Silly φ and π crackpottery

Over time, I’ve come to really, really hate the number φ.

φ is the so-called golden ratio. It’s the number that is a solution for the equation (a+b)/a = (a/b). The reason that that’s interesting at all is because it’s got an interesting property when you draw it out: if you take a rectangle where the ratio of the length of the sides is 1:φ, then if you remove the largest possible square from it, you’ll get another rectangle whose sides have the ratio φ:1. If you take the largest square from that, you’ll get a rectangle whose sides have the ratio 1:φ. And so on.

The numeric value of it is (1+sqrt(5))/2, or about 1.618033988749895.

The problem with φ is that people are convinced that it’s some kind of incredibly profound thing, and find it all over the place. The problem is, virtually all of the places where people claim to find it are total rubbish. A number that’s just a tiny bit more that 1 1/2 is really easy to find if you go looking for it, and people go looking for it all over the place.

People claim it’s in all sorts of artwork. You can certainly find a ton of things in paintings whose size ratio is about 1 1/2, and people find it and insist that it was deliberately done to make it φ. People find it in musical scales, the diatonic and pentatonic scales, and the indian scales.

People claim it comes up all over the place in nature: in beehives, ant colonies, flowers, tree sizes, tree-limb positions, size of herds of animals, litters of young, body shapes, face shapes.

People claim it’s key to architecture.

And yet… it seems like if you actually take any of those and actually start to look at it in detail? The φ isn’t there. It’s just a number that’s kinda-sorta in the 1 1/2 range.

One example of that: there’s a common claim that human faces have proportions based on &phi. You can see a bunch of that nonsense here. The thing is, the “evidence” for the claim consists of rectangles drawn around photographs of faces – and if you look closely at those rectangles, what you find is that the placement of the corners isn’t consistent. When you define, say, “the distance between the eyes”, you can measure that as distances between inner-edges, or between pupils, or between outer edges. Most of these claims use outer edges. But where’s the outer edge of an eye? It’s not actually a well-defined point. You can pick a couple of different places in a photo as “the” edge. They’re all close together, so there’s not a huge amount of variation. But if you can fudge the width a little bit, and you can fudge other facial measurements just a little bit, you’ve got enough variation that if you’re looking for two measurements with a ratio close to φ, you’ll always find one.

Most of the φ nonsense is ultimately aesthetic: people claiming that the golden ratio has a fundamental beauty to it. They claim that facial features match it because it’s intrinsically beautiful, and so people whose faces have φ ratios are more beautiful, and that that led to sexual-selection which caused our faces to embody the ratio. I think that’s bunk, but it’s hard to make a mathematical argument against aesthetics.

But then, you get the real crackpots. There are people who think φ has amazing scientific properties. In the words of the crank I’m writing about today, understanding φ (and the “correct” value of π derived from it) will lead humanity to “enter into a veritable Space Age”.

I’m talking about a guy who calls himself “Jain 108”. I’m not quite sure what to call him. Mr. Jain? Mr. 108? Dr 108? Most of the time on his website, he just refers to himself as “Jain” (or sometimes “Jain of Oz”) so I’ll go with “Jain”).

Jain believes that φ is the key to mathematics, science, art, and human enlightenment. He’s a bit hard to pin down, because most of his website is an advertisement for his books and seminars: if you want to know “the truth”, you’ve got to throw Jain some cash. I’m not willing to give money to crackpots, so I’m stuck with just looking at what he’s willing to share for free. (But I do recommend browsing around his site. It’s an impressive combination of newage scammery, pomposity, and cluelessness.)

What you can read for free is more than enough to conclude that he’s a total idiot.

I’m going to focus my mockery on one page: “Is Pi a Lie?”.

On this page, Jain claims to be able to prove that the well-known value of π (3.14159265….) is wrong. In fact, that value is wrong, and the correct value of π is derived from φ! The correct value of π is \frac{4}{\sqrt{\phi}}, or about 3.144605511029693.

For reasons that will be soon explained, traditional Pi is deficient because historically it has awkwardly used logical straight lines to measure illogical curvature. Thus, by using the highest level of mathematics known as Intuitive Maths, the True Value of Pi must be a bit more than anticipated to compensate for the mysterious “Area Under The Curve”. When this is done, the value, currently known as JainPi, = 3.144… can be derived, by knowing the precise Height of the Cheops Pyramid which is based on the Divine Phi Proportion (1.618…). Instead of setting our diameter at 1 unit or 1 square, something magical happens when we set the diameter at the diagonal length of a Double Square = 2.236… which is the Square Root of 5 (meaning 2.236… x 2.236… = 5). This is the critical part of the formula that derives Phi \frac{1+\sqrt{5}}{2}, and was used by ancient vedic seers as their starting point to construct their most important diagram or ‘Yantra’ or power-art called the Sri Yantra. With a Root 5 diameter, the translation of the Phi’s formula into a geometric construct derives the royal Maltese Cross symbol, concluding that Phi is Pi, that Phi generates Pi, and that Pi must be derived with a knowledge of the Harmonics of Phi. When this is understood and utilized, we will collectively enter into a veritable Space Age.

How did we get the wrong value? It’s based on the “fact” that the computation of π is based on the use of “logical” straight lines to measure “illogical” curvurature. (From just that one sentence, we can already conclude that Jain knows nothing about logic, except what he learned from Mr. Spock on Star Trek.) More precisely, according to Jain:

In all due good respects, we must first honour Archimedes of Syracuse 2,225 years ago, who gave the world his system on how to calculate Pi, approximated to 22÷7, by cutting the circle into say 16 slices of a pizza, and measuring the 16 edge lengths of these 16 triangular polygons (fig 3), to get a good estimate for the circumference of a circle. The idea was that if we kept making the slices of pizza smaller and smaller, by subsequently cutting the circle into 32 slices, then 64, then 128 then 256 slices, we would get a better and more accurate representation for the circumference. The Fundamental Flawed Logic or Error with Archimede’s Increasing Polygon Method was that he failed to measure The Area Under The Curve. In fact, he assumed that The Area Under The Curve, just magically disappeared. Even in his time, Archimedes admitted that his value was a mere estimate!

This explanation does a beautiful job of demonstrating how utterly ignorant Jain is of math. Archimedes may have been the first person from the western tradition to have worked out a mechanism to compute a value for π – and his mechanism was a good one. But it’s far from the only one. But let’s ignore that for a moment. Jain’s supposed critique, if true, would mean that modern calculus doesn’t work. The wedge-based computation of π is a forerunner of the common methods of calculus. In reality, when we compute the value of almost any integral using calculus, our methods are based on the concept of drawing rectangles under the curve, and narrowing those rectangles until they’re infinitely small, at which point the “area under the curve” missed by the rectangles becomes zero. If the wedge computation of π is wrong because it misses are under the curve, then so will every computation using integral calculus.

Gosh, think we would have noticed that by now?

Let’s skip past that for a moment, and come back to the many ways that π comes into reality. π is the ratio of the diameter of a circle to its radius. Because circles are such a basic thing, there are many ways of deriving the value of π that come from its fundamental nature. Many of these have no relation to the wedge-method that Jain attributes to Archimedes.

For example, there is Viete’s product:

\frac{2}{\pi} = \left(\frac{\sqrt{2}}{2}\right)\left(\frac{\sqrt{2 + \sqrt{2}}}{2}\right)\left(\frac{\sqrt{2 + \sqrt{2 + \sqrt{2}}}}{2}\right)(...)

Or there’s the Gregory-Leibniz series:

\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - ...

These have no relation to the wedge-method – they’re derived from the fundamental nature of π. And all of them produce the same value – and it’s got no connection at all to φ.

As supportive evidence for the incorrectness of π, Jain gives to apocryphal stories about NASA and the moon landings. First, he claims that the first moon landing was off by 20 kilometers, and that the cause of this was an incorrect value of π: that the value of π used in computing trajectories was off by 0.003:

NASA admitted that when the original Mooncraft landing occurred, the targeted spot was missed by about 20km?
What could have been wrong with the Calculations?
NASA subsequently adjusted their traditional mathematical value for Pi (3.141592…) by increasing it in the 3rd decimal by .003!

Let’s take just a moment, and consider that.

It’s a bit difficult to figure out how to address that, because he’s not mentioning what part of the trajectory was messed up. Was it the earth-to-moon transit of the full apollo system? Or was it the orbit-to-ground flight of the lunar lander? Since he doesn’t bother to tell us, we’ll look at both.

π does matter when computing the trajectory of the earth-to-moon trip – because it involves the intersection of two approximate circles – the orbit of the earth around the sun, and the orbit of the moon around the earth. (Both of these are approximations, but they’re quite useful ones; the apollo trajectory computations did rely on a value for π.

Let’s look at earth-to-moon. I’m going to oversimplify ridiculously – but I’m just trying to give us a ballpark order-of-magnitude guess as just how much of a difference Mr. Jain’s supposed error would cause. THe distance from the earth to the moon is about 384,000 kilometers. If we assume that π is a linear factor in the computation, then a difference in the value of pi of around 1 part in 1000 would cause a difference in distance computations of around 384 kilometers. Mr. Jain is alleging that the error only caused a difference of 20 kilometers. He’s off by a factor of 15. We can hand-wave this away, and say that the error that caused the lander to land in the “wrong” place wasn’t in the earth-moon trajectory computation – but we’re still talking about the apollo unit being in the wrong place by hundreds of kilometers – and no one noticing.

What if the problem was in the computation of the trajectory the lander took from the capsule to the surface of the moon? The orbit was a nearly circular one at about 110 kilometers above the lunar surface. How much of an error would the alleged π difference cause? About 0.1 kilometer – that is, about 100 meters. Less than what Jain claims by a factor of 200.

The numbers don’t work. These aren’t precise calculations by any stretch, but they’re ballpark. Without Jain providing more information about the alleged error, they’re the best we can do, and they don’t make sense.

Jain claims that in space work, scientists now use an adjusted value of π to cover the error. This piece I can refute by direct knowledge. My father was a physicist who worked on missiles, satellites, and space probes. (He was part of the Galileo team.) They used good old standard 3.14159 π. In fact, he explained how the value of π actually didn’t need to be that precise. In satellite work, you’re stuck with the measurement problems of reality. In even the highest precision satellite work, they didn’t use more that 4 significant digits of precision, because the manufacturing and measurement of components was only precise to that scale. Beyond that, it was always a matter of measure and adjust. Knowing that π was 3.14159265356979323 was irrelevant in practice, because anything beyond “about 3.1416” was smaller that the errors in measurement.

Mr. Jain’s next claim is far worse.

Also, an ex-Engineer from NASA, “Smokey” admitted (via email) that when he was making metal cylinders for this same Mooncraft, finished parts just did not fit perfectly, so an adjusted value for Pi was also implemented. At the time, he thought nothing about it, but after reading an internet article called The True Value of Pi, by Jain 108, he made contact.

This is very, very simple to refute by direct experience. This morning, I got up, shaved with an electric razor (3 metal rotors), made myself iced coffee using a moka pot (three round parts, tight fitted, with circular-spiral threading). After breakfast, I packed my backpack and got in my car to drive to the train. (4 metal cylinders with 4 precisely-fitted pistons in the engine, running on four wheels with metal rims, precisely fitted to circular tires, and brakes clamping on circular disks.) I drove to the train station, and got on an electric train (around 200 electric motors on the full train, with circular turbines, driving circular wheels).

All those circles. According to Jain, every one of those circles isn’t the size we think it is. And yet they all fit together perfectly. According to Jain, every one of those circular parts is larger that we think it should be. To focus on one thing, every car engine’s pistons – every one of the millions of pistons created every year by companies around the world – requires more metal to produce than we’d expect. And somehow, in all that time, no one has ever noticed. Or if they’ve noticed, every single person who ever noticed it has never mentioned it!

It’s ludicrous.

Jain also claims that the value of e is wrong, and comes up with a cranky new formula for computing it. Of course, the problem with e is the same as the problem wiht π: in Jain’s world, it’s really based on φ.

In Jain’s world, everything is based on φ. And there’s a huge, elaborate conspiracy to keep it secret. Any Jain will share the secret with you, showing you how everything you think you know is wrong. You just need to buy his books ($77 for a hard-copy, or $44 for an ebook.) Or you could pay for him to travel to you and give you a seminar. But he doesn’t list a price for that – you need to send him mail to inquire.

68 thoughts on “Silly φ and π crackpottery

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  2. Deen

    There’s a much simpler rebuttal, if you’re worried about missing the “area under the curve” by using the perimeter of an inscribed polygon, as in Archimedes’ method, just use the perimeter of the circumscribed polygon as well. The former will be an underestimate for pi, the latter an overestimate, bracketing pi in between. And they will both converge to the same value.

    According to this nifty little calculator I found, already at 128 sides, the circumscribed polygon has a smaller perimeter than what this guy claims.

    1. unicorndaniel

      Interesting….Archimedes used 64 sides, both inner and outer, to obtain 64.sin(Pi/64) < 223/71 < Pi < 64.tan(Pi/64) < 22/7. …A good approximation is 3 + (16/113) = 3.14159292… as Pi = 3.14159265… Of course Jain would say your calculator's calculations are based on "the lie".

      1. Liddz

        Traditional Pi = 3.141592653589793 is also false because infinite polygons cannot exist. A Polygon by definition is a plane figure that can fit into a circle with a limited amount of sides. Fractal geometry with the help of computer software has proven that it does not matter how many times we divide the circumference of a circle into different sections gaps will always exist upon the circumference when the curve of the circle is magnified and we zoom in to look as close as we can so the assumption that Archimedes made that enough divisions upon a circle’s circumference will cause the gaps to eventually disappear is false: : . A polygon and a circle are related but a polygon never becomes a circle. My dictionary defines a circle as a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). We know that a Decagon is a Decagon because a Decagon is identified as having 10 equal sides and can fit into a circle.
        Yes you are right to say traditional Pi 3.141592653589793 is the correct value of Pi for the method that was used to get Traditional Pi 3.141592653589793. Remember that traditional Pi 3.141592653589793 is gained from the multiple polygon method and that makes traditional Pi 3.141592653589793 appear to be the real Pi.
        I repeat a circle can never become a polygon and infinite sided polygons cannot exist. Traditional Pi 3.141592653589793 is accurate enough for the method that gave us traditional Pi 3.141592653589793

        I bet you do not even know that we can divide a line into the ratio Pi by multiplying the shortest edge of a Kepler right triangle 4 times on a straight line and dividing the 4 lines that all have the same measure as the shortest edge length of the Kepler right triangle by the second longest edge length of the Kepler right triangle. Remember that if the second longest edge length of a Kepler right triangle is accepted as the diameter of a circle then the shortest edge length of the Kepler right triangle can be equal to 1 quarter of the circle’s circumference.
        The multiple polygon method for gaining Pi only gives us approximations so traditional Pi 3.141592653589793 could never help us to create a perfectly round circle. Traditional Pi is good and okay if you are not worried about accuracy, but if you really want to get scientific then you will have to use the Kepler right triangle method for getting Pi and that method is simple and can be done in just 5 minutes or even less than 5 minutes and does not require a super computer with spread sheets, just a compass and straight edge and obviously a pencil and a calculator and knowledge of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895. Because I use the Kepler right triangle method to get Pi I am now able to square the circle with both equal perimeters and equal areas with just compass and straight edge. Traditional Pi is both irrational and transcendental so we cannot use traditional Pi to square the circle but Golden Pi 3.144605511029693 is irrational but Golden Pi 3.144605511029693 is not transcendental:

        4th dimensional equation/polynomial for Golden Pi = 3.144605511029693 (x4 + 16×2 – 256 = 0).

        So we can use Golden Pi 3.144605511029693 or Pi as 22 divided by 7 3.142857142857143 to square the circle with both equal perimeters and equal areas involving 100% accuracy.
        If you want to you can continue using traditional Pi 3.141592653589793 but if you want to square the circle you will have to get your value of Pi from the Kepler right triangle and that value is Golden Pi 3.144605511029693. Golden Pi 3.144605511029693 is also very close to Pi as 22 divided by 7 3.142857142857143. 22 divided by 7 is best if you hate using fractions but if you want to be more accurate and you are not irritated by decimal points then the True scientific Pi is Golden Pi = 3.144605511029693.
        3.144 is the value of Pi you can get if you measure a perfect CD disc properly and NOT traditional Pi 3.141592653589793.
        Please read the following article from a web link to confirm that 3.144 allow us to create perfect circles: The Great Pi conspiracy part 1:
        The Great Pi conspiracy part 2:
        Download for free and keep and read The book of Phi volume 8: The true value of Pi = 3.144, by Mathematician and author Jain 108:

        1. S Patrick

          Since pi is defined as the ratio of a circle’s area to the square of its radius (pi = area / radius^2) why not just compute the area beneath a unit quarter circle and multiply the result by four? It’s tedious and takes several thousand divisions of the x-axis from -1 to 0 but it does produce a result, and NOT this phony 3.144 crank value. So I suppose the definition of a circle is screwed if it results in computing the “traditional” value? Does this imply that everything in STEM is screwed up because it gives us the “traditional” results that we’ve seen for centuries, and somehow this Jain crank got it “right?” WRONG.

          BTW, I created an Excel spreadsheet in which I calculated pi in the above fashion using both rectangles and trapezoids, dividing the interval [-1,0] into 50,000 units. At this point the rectangular approximation converged to two decimal places while the trapezoidal method converged on five places (3.14159). Took less than ten minutes to perform each method, although rather tedious. But look at the results I obtained without using calculus! That second number is NOT 3.144… and will never round up to it. Guess why. JAIN’S PI VALUE IS WRONG!!!

          Cheers, all.

    2. E

      About the car pistons, being somewhat of a mechanic, the pistons aren’t perfect. It has to be as close as possible, but the pistons only need to slide smoothly yet with a tight enough fit oil doesn’t pass through. Piston rings help push and pull oil along the cylinder walls lubricating and allowing the oil to fill in any micro gaps as well

  3. dtm0

    The page and the lack of any evidence of an Australian DGR with the word “Mathemagics” makes me wonder what the penalties are in Australia for soliciting donations, claiming them to be tax-exempt, when in fact they aren’t. Were he in the US, the IRS doesn’t mess around with false claims of 501(c)(3) status; I don’t know how strict the Australians are on that.

    I also don’t know if Australian tax law requires the same sort of registration and extensive paperwork for something to be able to receive tax-exempt contributions as the US does, so my inability to find any registration might not mean anything.

    (There is an ABN assigned to the business name “Jain 108 Mathemagics”, but that isn’t a DGR so far as I can tell, it’s an ABN for an individual)

    1. unicorndaniel

      I\m Canadian but i get the impression from recent news items that Australia is more stringent on tax-exempt permits and more vigorous in enforcing compliance than America.

  4. Amir

    An excerpt from the interview in the video on the main page of his site:

    “I was one of the victims of the state where I got high grades in mathematics but I literally was forced to study higher-level mathematics.
    A bit like a robot, I had to pass calculus and all this difficult algebra but I honestly really didn’t understand what I was learning.
    So I entered a quest, my personal quest was to understand the truth of mathematics.”

    He then goes on to explain how his heritage and experience in brick-laying gave him a good intuition for areas and volumes. Huh.

  5. JoeBussen

    His real name seems to be given in his “about” section. He “recently” visited the US (in 2005), and opposes No Child Left Behind, because of a related Bill that requires that any child scoring below 50% be given Prozac!

  6. bryanmcc

    Not a mathematician, but doesn’t the fact that pi is transcendental, while phi is merely irrational, pretty much throw all of his (already garbage) theory out the window? Isn’t it impossible to construct transcendentals from a less-than-infinite series of algebraic numbers?

    1. John Armstrong

      That’s kind of begging the question, though.

      Let’s say there’s some ratio R of a circle’s circumference to its diameter (we know this is π, but go with me here). We know that some constant R exists because both are linear dimensions and all circles are similar; Euclid covers as much.

      This guy claims that R is a particular number X, but you complain that his X is algebraic while π is transcendental, so they can’t be the same. He responds that of COURSE X isn’t transcendental; that’s the whole point of his system. Not only is X simpler than π, it’s even ruler-and-compass constructible; he can square the circle!

      Just saying “X is algebraic while π is transcendental” doesn’t really get there. What you need is a proof that whatever R is, it must be transcendental, and that’s a lot harder than, say, circumscribing an N-gon for sufficiently high N and showing that he misses the upper bound.

    2. Liddz

      3.141592653589793 has been proven to be Transcendental in addition to being irrational. Traditional Pi 3.141592653589793 is Transcendental because Traditional Pi 3.141592653589793 does not fit any polynomial equations. Squaring the circle becomes possible and easy after traditional Pi 3.141592653589793 has been rejected and replaced with other values of Pi that are NOT transcendental. Golden Pi = 3.144605511029693 is irrational but Golden Pi is NOT transcendental because Golden Pi = 3.144605511029693 is the only value of Pi that fits the following polynomial equations: 8th degree polynomial for Golden Pi: π8 + 16π6 + 163π2 = 164.

      4th dimensional equation/polynomial for Golden Pi = 3.144605511029693 (x4 + 16×2 – 256 = 0).

      A polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1.
      Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

  7. Sean Holman

    There are actually subtle issues with the Archimedes calculation of pi, but they are related to (potentially) miscalculating the circumference rather than missing area. See this:

    Of course Archimedes got the correct value for pi, but it just shows there is a bit more to it than one might think at first.

  8. David Starner

    @Sean Holman That drove me nuts in high school, and I never did resolve it. My problem I think was clearer, since there was no pi involved; take the diagonal of a unit square, and approximate it by vertical and horizontal segments. You can get arbitrarily close, but the vertical and horizontal segments obviously add up to 2, whereas the diagonal is sqrt(2). I guess I learned something today.

    1. Sean Holman

      @David Starner You might be interested in this paper by Mandelbrot:

      He asks the seemingly simple, but actually fairly deep question:

      How long is the coast of Britain?

      As it turns out the length of coastlines isn’t a particularly well defined concept:

      The point is that the length of the coastline depends on what scale you use to measure. If you measure at the scale of km, the answer will be smaller than if you measure at the scale of metres or cm because at smaller scales you will capture many more small variations. This is because coastlines are “fractal like”. Mandelbrot’s point is that to measure such curves it is really more appropriate to introduce the concept of “fractional dimension” since these curves are in some sense more than 1 dimensional.

      It is the same phenomenon that is going on with this “proof” that pi = 4 and your example with the triangle. The curve you form as the limit using horizontal and vertical line segments is infinitely wiggly just like a coastline (i.e. it is a fractal). (One can argue whether coastlines are really infinitely wiggly when you get to the scale of atoms say, but that’s missing the mathematical point.)

  9. Jurgan

    “It’s the number that is a solution for the equation (a+b)/a = (a/b).”

    This sentence doesn’t make sense. Your equation has two variables, so a single number can’t be “a solution.” I assume one of those is a constant, perhaps 1?

    1. markcc Post author

      I should have said “It’s the unique ratio that’s a solution for…’ There’s only one value where that’s true.

  10. jc

    I guess the theory is that a portrait which is more than phi in its height:width ratio would look “too tall,” while one less than phi would look “too wide.” In other words, why paintings are generally neither squares nor long bars, but a certain shape.

    1. David Starner

      That’s the theory, but what are the ratios of portraits in practice? To one digit, The Mona Lisa is 1.5, The Girl with a Pearl Earring is 1.2, Van Gogh’s Starry Night was 1.3. The Persistence of Memory is 1.4. Leonardo da Vinci’s Last Supper is 1.9. In fact, not a single painting I looked at had a ratio of phi. I finally found Bottecelli’s Birth of Venus, which does have such a ratio, but it seems to be a rarity.

      Movies are neither squares or (with rare exceptions, long bars), but they range from 4:3 (1.33), 16:9 (1.78), 1.85:1, all the way to 2.39:1. 1.66:1 is the closest standard movie ratios come to phi, and that doesn’t seem particularly common or close.

      Paper sizes are 8.5 x 11 (1.29), An (n=4 for normal paper) (sqrt(2) ~ 1.414), or legal at 8.5 x 14 (1.65). Legal is sort of phi ratio, and yet no one seems to be demanding to switch to legal sized paper.

  11. KnBa

    This is a minor issue, but the statement that “In reality, when we compute the value of almost any integral using calculus, our methods are based on the concept of drawing rectangles under the curve, and narrowing those rectangles until they’re infinitely small, at which point the “area under the curve” missed by the rectangles becomes zero.” is dubious. As just one obvious example, it’s not what gets used in polar, cylindrical, or spherical coordinate systems.

    1. powerfulparadox

      Since what is at issue is the value of pi in a 2-dimensional flat coordinate system, your example seems a bit pedantic.

  12. Yo Soy

    What is the mean interest in hiding the true value of Pi?

    There are BIG interests that oppose to a corrected value of Pi.

    1. Khazar academic mafia does not want the freedom for humanity.
    2. A corrected Pi collides with the interests of the oil industry and the Khazarian control of petrodollar.

    When PI be corrected humanity will discover an endless source of energy that will liberate humanity from slavery and the dependence to other energy sources.

    The number Pi have be maliciously obfuscated to prevent the close of a cycle to some energetic resonance phenomenon which will take humanity to an ENERGETIC GOLDEN AGE and the conquest of deep space.


    Pi = 3.1446055110296931442782343433718357180924882313508929506596078804047281904892436548476515566340325422595160489765784452235018414818847721014580011238453531659969963123944614330895602447224013851373131501976513250168886718624703787313359434961827623424884419929696155384972370055738355223468907453641698014204369640943817463269453772663395414398903709747924249157889297802333906441767084172268827515380592173997026423023851194242244081992685573437499657987944611238911016107551387207358281657572181883283516336139159023992353694690024845170044516992781985453761660350519720800718970644071409668757828437246633219026822340025407725353821526637922670369853908547616452436921953232107331044735525949802311653660216067204763773809792592558234876801085351187469338952701406443781568048374310664077223404139952343917185562861066240175976669357645765480751311418697916950736513185281927426366978973484884146736468201663051035828968367940082442276210780785802770252790792921943126282608098219773061432750203769…


    1. markcc Post author

      In recent years, every mathematical crackpot seems to make random claims like yours, about how their better math will solve all of the worlds problems and give us the key to free energy.

      So please, explain how, if the value of π is off by less than 1%, correcting that will somehow produce free energy.

      Further, explain to me how, exactly, every company in the world that produces round products hasn’t noticed that they’re using *more* material than their calculations say they should?

      Answer those two, and maybe, just maybe, I’ll spend a couple more minutes looking at your rubbish.

      Until then, stop wasting my time.

      1. Kurt

        It would bring humanity into a new computing era where we could algebraically determine the value of key trigonometric functions. Essentially if you have ever used MatLab you would know the program takes a while to compute things and needs a lot of computing power because it has to run intense calculus and trigonometric functions to arrive at values. By making Pi algebraic as Phi it would simplify all of math.

        1. markcc Post author

          (a) Just because something would be nice doesn’t mean that it must be true. It would be nice if the square root of two was rational. But it isn’t.

          (b) Whether pi is algebraic or not has absolutely no effect whatsoever on the amount of time it takes to run complex computations. We use approximations of pi that are easy to compute with all the time. What makes computations slow is the intrinsic computational complexity of those.

          For one example, to train a deep neural network requires performing massive numbers of training steps, each of which involves a complex back-propagation of information through the multi-layered structure of the network. It is, by the nature of the problem, a complex multi-step computation. Even if you could replace all irrational and transcendental numbers by simple rationals, it wouldn’t change that. How do I know that? Because in computations, we already do that.

          For another example, weather prediction is a highly complex computation. The reason that it’s complex is that the calculations are based on a system of equations for which we have not discovered a closed form (and a closed form may not exist). That means that the only way we can perform the computation is by dividing space into tiny cells, and performing separate computations on each of those cells, and propagating information between them. By sequencing many of those cell-wise computations, we can produce highly accurate weather models. The problem in the computation isn’t that there are some weird numbers like pi – it’s that we need to perform lots and lots of computations.

    2. unknown

      you are absolutely right on this , understanding of the circle would lead humanity to understanding of the universe … you are right that , this brainwash is work of the cabal … i just add and vatican to … but this ratio is wrong …. circle has a finite circumference , that’s why it is wrong … this guy who wrote this article is missing one thing to .. our decimal math has nothing to do with nature and geometry .. and for example he has not knowledge that the most important formulas like C=2pi*r and A=pi*r^ have not proofs in geometry , he is just another brainwashed zombie and doesn’t understand that calculus is based on Pi , not Pi on calculus …. our Pi is wrong,no doubt about that ..but Jain Pi is wrong to … i recommend to watch this ..

  13. Barba truco (@barba_truco)

    Why does a helpless book (the book of jain pi) makes to tremble your archaic mathematics foundation in such a way!?

    Even you wrote rivers of paragraph trying to circularize the book of jain-pi.

    That means that this book is true.

    1. David Starner

      Let’s see: if no one said anything, you could say they were afraid to even respond. If everyone dismissed it tersely, you could say they didn’t bother to understand it. When someone wrote 2500 words on it, including quotes, you call that “rivers of paragraph” and say “that means this book is true”. No matter what, you can disregard what anyone actually said and claim the way it was said proves your case is true.

      Since this is true if no matter what your claim was, and thus could be used to prove anything, it’s obviously an incorrect argument.

    2. PGunn

      My book consists of the statement “You’re an alien from the planet Blarp.”
      That’s short, so it must be true, agreed?
      If so, please send me $77 and I’ll send you a copy.

  14. Pjs

    “π is the ratio of the diameter of a circle to its radius.”

    Might want to fix that typo, unless pi is now 2.

  15. Kaliman

    I can see fear and rage on words against Jain… why ? there is no need… you may not agree… but in a friendly way… that anger just demonstrates fear, or even envy. I really appreciate Jain’s works. And finally.. if he’s wrong…that’s it… he is wrong.. what’s the big deal ? but if he is right …. then I can bet this rage will multiply itself… for some period of time… then it will disappear… ignorance and rage have natural and implicit limits.

    1. markcc Post author

      Why, when I make fun of some idiot, do people insist on seeing it as fear or anger?

      Jain is full of shit, and I explained why. In great detail.

      When you claim something idiotic like “π” isn’t 3.14159…, you’re making a specific, testable claim. That test fails miserably in numerous different ways.

      It’s a failure mathematically, because π isn’t just some arbitrary number: it’s a foundational value in mathematics, whose value can be computed analytically.

      It’s also a failure in a very practical, physical sense. We manufacture round physical objects every day. If the value of π that we use were off by even a miniscule degree, that would have a very clear and measurable effect on the cost of manufacturing everything from cars to soda cans. And yet, no one has ever observed that “error”.

      But yeah, don’t worry about that. Attack the tone of my writing, because you can’t actually criticize the content of my arguments.

      1. Sandgroper

        You have done absolutely the right thing, Mark. If Jain has done all of the things he claims to have done, he has been benefiting financially from, inter alia, teaching his crackpottery to children for money. In other words, he’s a charlatan who has profited from seriously misleading kids. That needs to be exposed. ‘Fear and rage’ have nothing to do with it, although a certain amount of anger would be fully justified in the face of that bit of genuine nastiness. But Sydney seems to be full of charlatans, out of some misguided sense of tolerance. He wouldn’t last 5 minutes where I live, and rightly so.

        One of my favourite (not) Sydney charlatans is the woman who teaches people that they can get all of the nutrition they need from a diet of nothing but raw vegetables, because our closest relatives are gorillas (no, they’re not) and look at how big and strong they are! (And look at just how radically different their digestive systems are from those of anatomically modern humans.) Those who exploit gullible and vulnerable people for financial gain deserve to be held up publicly to ridicule. She wasn’t – her ‘work’ was promoted by government funded news media, paid for by taxpayers.

        On the other site you linked to, I particularly enjoyed the bit about how “Even the dimensions of our teeth are based on phi.” No, they’re not.

      2. bobonthatyouknownothinglooooooooooser

        Maybe worry about your own work, I mean ability to not be able to repeat properly. DERP DERP You Turd Tard “π is the ratio of the diameter of a circle to its radius.” AHAHAAHAHHAHAAHA What do you get paid per character? AHHAHAAHHAAA

  16. allen roberts

    i understand the point of your paper. jain is wrong. but there is a reason to change the value of pi when creating flight trajectories near objects with strong gravitational fields. space itself is compressed by gravity, and over such long distances, that could effect pi, space, distance in calculations. i would argue, though, that until we had earth to moon laser measurements, our miscalculations were very reasonable.

  17. Liddz

    The best method for proving that Golden Pi = 3.144605511029 is the correct value of Pi is to apply the Pythagorean theorem to all the edges of a Kepler right triangle after accepting that the second longest edge length of a Kepler right triangle as the diameter of a circle while the shortest edge length of the Kepler right triangle is equal to 1 quarter of the circle’s circumference that has a diameter equal to the second longest edge length of the Kepler right triangle. Also the hypotenuse of the Kepler right triangle divided by the shortest edge length of the Kepler right triangle produces the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887… : : : :

    1. S Patrick

      The best method to prove that it is NOT the correct value of pi is to compute the area of a unit circle and see if the result converges on your presumed “correct” value. I dare you to try that. I triple-dog dare you to try that. Have at it.

  18. Eratos

    *This is very, very simple to refute by direct experience. This morning, I got up, shaved with an electric razor (3 metal rotors), made myself iced coffee using a moka pot (three round parts, tight fitted, with circular-spiral threading). After breakfast, I packed my backpack and got in my car to drive to the train. (4 metal cylinders with 4 precisely-fitted pistons in the engine, running on four wheels with metal rims, precisely fitted to circular tires, and brakes clamping on circular disks.) I drove to the train station, and got on an electric train (around 200 electric motors on the full train, with circular turbines, driving circular wheels).*
    *All those circles. According to Jain, every one of those circles isn’t the size we think it is. And yet they all fit together perfectly. According to Jain, every one of those circular parts is larger that we think it should be. To focus on one thing, every car engine’s pistons – every one of the millions of pistons created every year by companies around the world – requires more metal to produce than we’d expect. And somehow, in all that time, no one has ever noticed. Or if they’ve noticed, every single person who ever noticed it has never mentioned it!*

    Not that easy to refute.
    To produce all those elements you name here, no one uses π to throw a cylinder or a piston. They all go by the diameter. And of course they will fit each other perfectly, but not because π 3.1415 is correct.

  19. Laurent Martenot

    Thank you for starting this page. What I just read is indeed some crazy stuff, not so much by the math demonstrations on both part, but by the sheer fact that the value of Pi is being challenged today. That really gets me interested.
    I love math, which is magic to me, but my high-school math level is very basic so I cannot comprehend nor refute any of the demonstrations. I will have questions later about the non-Archimedes methods but for now I’d like to participate by entering the conversion at the simple level of manufacturing parts or satellite calculation, which is easier to understand for the average person.
    As pointed at the beginning: “Knowing that π was 3.14159265356979323 was irrelevant in practice, because anything beyond “about 3.1416” was smaller that the errors in measurement.”
    Given this approximation, the difference between the Traditional Pi and the Golden Pi is 3.1416/3.1446 = 0.9990, so we are talking about a mere 0.01% difference.
    My question is: could this difference have an impact when manufacturing parts that are meant to be assembled? Or when launching a missile or satellite? What would the required precision typically be in industries where this difference could have a meaningful impact? If the required precision is lower than 0.01%, then it could very well be that nobody ever noticed.
    I don’t have the answer, nor do I want to push either side, I am simply fascinated by this topic and try to always keep an open mind to fully understand things.

  20. Chad

    I wrote a monte carlo simulator to calculate pi. It makes random numbers and uses the pythagorean theorem to check if it is inside the unit circle. This simulator makes no assumptions about boundaries of the circle or angles.

    After 9 million iterations it clearly converges to 3.141. If this result is wrong then it must mean either the pythagorean theorem is not valid or the computer is square root in some strange way.

    Are there any explanations about how this result might be incorrect?

    import numpy as np
    import math

    _in_circle = 0
    _in_square = 0
    _num_iter = 10000000
    _samples = []

    for _i in range(_num_iter):
    _pos = np.random.random(2)
    _x_pos = _pos[0]
    _y_pos = _pos[1]
    _dist = np.sqrt(_x_pos*_x_pos + _y_pos*_y_pos)

    if(_dist < 1.0):
    _in_circle += 1
    _in_square += 1

    if(_in_square % 400000 == 0):
    _pi_calc = (_in_circle/_in_square)*4
    _samples.append((_i, _pi_calc))
    _error = _pi_calc – math.pi
    print('{}/{} = {} (error={})'.format(_i, _in_circle, _pi_calc, _error))

    399999/314250 = 3.1425 (error=0.0009073464102069551)
    799999/628054 = 3.14027 (error=-0.0013226535897929992)
    1199999/942078 = 3.14026 (error=-0.0013326535897930647)
    7599999/5969700 = 3.141947368421053 (error=0.00035471483125970593)
    7999999/6283567 = 3.1417835 (error=0.00019084641020672422)
    8399999/6597955 = 3.1418833333333334 (error=0.0002906797435402453)
    8799999/6911834 = 3.141742727272727 (error=0.00015007368293407097)
    9199999/7226313 = 3.1418752173913043 (error=0.0002825638015111487)
    9599999/7540154 = 3.1417308333333334 (error=0.00013817974354024543)
    9999999/7854152 = 3.1416608 (error=6.814641020680412e-05)

  21. Chad

    This is a follow-up for my earlier post. I ran the monte carlo simulation again to calculate pi for a 3D sphere and 4D sphere. In both cases it converged to 3.141.

    It is fascinating how the pythagorean theorem is a 2D version of a vector length calculation that can be extended into higher dimensions. I can use completely different equations to calculate pi in higher dimensions and I arrive at the same number.

    It is also fascinating how phi can be used to approximate pi and there might be some practical uses to that.

  22. Harry Lear

    First, an error in the original email on this thread. Pi is not the ratio of a circle’s diameter to its radius. Pi is defined as the ratio of a circle’s diameter to its circumference. Actually Liddz and Jain are correct in that Pi = 4 / sqrt (Phi), where Phi = 1.618033989… . A very easy way to disprove whether Pi = 3.141592654… is to simply physically measure the circumference of a 1 unit diameter circle. Yes it can be done easily by using a CNC machine or a 1 meter Rotary Circle Cutter to cut your choice of medium (metal, hardwood, Foam Board). You will discover that the circumference of a 1 unit diameter (1,000 mm) circle is 3,144 mm and NOT 3,141. I have done this many times and have about 5 different videos on my web site for you to review. After you have accomplished this simple feat, you can then step through my step by step math proofs for the true value of Pi at . Creating the Kepler Triangle and then doing a “special squaring” of its sides will prove that as the circumference of the circle always equals the perimeter of the square, you can set the two equations equal to each other and Pi always falls out as Pi = 4 / sqrt (Phi). The calculus is a good approximation tool but it is not as accurate as the geometric tool. Try it. The physical measurement of Pi disproves all of those proofs that claim Pi = 3.141… . The difference between using Old Pi = 3.141… and True Pi = 3.144… to calculate the circumference of The Voyager I whose diameter from Earth is now about 12.5 billion miles, is 75 million miles off. Nobody cares about using Old Pi for your car tires. But everyone should care about using the correct value of Pi for deep space voyages and for Asteroid Defense and for redefining the new value for the Standard Kilogram (and the Mole, Ampere, and Kelvin) not to mention Planck’s short-h constant which is h / 2 Pi and is wrong at the NIST (National Institute for Standards and Technology). Good luck and if NASA JPL NEO does not change its value of Old Pi to True Pi = 3.144605511… , then you had better hope that NASA’s “near miss” for Asteroid 99942 striking planet Earth is corrected since using true Pi = 3.144605511… may well show that Asteroid 99942 is a direct hit to planet Earth on Apr 13, 2029, or 2036 if it sling shots through Earth’s Gravity Keyhole in 2029.

    1. S Patrick

      Regardless of what the actual numerical value of pi is, any “true” value would and must conform to know identities and theorems. Because of this the cosine and sine value of any “true pi” must be -1 and 0, respectively.

      This can be easily tested by inserting the values for Golden Pi and “Old Pi” into the respective infinite series for the cosine and sine function and determining what values each series converges to. This can be done using any spreadsheet application. I’ve done this with ten decimal place precision using values of 3.1446055110 for Golden Pi and 3.1415926536 for “Old Pi,” using 25 terms for each series.

      For Golden Pi the cosine series converges on -0.9999954613 at 10 terms while the sine series converges on -0.0030128529 also at 10 terms.

      OTOH, when using “Old Pi” the cosine series converges on -1 at 11 terms; the sine series converges on 0 at 10 terms. Both of these results are the expected ones, while the results for Golden Pi are not.

      From this experiment it is therefore logical to conclude two things:
      1) The value of Golden Pi is incorrect when used as a substitute/replacement for “Old Pi;”
      2) The value of “Old Pi” is the actual, TRUE value of pi.

      You’re welcome.

      P.S.- If I could post a screen capture of my work so that everyone could see my work I would. This should be easy enough for anyone involved in this discussion/argument to perform themselves.

  23. Big Rich

    It’s a no brainer Pi is Pi is Pi.

    Just one point of interest I wanted to add…
    Mark says “…got in my car…(4 metal cylinders with 4 precisely-fitted pistons in the engine…”

    Believe it or not the cylinders of an internal combustion engine are NOT true circles.
    It’s hard to believe when we see this perfectly machined cylinder that looks round to the eye, but in reality they are designed to be elliptical.

    This “ovality” is needed because a piston doesn’t just move up and down.
    Due to thrust forces imparted by the crank via the connecting rod, it is getting pushed to one side.
    If it were truly round, in a truly round hole, a piston would bind.
    Or at least wouldn’t move as freely, causing wear and loss of seal.

    Of course this doesn’t mean that they aren’t “precisely-fitted” as Mark said.
    Some engineer designed them to be a very specific ellipse.
    And the formula C = 2 x π x √((a2 + b2) ÷ 2) to determine the circumference of an ellipse of course contains Pi! The REAL Pi. 😉

  24. YouDiDn'tKnowTheAnswerToLifeYaWastOfLifeDouche

    I have an easy way to shut your ignorance up. The field around a polarized magnet is … You guessed it. Well you didn’t. You haven’t a clue in life. OH WOW, now you can extrapolate out the micro-macro. So many useless bean counters who have a lot of nothing to say as they pick their bums all day. You are a total idiot by the way. Nature ‘4’ the WIN!!! It must be fun counting the hairs on your knuckles you monkey.

  25. 99bobster99

    I live by the motto that not everything we are taught/told by the masses is always the truth. We understand very little about how the universe works (myself included, even with all the reading I do on the subject). I try to keep an open mind to everything and don’t simply throw out ideas because they don’t align with the general public’s viewpoint. If it weren’t for Nicolaus Copernicus, we would all still think that the universe revolves around the earth …

  26. Gem

    Why spend time writing rebuts about other people on the internet?? why don’t you write your own books and promote those, Jain speaks with much knowledge and understanding, he speaks with passion and love, his enthusiasm for maths, spirituality and science is catching and that’s why he is well liked and doing so well…. instead of being jealous make the time to do the same, people whom are happy don’t try and bring others down.. So maybe go and love yourself 💗

  27. Terry Moore

    While I agree with most of your article, your refutations are not valid. For example using the wrong value of pi would affect both the piston and the cylinder bore. And anyway, the piston is not designed to fit. Piston rings take up the slack and the slack is important to allow for different expansion of the piston and cylinder as well as to allow for adequate lubrication.

    By the way, we know exactly why the landing site for Apollo 11 was 20km out. The planned area was to rocky for a safe landing and the pilot delayed the final landing until a suitable area arose (nearly running short of fuel in the process).

  28. Rogério PennaRogerio

    “Also, an ex-Engineer from NASA, “Smokey” admitted (via email) that when he was making metal cylinders for this same Mooncraft, finished parts just did not fit perfectly, so an adjusted value for Pi was also implemented. At the time, he thought nothing about it, but after reading an internet article called The True Value of Pi, by Jain 108, he made contact.”

    Probably this Jan idiot was FISHBAITED.
    Conspiracy Theorists believe in any crackpottery that confirms their theories they get by email.

    Check out this episode of SciManDan where they catfish some Flat Earthers, by saying they are Aircraft pilots and they discovered the “truth”

  29. LukiePoole

    Funny enough. All the comments are just talks instead of attempting to try to prove it. Pathetic. Draw a circle and then draw a perpendicular line and mark the intersections A and B. Let the length of the diameter be 1, 16, or 256. Draw a chord left or right side, between 90 degree to 180 degree from point A, and assume it to be Circumference divided by 4. Mark the point as C. Draw a line perpendicular to line AB and crossed point C. Mark the point as D. Repeat the process a bunch of times as many times as you want. Mark all the points E,F,G,H…. Now, use Euclid’s Elements Book VI Proposition 8 and trigonometric identities to get the ratio of each unknown length. You can now calculate all the segments individually. Upon finish calculating, you will reach a biquadratic equation of x^2 + 16x^2 = 256, or x^2/16 + x^2 = 16 or x^2/256 + x^2/16 = 1. The root is exactly 4/sqrt phi which is equal to the correct value of pi when you let x=pi.

    THIS, IS WHY you don’t approximate anything. Approximation ALWAYS give the WRONG value. Euler’s constant which is APPROXIMATED is wrong. Archimedes Pi which is APPROXIMATED is wrong. The worst assumption is to assume the second lower limit of the range of the true lower limit of pi is magically the true upper limit of the range of the exact value of pi. Archimedes method of exhaustion has NO approximation from outside the circle. It is ALWAYS inside the circle. Using straight edge to approximate curve is WRONG. You’re not suppose to do that. You’re suppose to find pi using biquadratic equation. THIS is how you’re suppose to do it and not approximate shit.

    1. S. Patrick

      “Upon finish calculating, you will reach a biquadratic equation of x^2 + 16x^2 = 256, or x^2/16 + x^2 = 16 or x^2/256 + x^2/16 = 1. The root is exactly 4/sqrt phi…”

      Since the first two terms of the polynomial are of the same order they can be added to yield the equation 17x^2 = 256. The two roots of this equation are (obviously) ±√(256/17), which when expressed as decimal numbers are ±3.88057. The positive root is clearly not equal to the value which you claim it to be, 4/√phi or 3.14460551103…

      If your basic arithmetic is this flawed then how can anything you post be regarded any credibility?

  30. blademan9999

    I made this code in MATLAB
    for I=1:t;
    for J=1:t;
    if I^2+J^2<t^2;
    for I=0:t-1;
    for J=0:t-1;
    if I^2+J^2<t^2;
    fprintf('%.6f %.6,b,c);

    I got
    3.141190 3.141990
    so in otherwords 3.141190<pi<3.141990


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