When Pi is not 3.14 – by PBS America

Posted: March 28, 2020 by oldbrew in Maths

A simple practical demo here…

Wikipedia explains: The arc length of the cycloid.

[Credit: Zorgit @ Wikipedia]

Taxicab geometry – Wikipedia

  1. When I was watching the first video I recalled Miles Mathis’s paper then lo and behold there was a demonstration of Miles Mathis’s proposition in the 2nd video. I think one can describe Miles as a polymath but more than that he is a talented artist. Another who is excellent at maths is Prof Claes Johnson (https://claesjohnson.blogspot.com/) but he has truly made a contribution to fluid dynamics. He was award the Prandtl medal but turned it down as he was not allowed to say that Prandtl was wrong. He thoughts on the 2nd law of Thermodynamics is worth noting as it shoots down backradiation which can not exist.

  2. Miles has added to his Pi papers here PAPER UPDATE, 12/10/2012. The Extinction of Pi. In an important update, I show that my pi=4 metric is basically equivalent to Hilbert’s Taxicab or Manhattan metric, where pi also equals 4. This should silence my critics on this issue.
    Here is one of Miles early papers on Einstein
    NEW PAPER 5/22/2011. Einstein was Right: modern physicists and reporters are just party people. New mainstream “confirmation” of dark matter and a dark universe is raw speculation, based on bad math and theory.
    It appears the links are not coming up so you may have to go to his web site here http://milesmathis.com/index.html and then click on updates.to find the date and the paper.

  3. oldbrew says:

    cement – open the second video and click on ‘SHOW MORE’ under the video itself, below ‘Extraordinary Experiments’. The Mathis links are there.
    – – –
    The first video shows why Pi = 3.14~ is the *minimum* value of Pi. The second video mirrors the cycloid: imagine a bike wheel, where a point at the centre of the wheel (hub) moves in a horizontal line relative to flat ground whereas a point on the rim has a cycloid motion. Where motion is involved, the maths changes.

    If Pi must be a constant, some other name should be given to its non-constant cousins. Wikipedia confuses things by using a rolling wheel in its explanation of Pi as a constant. I call this animation out as a fake, or at least misleading. It appears to show the amount of movement of the blue point but in fact shows the movement of the centre of the wheel. 🤔


  4. Hifast says:

    The second video is so filled with errors, and the experimenter’s comments to critiques so filled with arrogance and hubris, it’s not worth watching.

  5. oldbrew says:

    Hifast – feel free to name one or more of the errors. Assertion isn’t enough.

  6. Hifast says:

    2nd video:

    The experimenter correctly demonstrates each ball is initially traveling at the same speed through the timing gates.

    However after that, all he has demonstrated is that the ball traveling in the circle decelerates and travels about 55 to 59 cm in the same amount of time the other ball travels linearly 70.6 cm. The video does not show that the outstretched circular tubing length matches the linear tubing length. I submit they are not the same length. I estimate the circular path is about 59 cm using the inner-outer diameter of the tubing 18.8…then again, the tubing is further shortened by the fact the diameter is spirals inward at the point of origin.

    The experimenter measures (imprecisely and inaccurately) the diameter of his circle as 17.6cm, yielding a circumference of about 55.3 cm. I estimate the circumference of a circle traveled by the ball being about 59 cm (using the outer side of the inner diameter of the tubing).

    The axis of rolling rotation of the ball in the circle changes from the horizontal to the near vertical. Frictional forces on the ball from the tubing effect that change. That is, the angular velocity vector vector is initially parallel to the table pointing to the top of the screen. That vector changes to pointing nearly perpendicularly downward toward the table due to the frictional forces exerted by the tubing.

  7. Hifast says:

    2nd video (continued)

    Frictional forces from the tubing continue to be exerted on the ball to change its translational velocity vector from that of the original (to the right of the screen) anti-clockwise around full circle.

    Additionally, because the circular segment of the tubing is slightly crimped, the inner diameter of the circular tubing is less than the linear tubing creating more aerodynamic damming ahead of the ball in the circle. More deceleration forces on the ball.

  8. oldbrew says:

    If the ball is decelerating e.g. due to friction, it should take longer to complete each successive quarter segment, but it doesn’t.

  9. Hifast says:

    One ball travels its circle, about 59 cm, in the same amount of time the other travels linearly 70.6 cm.

  10. oldbrew says:

    If you measure one of the two lines forming the yellow ‘X’ inside the tube circle, and multiply by Pi, it equals the length from the ‘O’ to the Pi symbol on the straight length of tubing, which seems fair?

    – – –
    One ball travels its circle, about 59 cm, in the same amount of time the other travels linearly 70.6 cm.
    That’s the point of the experiment – the ratio should be Pi:4. Again, the velocity within the circular tube is constant and we can see that.

  11. E.M.Smith says:

    Key points from video one:

    “Math is not restricted to reality”. All those non-Euclidian values of a hypotheticsl Pi are not real.

    Playing with distance via definition warping is a non-real lie of sorts. The kind of stupid human game math folks love to play. Don’t let that confuse reality. It’s just a parlor word trick at heart.

    It was that kind of silly stuff that helped me decide to not be a math major (despite excellent test scores and a math award / scholorship out of high school). Some few of them become useful (imaginary number math) while many are just silly.

    Per the second video:

    Unless the tubing lenght is shown to be identical, all you have is a tuned fraud.

    The accelleration needed to curve the path must be powered from the energy in the curving ball.

    Added rolling resistance will result from that added force against the tubing.

    Looks to me like all he shows is that the ball slows in the curved section, but not so much you notice in a video, and tuning the lengths can make it a 4.

  12. oldbrew says:

    EMS – Added rolling resistance will result from that added force against the tubing.

    Again, we observe that there’s no reduction in velocity from one curved segment to the next, so no build-up of resistance. The lengths of tubing can be measured and calculated from the photo provided above or from the video.

    All the info is provided for a repeatable experiment, as the presenter says.

  13. oldbrew says:

    Miles Mathis has a paper on the second video (the experiment) and goes into plenty of explanatory detail: http://milesmathis.com/pi7.pdf

    I predict the main response to the video will be that the ball in the curve is feeling more friction. However, it is clear at a glance this is not the case. To start with, the ball in the curve would have to be feeling over 20% more friction than the straight ball. Again, the difference between 3.14 and 4 is not marginal. It is huge. There is no way to account for a difference that large with a difference in friction. Plus, if friction were the cause, the ball in the curve should be slowing down as it progresses around the curve. Friction is of course cumulative, so we would expect a ball feeling an excess 21% of friction to be going slower in the fourth quadrant of the circle than in the first. But we see with our own eyes that isn’t true. Steven marks all four quarter points in the circle, and the ball hits them all perfectly in sync with the straight ball. If the ball in the curve were feeling more friction, we would expect it to hit the ¾ mark and final mark noticeably late compared to the ¼ mark. It doesn’t. This indicates very strongly that neither friction nor any other cumulative effect in the curve is causing the difference. The ball in the curve is NOT slowing relative to the straight ball. This should look as curious to you as pi being 4. Given current theory, it is just as mysterious.

    Also consider this. If you are arguing there is more friction in the circle because the tube is curved, ask yourself this: What are the odds that the extra friction in the circle would be exactly the amount to fill the difference between pi and 4?

  14. Stuart Brown says:

    Friends, seriously off topic but here in the UK it is twenty minutes to Earth Hour. Don’t forget to turn on your cooker, washing machine, dishwasher and do a bit of arc welding.

    Last year we managed to raise the demand at 8:30. Let’s do it again!

  15. Stuart Brown says:

    And they’re off! Peak demand in the UK was 33544MW at 17:05. It dropped more or less linearly until 20:25, then there is a slight dip at 20:30 before joining the line again at 20:35. (BM Reports)

    The National Grid rolling demand shows a slight rise between 20:30 and 20:31 however, so well done folks! https://extranet.nationalgrid.com/RealTime if you are quick – shows last 60 mins

  16. chickenhawk says:

    I watched the first video. I’m probably not qualified to respond here, but it seemed that pi equals 3.14 for a circle, but not 3.14 when the circle looks like a square.

    In the second video, I was hoping to see the tubes side by side before bending the first one into a circle. I would like to see that length demonstrated.

  17. Fast says:

    This just shows that velocity is a vector quantity and direction matters.

  18. ivan says:

    Somehow I get the feeling we are talking about two different things. Pi=3.14 applies to the relationship between parts of a circle. Rolling something along the ground, down a ‘non precision’ tube are not the same especially from a practical engineering viewpoint.

    Running ball bearings down a plastic tube, especially one that is curved, does not take into consideration air pressure build up slowing. For that experiment to be valid the tubes would have to be evacuated and made from precision glass with a ground and polished bore.

  19. ivan says:

    I should have added the fact that there would need to be a close spaced optical speed measuring system set to measure not only the start but the actual speeds of the balls down the tubes.

  20. Oldbrew, above I gave a link to Miles web site so they could look up the papers on pi. Below I have copied the abstract of the paper I mentioned
    Abstract: I show that in all kinematic situations, π is 4. For all those going ballistic over my title, I repeat and stress that this paper applies to kinematic situations, not to static or geometric situations. I am analyzing the equivalent of an orbit, which is caused by motion and includes the time variable. In that situation, π becomes 4. I will also remind you this is not just a theory: it has been indicated by many mainstream experiments, including rocketry tests and quantum experiments (see links below). It has also now been proven by my own experiments (see link below).

    Miles has some interesting theories. I do not agree with all. He is indicating that the next (or present ie 25) sunspot cycle will be greater (from his theory of charge field and planet alignment) when many are predicting that it will be less and the potential for cooling at least like the 1970’s. (note in the winter of 1969-1970 I saw the Niagara Falls frozen solid, we were living besides Lake Ontario and could walk out on ice about 200m, the St Lawrence River was frozen across at Quebec City). Time will tell. I thought the SOI would by now be in the positive area (ie moving away from El Nino) but it is still negative with the 30d average at -6.05. On the other had we had double (520mm) average rainfall in February and hitting average rain (around 260mm) this month.

  21. oldbrew says:

    Both balls are experiencing the same test conditions. What has to be explained is why the ratio of distance covered is pi:4 in both tests. It can’t be due to deceleration by friction *during* the loop because the time between each quarter segment matches the markers of the straight ball, whereas friction accumulates.

    It appears [sic] that the curving ball loses a specific amount of its momentum at the start of the loop, i.e. as it diverges from the straight ball. Maybe it has to do a specific amount of extra work to make progress relative to the straight ball, because it wants to go in a straight line but external forces don’t allow it to – a bit like a planetary orbit 😎

    Note that with the cycloid demo the ratio of distance covered by the centre point and the outer point is also pi:4. Wikipedia has an arc length equation (link in post) for that with a result of 8 radii = 4 diameters, confirmed here:

    Length of an arch: 8R
    The cycloid can also be defined as the trajectory of a movement composed of a uniform linear motion and a uniform circular motion of equal speed
    [bold added]

    The link has animations of the cycloid. In this one, the ratio of the circle’s diameter to the blue base line is 1:Pi.

  22. “Both balls are experiencing the same test conditions” but they are not, since one ball is constantly changing direction, whereas the other is not.

    [reply] that’s the whole point of the experiment

  23. EternalOptimist says:

    A body will continue in a state of rest or uniform motion in a straight line unless it is forced to change by the action upon it of an external force.

    I think there is a force and its not friction. the force is a vector and does not increment so the speed of the ball in the loop is constant


    when the balls reach the pi mark they have travelled the same distance in different time, that means they must be travelling at different speeds

  24. oldbrew says:

    when the balls reach the pi mark they have travelled the same distance in different time, that means they must be travelling at different speeds

    Of course. The ratio of their speeds after passing the ‘O’ point is pi:4, which is a repeatable result given the same initial conditions of the essential factors.

  25. EternalOptimist says:

    then the question is why has the speed of the balls changed and not whether pi has changed.

    is it april 1st yet

    or am i thick.

    ok im thick

  26. JB says:

    The simplest answer is when everyone has had their share and it reduces to zero.

  27. oldbrew says:

    Why has the speed of the looping ball changed? Non-technical answer: because curved motion is not equivalent to straight line motion.

    Look at the setup: the four marked segments of the straight tube are *1 diameter* each.

    Therefore if each segment was cut out and put next to the circular tube it would form a square whose sides touch the circle.

    The ratio of the perimeters of the circle and square is pi:4, the same as the ratio of the speeds of the two balls in the experiment (after they pass the ‘O’ point). So we have a formula for the difference between circular and straight line motion where conditions are equal. [‘Conditions’ means: tubes, balls, any other materials used, atmosphere, etc.]

    Each side of the square is 2 radii long, total 8 – which matches the 8r in the cycloid formula.
    – – –
    Uniform Circular Motion
    Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object’s motion, the velocity vector is directed tangent to the circle as well. [bold added]


    The sides of the square shown above are also tangent to the circle. Imagine the circle as fixed with the square rotating, and with the ball constantly at one of the four moving points of contact [of the square with the circle]. When the ball has completed one loop, the square has returned to its original position.

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