ \frac{H^2}{ ‭ה^2} = \frac{8 \pi}{25} ‭\\ ה^2 = \frac{25}{16} \\ H^2 = \frac{\pi}{2} \\ 2 = 1 + 1 = \frac{\pi}{H^2} = \frac{\; \frac{25}{8} \; }{‭ה^2} = \frac{25}{8 ה^2} \\ H^2 ‭ה^2 = \frac{25 H^2}{16} = \frac{\pi ‭ה^2}{2} = \frac{25 \pi}{32} \\ 2 ‭ה^2 = \frac{25 \pi}{16 H^2} = \frac{\pi ‭ה^2}{H^2} = \frac{25}{8} \\ \pi = 2 H^2 = \frac{25 H^2}{8 ‭ה^2} = \frac{25 \pi}{16 ‭ה^2} \\ 4 = \frac{25 \pi}{8 H^2 ‭ה^2} = \frac{25 \pi}{8 H^2 ‭ה^2} = \frac{25}{4 ‭ה^2} = \frac{2 \pi}{H^2} \\ 2 H^2 ‭ה^2 = \frac{25 H^2}{8} = \pi ‭ה^2 = \frac{25 \pi}{16} \\ 2 \pi = 4 H^2 = \frac{25 \pi}{8 ‭ה^2} = \frac{25 H^2}{4 ‭ה^2} \\ 4 H^2 ‭ה^2 = \frac{25 \pi}{ 8}$​
So $1 < \frac{8 \pi}{25} < \frac{25}{16} < \frac{\pi}{2} < 2 < \frac{25 \pi}{32} < \frac{25}{8} < \pi < 4 < \frac{25 \pi}{16} < 2 \pi < \frac{25 \pi}{ 8}$ and other facts about algebra and the real numbers remain true regardless of your new names.

You can't equate 1/2 diameter of a circle with 1 radian because they don't have the same units and don't measure the same thing.
That is true always, not just because of your assumptions.
You have that backwards. Here you introduce L for the first time, so therefore L is defined in terms of r. $L^2 = 2 r^2$.
That does not follow.
$\left( \frac{5}{4} L \right)^2= 2 \quad \Rightarrow \quad \frac{25}{16} L^2 = 2 \quad \Rightarrow \quad r = \frac{4}{5}$ follows. This constrains us to speak of a circle of a certain size.
No, you demonstrated the ratio r:L is the same as the ratio 1:c and since $r = \frac{4}{5} = 1/1.25$, you have left it for the reader to infer that L = c/1.25 or c = 1.25 L.
It lacks a statement of the givens. It lacks a statement of what is to be proven. It lacks a rigorous chain of explicitly justified statements that explain every step of the reasoning and connect the givens with the statement of what is to be proven. It has questions. It has false statements. There may be more problems.

Because r cannot be 1 ever since you asserted (L*1.25)^2 = 1.25 (2 r²)= 2. "[Y]ou are responsible for what you believe" and you are likewise responsible for what you communicate and assert.

You asserted that. You did not show that, because "c" didn't enter the conversation before.
The exact quantity you reached was $r = \frac{4}{5}$ which was neither your stated goal nor a conclusion you reached on your own.

You didn't confuse (just) me. You got it wrong for EVERYONE.

Only if the radius of the circle is $r = \sqrt{ \frac{2}{\pi} } \approx \frac{4}{5} - \frac{7}{3309}$
As above, this statement requires $L = \sqrt{\frac{32}{25}} = \frac{4}{5} \sqrt{2}$ (assuming L>0 as is typical in geometry).
As above, this statement requires $r = \frac{4}{5}$ which contradicts the implication of asserting the area of the circle is 2. Since you contradict yourself, you have not meaningfully related circles and squares.

As above, this relationship is incompatible with asserting a relationship between L and the two definitions of r. You have not related circles and squares.

r=1 contradicts both $r = \sqrt{ \frac{2}{\pi} }$ and $r = \frac{4}{5}$ so it is no surprise that you spout further contradictions yourself when you deny 2 and π are different numbers. Actually $\sqrt{2} \lt \sqrt{3.125} \lt \sqrt{\pi}$.
It's actually worse than "weak" or "circular". It's completely wrong, based on false premises, self-contradictory and advertises the incompetence of the author to discuss geometry and algebra.

Last edited: Jan 12, 2015

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16. ### Jason.MarshallBannedBanned

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72 and God are synonymous just like 9 and 90 is also synonymous with God they are factors of each other separated by H

17. ### rpennerFully WiredStaff Member

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The rule of 72 is the observation that an effective interest rate (expressed in percentage points) near 7.84687 takes about 72/r periods to double the investment.

In fact $4 \lt r \lt 100 \Rightarrow \left| \frac{ \log 2 }{\log ( 1 + \frac{r}{100} ) } - \frac{72}{r} \right| \lt \frac{1}{3}$ so it's generally good for investments that are expected to double in a human time-frame.

18. ### Jason.MarshallBannedBanned

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So what do you think of my proof format obviously I have to work it all out in detail this is just the short form am basically saying if the sqrt {pi}= sqrt{3.125} =c... and 3.125 is rational number then pi must also converge to a rational number after it is defined with the infinite set described by sin(x) and the zeta function. and then you can derive area of a circle and then transform that area into a square equivalent a^2+b^2=
"c^2 " with is the solution for the quadrature of a circle? What I said about 72 is not part of my proof just speculation which I may prove at another time.

19. ### Jason.MarshallBannedBanned

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"[Y]ou are responsible for what you believe" and you are likewise responsible for what you communicate and assert." Rpenner said

I agree

"so it is no surprise that you spout further contradictions yourself when you deny 2 and π are different numbers. Actually $\sqrt{2} \lt \sqrt{3.125} \lt \sqrt{\pi}$.
It's actually worse than "weak" or "circular". It's completely wrong, based on false premises, self-contradictory and advertises the incompetence of the author to discuss geometry and algebra." Rpenner said

Here I never explained myself correctly, what I was trying to express is that quantities are related in the same family and are the same but only differ by means of translation they either get smaller or bigger but have an identical structure this is demonstrated in my proof.

20. ### LiddzRegistered Member

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2
Creating a circle and a square with equal areas involving 100% accuracy solved.

From: Liddz.

It is almost impossible to create a circle and a square with equal areas of measure with 100% accuracy due to the transcendental nature of the modern traditional version of the ratio Pi 3.141592653589793. Remember that there are also 2 other modern values of Pi in addition to the traditional most common value of Pi that is 3.141592653589793. The 2 other values of Pi are: 3.146446609406726 and also 3.14460551102969. 3.146446609406726 is the result of 14 subtract square root of 2 = 1.414213562373095 = 12.585786437626905 and then 12.585786437626905 is divided by 4. 3.14460551102969 is the result of 4 divided by the square root of the Golden ratio = 1.272019649514069. 1.272019649514069 squared is the Golden ratio of 1.618033988749895. Please remember that the Golden ratio can be obtained in Trigonometry through the formula Cosine (36) multiplied by 2. All modern Pi values must be approximated meaning the results that are given to us by the 3 modern Pi values must be reduced to 4 or 5 decimal places resulting in multiple approximations for the 3 main Pi values. There is a debate among scholars regarding which version of the 3 values of Pi are better to use when dealing with circles and geometrical figures. The view of this author is that all 3 of the values of Pi are important and all the 3 values of Pi must be studied as much as possible to achieve accuracy. The 3 values of Pi 3.141592653589793 and 3.146446609406726 and 3.144605511029693 must be compared to each other so the geometrician can determine which value is best suited for the desired task.

I think that I have solved the problem of creating a circle and a square with equal areas involving 100% accuracy:

Requirements for creating a circle and a square with equal areas involving 100% include:

1. The surface area of the circle that is to be equal to the surface area of a square can be derived from the surface area of 2 squares with rational widths of measure but does not always have to be.

2. The square that has a surface area equal to the surface area of the circle can have a width of an irrational measure or a width of rational measure.

3. The Pythagorean theorem is required to construct the square that has an irrational width of measure and a surface area equal to the surface area of the circle. The Pythagorean theorem is also required to test the accuracy of the construction of a circle plus a square that has an irrational width of measure with equal areas involving 100% accuracy. The Pythagorean theorem is based upon a scalene triangle and says that the amount of squares on the hypotenuse is equal to the sum of all the squares that are located on both the adjacent edge of the scalene triangle and also the opposite edge of the scalene triangle. The width of the square with a surface area that is equal in measure to the surface area of the circle must be equal in measure to length of the scalene triangle’s hypotenuse.

http://www.jainmathemagics.com/

http://www.iosrjournals.org/iosr-jm/papers/Vol10-issue1/Version-4/C010141415.pdf

My question is it possible to create a circle with a surface area of 106 equal units because if we can create a circle with a surface area of 106 equal units of measure then we can also create a square with a surface area of 106 equal units of measure by creating a scalene triangle with the longest edge length as 9 equal units of measure taken from the diameter of the circle that has a surface area of 106 equal units of measure, while the shortest length of the scalene triangle has 5 equal units of measure. The hypotenuse of a scalene triangle with the second longest length as 9 equal units of measure and the shortest length of the scalene triangle as 5 equal units of measure is equal in measure to the width of a square that has a surface area of 106 equal units of measure. We can use the theorem of Pythagoras: https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has 106 equal units of measure.

Area of circle = 106.

Diameter of circle = 11.62.

Circumference of circle = 36.5.

9 squared = 81.

5 squared = 25.

81 + 25 = 106.

Most values of Pi can confirm that if a circle has a diameter of 11.62 equal units of measure then the surface area of the circle with a diameter of 11.62 equal units of measure is 106 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 117 square units because if we can then we can create a square with the same 117 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 9 units of measure from the circle’s diameter with an area of 117 units of equal measure. The shortest length of the scalene triangle must have 6 equal units of measure that are also taken from the circle’s diameter with an area of 117 equal square units. We can use the theorem of Pythagoras: https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 117 equal units of measure.

Area of circle = 117.

Diameter of circle = 12.22

Circumference of circle is 38.39.

Traditional Pi is approximated to: 3.141571194762684.

9 squared = 81.

6 squared = 36.

81 + 36 = 117.

Most values of Pi can confirm that if a circle has a diameter of 12.22 equal units of measure then the surface area of the circle with a diameter of 12.22 equal units of measure is 117 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 153 square units because if we can then we can create a square with the same 153 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 12 units of measure from the circle’s diameter with an area of 153 units of equal measure. The shortest length of the scalene triangle must have 3 equal units of measure that are also taken from the circle’s diameter with an area of 153 equal square units. We can use the theorem of Pythagoras: https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 153 equal units of measure.

Area of circle = 153.

Diameter of circle = 13.96

Circumference of circle is 43.85.

Traditional Pi is approximated to: 3.141117478510029.

12 squared = 144.

3 squared = 9.

144 + 9 = 153.

Most values of Pi can confirm that if a circle has a diameter of 13.96 equal units of measure then the surface area of the circle with a diameter of 13.96 equal units of measure is 153 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 365 square units because if we can then we can create a square with the same 365 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 14 units of measure from the circle’s diameter with an area of 365 units of equal measure. The shortest length of the scalene triangle must have 14 equal units of measure that are also taken from the circle’s diameter with an area of 365 equal square units. We can use the theorem of Pythagoras: https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 365 equal units of measure.

Area of circle = 365.

Diameter of circle = 21.56

Circumference of circle is 67.73.

Traditional Pi is approximated to: 3.141465677179963.

14 squared = 196.

13 squared = 169.

196 + 169 = 365.

Most values of Pi can confirm that if a circle has a diameter of 21.56 equal units of measure then the surface area of the circle with a diameter of 21.56 equal units of measure is 365 equal units of measure.

21. ### LiddzRegistered Member

Messages:
2
Creating a circle and a square with equal areas involving 100% accuracy solved.

From: Liddz.

It is almost impossible to create a circle and a square with equal areas of measure with 100% accuracy due to the transcendental nature of the modern traditional version of the ratio Pi 3.141592653589793. Remember that there are also 2 other modern values of Pi in addition to the traditional most common value of Pi that is 3.141592653589793. The 2 other values of Pi are: 3.146446609406726 and also 3.14460551102969. 3.146446609406726 is the result of 14 subtract square root of 2 = 1.414213562373095 = 12.585786437626905 and then 12.585786437626905 is divided by 4. 3.14460551102969 is the result of 4 divided by the square root of the Golden ratio = 1.272019649514069. 1.272019649514069 squared is the Golden ratio of 1.618033988749895. Please remember that the Golden ratio can be obtained in Trigonometry through the formula Cosine (36) multiplied by 2. All modern Pi values must be approximated meaning the results that are given to us by the 3 modern Pi values must be reduced to 4 or 5 decimal places resulting in multiple approximations for the 3 main Pi values. There is a debate among scholars regarding which version of the 3 values of Pi are better to use when dealing with circles and geometrical figures. The view of this author is that all 3 of the values of Pi are important and all the 3 values of Pi must be studied as much as possible to achieve accuracy. The 3 values of Pi 3.141592653589793 and 3.146446609406726 and 3.144605511029693 must be compared to each other so the geometrician can determine which value is best suited for the desired task.

I think that I have solved the problem of creating a circle and a square with equal areas involving 100% accuracy:

Requirements for creating a circle and a square with equal areas involving 100% include:

1. The surface area of the circle that is to be equal to the surface area of a square can be derived from the surface area of 2 squares with rational widths of measure but does not always have to be.

2. The square that has a surface area equal to the surface area of the circle can have a width of an irrational measure or a width of rational measure.

3. The Pythagorean theorem is required to construct the square that has an irrational width of measure and a surface area equal to the surface area of the circle. The Pythagorean theorem is also required to test the accuracy of the construction of a circle plus a square that has an irrational width of measure with equal areas involving 100% accuracy. The Pythagorean theorem is based upon a scalene triangle and says that the amount of squares on the hypotenuse is equal to the sum of all the squares that are located on both the adjacent edge of the scalene triangle and also the opposite edge of the scalene triangle. The width of the square with a surface area that is equal in measure to the surface area of the circle must be equal in measure to length of the scalene triangle’s hypotenuse.

http://www.jainmathemagics.com/

http://www.iosrjournals.org/iosr-jm/papers/Vol10-issue1/Version-4/C010141415.pdf

My question is it possible to create a circle with a surface area of 106 equal units because if we can create a circle with a surface area of 106 equal units of measure then we can also create a square with a surface area of 106 equal units of measure by creating a scalene triangle with the longest edge length as 9 equal units of measure taken from the diameter of the circle that has a surface area of 106 equal units of measure, while the shortest length of the scalene triangle has 5 equal units of measure. The hypotenuse of a scalene triangle with the second longest length as 9 equal units of measure and the shortest length of the scalene triangle as 5 equal units of measure is equal in measure to the width of a square that has a surface area of 106 equal units of measure. We can use the theorem of Pythagoras: https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has 106 equal units of measure.

Area of circle = 106.

Diameter of circle = 11.62.

Circumference of circle = 36.5.

9 squared = 81.

5 squared = 25.

81 + 25 = 106.

Most values of Pi can confirm that if a circle has a diameter of 11.62 equal units of measure then the surface area of the circle with a diameter of 11.62 equal units of measure is 106 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 117 square units because if we can then we can create a square with the same 117 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 9 units of measure from the circle’s diameter with an area of 117 units of equal measure. The shortest length of the scalene triangle must have 6 equal units of measure that are also taken from the circle’s diameter with an area of 117 equal square units. We can use the theorem of Pythagoras:https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 117 equal units of measure.

Area of circle = 117.

Diameter of circle = 12.22

Circumference of circle is 38.39.

Traditional Pi is approximated to: 3.141571194762684.

9 squared = 81.

6 squared = 36.

81 + 36 = 117.

Most values of Pi can confirm that if a circle has a diameter of 12.22 equal units of measure then the surface area of the circle with a diameter of 12.22 equal units of measure is 117 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 153 square units because if we can then we can create a square with the same 153 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 12 units of measure from the circle’s diameter with an area of 153 units of equal measure. The shortest length of the scalene triangle must have 3 equal units of measure that are also taken from the circle’s diameter with an area of 153 equal square units. We can use the theorem of Pythagoras:https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 153 equal units of measure.

Area of circle = 153.

Diameter of circle = 13.96

Circumference of circle is 43.85.

Traditional Pi is approximated to: 3.141117478510029.

12 squared = 144.

3 squared = 9.

144 + 9 = 153.

Most values of Pi can confirm that if a circle has a diameter of 13.96 equal units of measure then the surface area of the circle with a diameter of 13.96 equal units of measure is 153 equal units of measure.

Also is it possible to create a circle geometrically on paper with a surface area of 365 square units because if we can then we can create a square with the same 365 units by simply constructing a scalene triangle with the second longest length of the scalene triangle being equal to 14 units of measure from the circle’s diameter with an area of 365 units of equal measure. The shortest length of the scalene triangle must have 14 equal units of measure that are also taken from the circle’s diameter with an area of 365 equal square units. We can use the theorem of Pythagoras:https://en.wikipedia.org/wiki/Pythagorean_theorem to prove that the square with a width equal to the longest length of the scalene triangle also called the hypotenuse also has a surface area of 365 equal units of measure.

Area of circle = 365.

Diameter of circle = 21.56

Circumference of circle is 67.73.

Traditional Pi is approximated to: 3.141465677179963.

14 squared = 196.

13 squared = 169.

196 + 169 = 365.

Most values of Pi can confirm that if a circle has a diameter of 21.56 equal units of measure then the surface area of the circle with a diameter of 21.56 equal units of measure is 365 equal units of measure.

22. ### originTrump is the best argument against a democracy.Valued Senior Member

Messages:
9,453
You say it the 2 values are 100% accurate, but you are using an approximation of pi. If you are using and approximation of pi doesn't that necesarily mean that the are of the circle is an approximation?

23. ### Write4UValued Senior Member

Messages:
3,862
The OP speaks of "squares". Question:
Wouldn't using triangulation (pentagons or hexagons) yield an instant result of total surface area of a globe?Fractals can be used to measure all irregular or variable measurements of all natural shapes, down to the geometry of the fabric of spacetime itself..

Last edited: Apr 21, 2017