Centripetal Acceleration

Abstract: Mathis proves that even high school math (The Pythagorean Theorem), is far beyond his reach.

This paper will analyze the following article and examine the authors claim that the centripetal acceleration is equal to half the radius (a = r/2):

Clarification of the equation a = v2/r

In addition, this paper will also bring to light, for the first time, the heretofore overlooked assertion that the circumference of a circle is equal to 4r:

“The equation a = r/2 gives us a distance of acceleration over 1/8th of the orbit, so the total distance of acceleration over the entire orbit is 4r.” — Miles Mathis

We’ll examine acceleration in a moment, but first let’s discuss the circumference. Those who have followed the pi=4 controversy have witnessed Mathis fiercely defend his pet theory (simply stated as the circumference of a circle equals 8r). With that in mind, take a look at this perplexing quote from his article:

“Since the Moon is orbiting at 384,400 km, the total distance of acceleration over the orbit is 4 times that…” — Miles Mathis

Four times the radius? In case you think this is merely a simple mistake or typo, well that’s just not the case. Mathis does indeed require the circumference to be 4r (see analysis below), otherwise his acceleration equation is wrong. But he also requires the circumference to be 8r, otherwise the pi=4 theory is wrong. Oh, and let us not forget, there is also a static value (2πr) for the circumference too. So the circumference must take on three different values to support his half-wit theories.

As it turns out, this is not a new or recent claim; its actually been there all along. Mathis makes this same assertion in his infamous article “The Extinction of Pi“; that’s right, he claims the circumference is 4r in that article too. In fact, in that single article alone he claims the circumference is 4r, 8r, and 2πr; all in the same paper no less.

Now let’s examine the preposterous claim that a = r/2. According to Mathis, our current equation for centripetal acceleration is wrong. The equation commonly used today is this one: \space a = v^2/r. \space But Mathis claims this equation is off by half; that is, the equation should be: \space a = v^2/2r.

In his article, Mathis argues that if v = r, the acceleration will reduce to r/2; he even provides a geometrical proof for this hogwash. And it is this geometrical proof that will be examined in this paper. In a future paper we will look at his idiotic claim that \space a = v^2/2r (yes, that’s wrong too). But for now, let’s start by knocking down this dopey and lamebrain assertion that a = r/2. Here is a quote from Mathis as he makes a clumsy and misguided attempt to prove, using a circle and a triangle, that a = r/2:

“With all this under our belts, we are now in a position to see that we may assign the acceleration ‘a’ to the line segment BC. Furthermore, if \space a = v^2/2r, and AB = r, then r = v, and a = r/2. Consulting the diagram, that is also 2BC = CO. What this means is that we have a new way to find a centripetal acceleration, currently called gravity. The equation a = r/2 gives us a distance of acceleration over 1/8th of the orbit, so the total distance of acceleration over the entire orbit is 4r.” — Miles Mathis (See Figure 1)

Figure 1

r = v = AB = AO = CO = 2BC
a =v^2/2r = r^2/2r = r/2 = BC

So that’s the analysis as presented by Mathis. There’s just one colossal problem though, Mathis is flat-out wrong. We can apply the pythagorean theorem to the above triangle to check the accuracy of his analysis, thus proving he’s wrong. According to Mathis, a = r/2. So let’s crunch the numbers and see what we get:
(BC + CO)^2 = (AO)^2 + (AB)^2
(a+r)^2 = r^2 + v^2 = r^2 + r^2
(a+r)^2 = 2r^2
a+r = \sqrt{2} * r
a = (\sqrt{2} * r) - r
a = (\sqrt{2} - 1)r
a \approx 0.414r

As you can clearly see, the centripetal acceleration does not equal r/2. Even when using Mathis’ own diagram and his foolhardy assertions, \space a \neq r/2.

In closing, this paper has shown that Mathis’ theories require a total of three distinct values for the circumference of a circle (4r, 8r, and 2πr). Further, it was also shown that his geometrical analysis for the centripetal acceleration is plagued with errors and “slippery math”.

The Extinction of Pi
A Correction To The Equation a = v2/r
Clarification of the equation a = v2/r

Note: This paper was last revised on 04/23/2013


36 thoughts on “Centripetal Acceleration

  1. “The equation a = r/2 gives us a distance of acceleration over 1/8th of the orbit, so the total distance of acceleration over the entire orbit is 4r.” — Miles Mathis

    See my reply to pi=4

    Since the orbit is a cycloid with an arc length = 8r
    the total distance of acceleration is 4r.

    The key to all of this is Mathis suckered us in with the statement pi=4. This was done to draw attention to what he has to say and it worked. The man is no crackpot and neither are his ideas.

    Straight line motion is depicted by a circle = 2 pi r
    Circular motion (Orbit) is depicted by a cycloid = 8r = 2*4*r
    These two expression have nothing to do with each other but if I want to get someone’s dander up I say” look for an orbit pi=4″ and the shouting starts!
    We have intuitively accepted an orbit as being a circle without giving it a second thought, well it isn’t. its a cycloid.

    • All orbits are in the shape of an ellipse — this was first discovered by Kepler, and the data confirms this. All of Kepler’s laws would be invalid if the orbits were cycloids. Mathis is wrong again (which is no big surprise).

        • No, Mathis is just spouting more of his crackpottery. All naturally occurring orbits are elliptical. Only man made orbits, which require a periodic readjustment via thrusters, deviate from an elliptical path.

  2. Hi Steve,

    You are the one making the mistake of applying kids’ math to a real world problem. Just because you see a triangle you blindly apply Pythagoras. However Mathis diagrams velocities and accelerations here. Two velocities added over the same time interval equate to an acceleration. If that is too hard to follow I would suggest starting with one of his simpler papers.


    • You can spin and hand wave to your heart’s content. But the facts are in: Mathis can’t even do high school math. Ouch! Perhaps you can get him enrolled in a remedial math class; but that’s likely to be way over his head too. Better yet, just leave him alone and let him play with his coloring book and crayons. Yeah, he’s the New Leonardo.

      • Thanks for your detailed and pointless answer. I guess you had to spend a long time in the educational system to lose all capability for independent critical thought.

    • People like Mathis and yourself (assuming that you are not one and the same) do not even comprehend the true depth of their ignorance. To some extent, this is forgiveable; students are taught on a ‘need-to-know’ basis and, when someone with a much deeper understanding of a topic comes along, they often react with hostility and think that the expert is a crackpot. Try telling the average electrical engineer that a simple square circuit must have static charges at its corners in order to satisfy physical laws. He will laugh. However, their presence can be demonstrated experimentally. Similarly, if we tell some of the critics here that an object travelling in a straight line has angular momentum they will think that they have another Mathis on their hands. Nevertheless, it is true. Denying it leads to a baffling paradox. So our point is that Mathis is not only below the average level of understanding, he is even further below the very highest level of understanding!

      • ”People like Mathis and yourself (assuming that you are not one and the same)…”

        That issue comes up all the time. Is Oostdijk a Mathis sockpuppet? I don’t know, and can’t say for sure. But everytime the name Mathis is mentioned, you can count on Oostdijk to rush to his defense. Why is that? He even defends the pi=4 theory, for crying out loud. Are these two madly in love? Is it hero worship? Or do they just happen to share identical mental afflictions? Whatever the case, there is an unseemly creepiness to their association; it’s weird behavior.

    • I suspect that Mathis already knows there are problems with his theories. But I can’t say for sure whether he is aware of the specific errors that are mentioned at this blog. Don’t know.

        • Can’t say I’m surprised. Mathis has never shown any interest at all in getting it right; he’s more concerned with keeping the web kitty well-fed. Besides, why tamper with a perfect track record? He’s been habitually wrong all along; why change course now?

        • Not interested… are you f-ing kidding me… that tells me all I need to know about Mr Mathis… he’s not a scientist… he’s a hack.

    • No, I don’t have any plans to analyze the Mathis charge field. I only point out his obvious errors and mistakes that relate to well established and tested science. The charge field is a pure Mathis invention; I have nothing to compare it to, or any way of testing it. So for the time being, I will probably just steer clear of it altogether. Same thing with stacked-spins; just another absurd Mathis fantasy.

    • It’d be kind of like analyzing someone’s uninformed opinion on the debt crisis — someone who thinks that debt is something other than what it is, thinks a crisis is something other than what it is, and considers the economy a mass conspiracy anyway.

    • ”I think his insights into the possible connections between charge and mass are particularly remarkable but I don’t agree with how the unified idea is subsequently developed.”
      – Dr. Tahir Yaqoob, NASA Astrophysicist (September 3, 2012)

  3. How does Miles arrive at 2BC = CO? By eyeballing the diagram?

    What r does one use for an elliptical orbit, which is to say all orbits?

    If a = r/2 is a proper equation, what units are used there? An example, with units, would have been helpful.

    • Well, that’s two additional errors that Mathis made in his article.

      1) Mathis is actually describing uniform circular motion, not gravitational orbits. So his repeated references to gravity and orbits are technically inaccurate; gravitational orbits are always elliptical (Kepler’s first law).

      2) The units are all wrong, and don’t match up. If r = v, then the units for a = r/2 would have to be meters per second; which is a velocity, not an acceleration. Just that alone sinks his theory.

      And finally, 2BC = CO must have come from merely eyeballing the diagram. It’s clear that Mathis never actually preformed the mathematics; which is truly funny when you consider this quote, with reference to Isaac Newton:

      “I am analyzing his geometry with greater rigor than even he achieved.” — Miles Mathis

      The eyeballing method of analysis? Good grief!

      • Gosh, even Newton had a ruler! I don’t know about anyone else, but 2BC = CO doesn’t work when I measure it out on my monitor screen. Maybe Miles has a special display for mathematicians more rigorous than we could ever hope to be.

    • I have given it my best effort, but can’t seem to get under his skin the way you can. I don’t know how you managed to do it (maybe it’s just the clever way you phrase things), but you have unquestionably struck a raw nerve. Mathis refers to you by name, and even writes articles about you:

      “The humble Michael Norris, full of opinion, finds me lacking in humility. Norris would be better off showing precisely where I am wrong. That appears to be beyond him. … The protectors of the status quo like Norris have always used the same tactics to suppress new ideas. …Norris’ comments are just another example of this control: he appears to think I don’t have the right to say what I think.” – Miles Mathis (My Opposition)

      Reference: Mathis-Watch

      • If only he had remained engaged, there might actually be an exchange of ideas. I think he’s adopted a “don’t feed the trolls” attitude at this point, but as long as he keeps supposin’, we’ll keep calling him out on it.

        Speaking of trolls, I had a thought about Miles Mathis. For a long time I’ve wondered if he believed anything that he wrote. Stuff like the coriolis article is so disingenuous, it’s hard to believe there’s well-meaning intent behind it. Is he a total charlatan, or merely misguided and delusional?

        Then I realized, it’s probably both. As a classic and consistent case of narcissistic personality disorder, he truly believes that Sandy Hook was a conspiracy and that “big science” is a conspiracy, too. So, he’s trying to one-up the conspirators, by intentionally fudging and finessing and hand-waving in exactly the fashion he sees real physicists and mathematicians doing. What’s good for Alan Guth is good for the gander, he figures. And actually, this kind of mathematical flummoxing does legitimately happen occasionally; see Joy Christian’s recent attempt to disprove Bell’s theorem. But if it didn’t work for Christian — his math has been widely discredited — it’s not going to work for our painter/model friend and his poor grasp of 9th-grade geometrical proof, is it?

      • Incidentally, if you aren’t familiar with Joy Christian, look into him. Boy is he a piece of work. Imagine a Miles Mathis who actually has a Ph.D., and once had associations with Oxford and the Perimeter Institute, but who — after self-publishing a book claiming to overthrow a basic theorem — now finds his way onto every blog discussing his work, always to call his detractors mathematically incompetent, liars, slanderers, etc. He and his several fanboys (who also gave his book five stars on Amazon, of course) are all over the discussion pages for the Wikipedia Bell’s theorem article as well. His disproof has never passed peer review, after years of arxiv uploads, but I wouldn’t be surprised if he found a way to comment here!

      • We used to be able to drive Myron Evans to the point of setting police on us, but now we seem to be unable to rile him. One of our number has been described as ‘being able to start a fight in a Christian Science reading-room … between Quakers!’, and he has a trick or three up his sleeve, so …

    • There seems to be an entire industry devoted to pseudoscience; and business is thriving. Mathis, for example, is preparing his third book for publication.

      I haven’t read Joy Christian’s book yet, but he appears to be up to all the same shenanigans as Mathis. The over abundance of glowing 5-star reviews for a fringe theory, strongly suggest that at least a few, if not all, were self-written (the Mathis/Oostdijk routine).

      Before you can even finish discrediting one crackpot, another has popped-up. Now some are obvious hoaxsters (Richard Hoagland, Graham Hancock, Erich Von Daniken, et al). But oddly enough, a few of these crackpots have actual scientific credentials (Joy Christian, Myron Evans, Jeremy Dunning-Davies, et al).

      I’m overwhelmed by the growing number of charlatans with all their books, youtube videos, websites, and newsletters. Who can keep up?

      Reference: Disproof of Bell’s Theorem

      • “Mr Norris, Why are you making slanderous personal claims about me… Please give me one reason why I should not seek legal action against you for making such a libellous claim.” — Joy Christian (Feb 1, 2013)

        You have once again struck a raw nerve. As I mentioned before, you seem to have a unique talent for pissing-off crackpots. Not even Mathis, to his credit, has ever threatened legal action over an unfavorable book review. To call Joy Christian thin-skinned would be a gross understatement. Legal action? Utterly ridiculous; in fact, delusional. Anyway, we offically have the birth of a new crackpot watch.

        Reference: Joyless-Watch

        • We think that it is important to recognise that scientific qualifications are no guide to sanity or intelligence. The history of science and technology tends to be ‘sanitised’, and the wrong ideas and outlandish private lives of now-famous scientists have long been swept under the carpet (together with suspicions of rape and attempted murder). The problem these days is that crackpot ideas get far greater attention because of the general dumbing-down of education.

      • Yes, Miles has the restraint of ten men compared to Dr. Christian. Me, I couldn’t resist leaving a follow-up comment on the review. It would be nice if Christian had a sense of humor, but did you see his picture on his LinkedIn page? A more joy-less person I have never seen.

        • Michael,

          I’ve added a couple of comments to your review of Joy’s book. But Amazon is a pretty crap discussion site. Barely worth the effort.

          You’ve realized his primary vulnerability — apart of course from being plain wrong — is his claim to official status at Oxford. Like you I don’t think he has any. And this link is to a new blog site he’s setting up … “embarrassing” doesn’t begin to describe the bare-assed bogosity, the empty megalomania, the rank stench of flop sweat.


          Sascha Vongehr, who strung him along for quite a while, believes that on some level below waking consciousness JC knows he’s wrong but it’s too late now. How much does that matter?

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