**An Orange Preface: **

*"This is important because this is precisely what we think π is telling us. We think it is telling us that the circumference is 3.14 times the diameter. But it isn’t. About real circles, π is telling us nothing. About abstract circles, π is telling us that if the circumference were a straight line, it would be π times the diameter. But since the circumference is not a straight line, π is telling us nothing useful there either. In reality, π is precisely as useful as some numerical relationship between apples and oranges, one that began with the postulate “if oranges were apples” and finds “then oranges would be π times redder than they are.” All very edifying I am sure, but since oranges are not apples, any number found is just a ghost."*

*Miles Mathis, "The Extinction of π"*

### This is a response to this article by Miles Mathis:

"The Cycloid and the Kinematic Circumference "

**Mr. Mathis would seem to be confusing apples and oranges**

"*Let us go back to the wheel rolling on the ground, that we started with. Notice that when we draw the normal circumference on the ground with the wheel, we aren't following any one point. No point on the wheel is moving along that line, and no point on the earth is, either. We are told we are letting points on the circle match points on the ground, and most people accept that, since it seems to make sense. But it cannot be demonstrated and never has been. Yes, you can paint lines on the ground with wet paint, roll the wheel over them—getting the paint on the wheel —and then claim that the distance between lines on the ground and on the wheel is the same, but it doesn't prove anything of the sort. *"

*Miles Mathis, "The Cycloid and the Kinematic Circumference "*

**Never Demonstrated? Really?**

Nothing like confusing the real world path with the motion an imagined point along an imagined arc makes. Here Mr. Mathis confuses geometry with the kinematics of an imagined point. It is as simple as that. There is nothing more to explain and nothing more to this particular online "stage illusion style, mental magic trick". Please notice the bait and switch mental gameplay at work here. Pi is clearly a demonstrably valid value of being 3.14..... it is not 4. Miles Mathis keeps insisting that it is and that he can demonstrate it is. The thing is, he can demonstrate no such thing. In fact I'd say his insistence on sticking to this illogical position is telling, but that is something for you, "dear reader" to decide, if you so choose to decide anything at all. As we can see (and demonstrate in real life) Pi is 3.14... and not 4.

### Mr. Mathis seems to come right and and tell us that he is pulling our legs. This reads like some kind of brainteasing style fun to me. The logical fallacies seem obvious to me, but hey your results might vary. It seems to me this is just someone confusing reality with fantasy.

**Miles Mathis confuses the subject of geometry with the subject of kinematics. **

**Please Keep Your Eye On The Ball**

Please keep you eyes on the blue diamond, we shall call this diamond point (A). It proves Mr. Mathis is incorrect in his underlying assumptions.

image source: http://imgur.com/gallery/YmIH7

**Two Videos Below Demonstrate The Same Thing With Real World Objects**

*"This is important because this is precisely what we think π is telling us. We think it is telling us that the circumference is 3.14 times the diameter. But it isn’t. About real circles, π is telling us nothing. About abstract circles, π is telling us that if the circumference were a straight line, it would be π times the diameter. But since the circumference is not a straight line, π is telling us nothing useful there either. In reality, π is precisely as useful as some numerical relationship between apples and oranges, one that began with the postulate “if oranges were apples” and finds “then oranges would be π times redder than they are.” All very edifying I am sure, but since oranges are not apples, any number found is just a ghost."*

*Miles Mathis, "The Extinction of π"*

**What is the value for that point? Is it not 3.14.... as advertised?**

### What does this misleading illustration tell us?

The illustration below is from the Miles Mathis paper. Here we have a very confusing and obviously misleading illustration of this problem. Compare to the above gif sequence. Which is the better communicated graphic representation of Pi and why? Do you really think Pi is anything but the value advertised? Do you not notice how Miles Mathis confuses the path itself with the motion of the wheel in an illogical manner? The arc and point he is referring to are simply not relevant to anything at all; or can you explain how they are?. This illustration is an example of terrible visual communication, by the way, no offense intended to the fine artist who crafted this bit of online mathematical propaganda, but it does not illustrate his idea in any kind of clearly communicated manner. The arc has nothing to do with any real measure of kinematics or geometry.

**This red arc is not a path that the wheel follows. It is an irrelevant artifact of the imagination.**

### What does this apple red "herring" have to do with modeling the motion of the wheel or even an orbit?

Is that where center of mass is supposed to be? Of course not. This arc seems quite irrelevant to the task of modeling orbits or rolling wheels.

**Pi=3.14... Moving Ghosted Goal Posts?**

*"If you roll a wheel on the ground one full rotation, it will mark off a path on the ground that is 2πr in length, as most people know. That length has been assigned to the circumference of the circle or wheel, which assignment is correct as far as it goes. My papers have not questioned that. However, if you do the same thing but follow the motion of a given point on the wheel (point A in the diagram above, for instance), it draws the red curve. That is called the cycloid. Obviously, the red curve is not the same length as the line on the ground. It is considerably longer, being 8r in length. That is 21% longer than the circumference."*

*Miles Mathis, "The Cycloid and the Kinematic Circumference, 2016*

**VS**

*"This is important because this is precisely what we think π is telling us. We think it is telling us that the circumference is 3.14 times the diameter. But it isn’t. About real circles, π is telling us nothing. About abstract circles, π is telling us that if the circumference were a straight line, it would be π times the diameter. But since the circumference is not a straight line, π is telling us nothing useful there either. In reality, π is precisely as useful as some numerical relationship between apples and oranges, one that began with the postulate “if oranges were apples” and finds “then oranges would be π times redder than they are.” All very edifying I am sure, but since oranges are not apples, any number found is just a ghost."*

*Miles Mathis, "The Extinction of π", 2008*

### What is he talking about? We can model a wheel rolling with traditional value for Pi.

**How Many Radii Can You Count?**

### Where are the eight radii Mr. Mathis refers to?

How is Miles Mathis measuring this arc that is not even a half a circle? Is that arc actually part of a circle or part of an ellipse? What does Mr. Mathis mean by his use of eight radii? Does he mention that? Does it matter? He has marked off the radius of the circle and yet he does not visually apply this measure in any kind of comparative way.

This red arc has no bearing on the motion of the wheel or the path the wheel takes. It seems very irrelevant to modeling how a wheel rolls. In fact this is not how anyone would model a wheel rolling with math. Computer 3d animation programs demonstrate this basic truth.

**Where Are The Eight Radii Hidden?**

*"Obviously, the red curve is not the same length as the line on the ground."*

*"It is considerably longer, being 8r in length. That is 21% longer than the circumference."*

### What does this imagined curve have anything to do with mathematically modeling the rolling wheel?

**Stating It In Typography On A Screen Is Not A Magic Spell: Miles Mathis Is Demonstrably Wrong**

*"Notice that when we draw the normal circumference on the ground with the wheel, we aren't following any one point. No point on the wheel is moving along that line, and no point on the earth is, either. We are told we are letting points on the circle match points on the ground, and most people accept that, since it seems to make sense. But it cannot be demonstrated and never has been. Yes, you can paint lines on the ground with wet paint, roll the wheel over them—getting the paint on the wheel —and then claim that the distance between lines on the ground and on the wheel is the same, but it doesn't prove anything of the sort. All it proves is that curve and the line match up that way when rolled, but it doesn't prove the distances are the same"*

*Miles Mathis, "The Cycloid and the Kinematic Circumference*

**If we follow a point on the wheel, Pi is still 3.14.. it does not magically become 4.**

**The blue arrow (point A) is the point on the wheel Miles Mathis refers to and as you can see the value is 3.14...**

What is the "point"? Mr. Mathis refers us to the idea that no imagined points touch the ground, yet the wheel clearly does and if this were a spool of twine, we would have unrolled a set amount that would look like a straight line. This would all be as advertised and Pi would be the 3.14… as it is claimed to be.

### The curve Mr. Mathis refers to has nothing to do with either the path (geometry) or the kinematics.

* ***Pi=4 **

*"Those of you who have read my papers on π=4 will know I have explained that problem using many visualizations and arguments, but after several years I have decided the best way to teach the new physics is by starting with the cycloid. Whenever I have to explain my physics to young people, this is now how I start. "*

*"If you roll a wheel on the ground one full rotation, it will mark off a path on the ground that is 2πr in length, as most people know. That length has been assigned to the circumference of the circle or wheel, which assignment is correct as far as it goes. My papers have not questioned that. However, if you do the same thing but follow the motion of a given point on the wheel (point A in the diagram above, for instance), it draws the red curve. That is called the cycloid."*

*"Obviously, the red curve is not the same length as the line on the ground. It is considerably longer, being 8r in length. That is 21% longer than the circumference."*

*"Obviously, the red curve is not the same length as the line on the ground. It is considerably longer, being 8r in length. That is 21% longer than the circumference."*

*"What we will discover is that there are actually two correct circumferences. There is a geometric circumference and a kinematic circumference. The first is the familiar circumference you know about, and is just the perimeter of a given circle. But it implies no motion and allows for no motion. I call it geometric because it comes from geometry, which is static. No motion is involved. No motion is involved in geometry because no time is involved. It is lengths only, with no time or velocity. But if motion is involved, you must use a kinematic circumference. “Kinematic” just means having to do with motion. It is a cousin of the word “dynamic”. Kinematics and dynamics are classical subfields of physics, and they go beyond geometry by including time and motion. What we are about to see is that the cycloid tells us the kinematic circumference."*

*"**What I am trying to get you to see is that it is this match-up that is actually slippery. The mainstream has tried to claim it is my math or ideas that are slippery, but the reverse is true. When you roll a wheel along the ground, and then monitor that line created, you aren't actually monitoring one point or one event. You are monitoring a series of events in a very offhand and imprecise manner. The claim at the end that points have matched up or that distances are equal is just a claim, with nothing at all to support it. Just as measuring curves with straight lines is extremely complex and difficult, measuring straight lines with curves is just as difficult and problematical, and cannot be glossed over so casually, as if it is *

*self-apparent. "*

http://milesmathis.com/cycloid.pdf

**First posted September 9, 2008:**

*"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)."*

*"What if you are measuring the length of a curve on the ground, using a surveyor's wheel? By using pi, you assume the curve is just like the straight line, and indeed that is what the surveyor's wheel tells you. But if instead of measuring the length of the curve on the ground, what if you wished to measure the new curved cycloid you have drawn in the air with your wheel? In other words, you have taken a cycloid and wrapped it around a curve. Will the length stay the same? I suppose the mainstream would say yes, but the obvious answer is NO."*

*Miles Mathis, "The Extinction of π"*

http://milesmathis.com/pi2.html

**Want A Slice of Papa John's Pi?**

### "*But if instead of measuring the length of the curve on the ground, what if you wished to measure the new curved cycloid you have drawn in the air with your wheel? "*

*"Maybe some of my readers can grasp that, given that the cycloid is planar rather than linear. It may help them visualize this. Take the red cycloid curve in the diagram above and imagine curving the entire diagram. If you don't see what I mean, think of cutting the whole curve out with scissors and pasting it onto a curved surface, like a soup can. After you do that, answer me this question: is that new curved curve you have created the same as the flat curve above? No, of course not. If you were writing an equation for it, you couldn't use the same equation. You would have to write a new more complex equation, with an extra variable in it to express the new curvature. Since that new variable could not be zero, it would necessarily change the length of the curve. Well, if that is true, then the same logic must apply to any curve, whether is it wrapped by a cycloid or wrapped by a simple line. The length of the curve cannot be measured in the same way you measure a straight line, since the curve will always have an additional non-zero variable to integrate into the math. The length of the curve will always be greater than the length of the “equivalent” straight line. *

*Some will say, “That may be true, but using cycloid math in a surveyor's wheel won't solve it.” True enough. I didn't mean to imply that using cycloid math would give you more useful numbers for the wheel. I meant that using pi and the naive math they do use was a cover up, since it hid the problem I have just shown you. And I meant that by using cycloid math, I could show why the surveyor's wheel must fail to correctly measure any curve."*

*Miles Mathis, "The Extinction of π"*

**Miles Mathis claims we cannot demonstrate something we clearly can.**

He claims we cannot take real world objects and demonstrate the reality of the concept of Pi. Yet we can do exactly this. Mr. Mathis claims we can only do this with abstract circles, yet he is the one who has to depend on such an imaginary abstraction to support his fallacious reasoning.

Miles Mathis acts as if we cannot use spools of thread to prove him wrong.

### What does that imagined red arc have to do with anything? It is not the path of the imagined planet orbiting the Sun. Is it supposed to be a point on the Earth's supposed rotating surface? What does this have anything to do with modeling Newtonian-style mechanics?

**Setting Pi Straight**

Circumference and Pi source: bvcmath

"* All it proves is that curve and the line match up that way when rolled, but it doesn't prove the distances are the same.*"

*"You can't match curves to lines and say they are the same, because they aren't created the same way, they don't have the same math, and they aren't traveled in the same way."*

*Miles Mathis, "The Cycloid and the Kinematic Circumference*

**The distances are not the same? Miles Mathis is confusing geometry with kinematics again.**

### Does Miles Mathis believe The Earth to be some kind of Pizza Pi Flat Plane?

As we can demonstrate geometrically the straight path is the same distance as the curved path. In terms of kinematics there is a very real world difference in terms of how an object follows the path. One is apples and the other is oranges. There's not only a difference between geometry and kinematics, there is also a difference between types of motion as well. Not only is there a difference between relatively linear motion and circular motion, there are also different ways one can make an object follow a circular path. One can use a clock like arm. One can use a self propelled vehicle of some kind. One could make some kind of track and have an object be pulled along that track. One could imagine magical forces that can perform all sorts of genie like effects and when one does, one may find they get into trouble, somewhere down the proverbial line.

There's a difference between riding on a merry go round and the imagined orbits of Newtonian mechanics. One is real and the other relies on a thought experiment that demonstrable ballistics physics disproves. Circular motion is better modeled as rotation and not as some kind of linear process. A person standing at the center of a merry go round simply seems to spin. Another person at the circumference of the merry go round seems to have a orbital kind of motion. Both people are on the same rotating platform.

There's a difference between a car turning to create a circle and tying a ball to the end of a string and whirling that ball above one's head to mimic Newtonian orbital mechanics. *(Which contradicts demonstrable gravity, by the way;* maybe that's part of the problem here.)

**Don't Forget NASA's Torqued Tongue: It Seems Like Mr. Mathis Did**

### Everything Moves As One

image source: Torque - Wikipedia

**Let's Get Pi Eyed**

*"In planetary orbits, you have the Sun creating the centripetal motion. But if you are just walking in a circle, you have to create it yourself. For instance, you can lean toward the center of the circle and let gravity create some of it for you. Or you can push more on your outer leg. It doesn't really matter, except that you understand that circular motion isn't just like straightline motion, and that the mainstream knows that and admits it. So walking 2πr in a straight line and walking 2πr in a circle is not the same: not physically, not mathematically, and not in any other way.*

*It gets a little more difficult from here on out. If this were really easy, it wouldn't just now be discovered, so press yourself a bit. Let us go back to the wheel rolling on the ground, that we started with. Notice that when we draw the normal circumference on the ground with the wheel, we aren't following any one point. No point on the wheel is moving along that line, and no point on the earth is, either. We are told we are letting points on the circle match points on the ground, and most people accept that, since it seems to make sense. But it cannot be demonstrated and never has been. Yes, you can paint lines on the ground with wet paint, roll the wheel over them—getting the paint on the wheel —and then claim that the distance between lines on the ground and on the wheel is the same, but it doesn't prove anything of the sort. All it proves is that curve and the line match up that way when rolled, but it doesn't prove the distances are the same. Again, you can only compare straightline distances to other straightline distances. You can't match curves to lines and say they are the same, because they aren't created the same way, they don't have the same math, and they aren't traveled in the same way."*

http://milesmathis.com/cycloid.pdf

**Around & Around On A Typical, Stubborn, Online Merry Go Round Ride of Nonsense Sold As Some Kind of "Science"**

Circumference defines a geometric parameter. Circumference does not define a dynamic value. Mr. Mathis would appear to be confusing the subject of geometry with the subject of the mathematical modeling of objects in (circular) motion. There's a difference between torqued motion and relative linear motion.

*"A child riding on a carousel, you riding on a Ferris wheel: Both are examples of uniform circular motion. When the carousel or Ferris wheel reaches a constant rate of rotation, the rider moves in a circle at a constant speed. In physics, this is called uniform circular motion.*

*Developing an understanding of uniform circular motion requires you to recall the distinction between speed and velocity. Speed is the magnitude, or how fast an object moves, while velocity includes both magnitude and direction. For example, consider the car in the graphic on the right. Even as it moves around the curve at a constant speed, its velocity constantly changes as its direction changes. A change in velocity is called acceleration, and the acceleration of a car due to its change in direction as it moves around a curve is called centripetal acceleration. "*

Uniform circular motion: Movement in a circle at a ... - Montville.net

**What Does The Miles Mathis Red Arc Have Anything To Do With This?**

Does it do anything to really help model the motions of a car on a round race track?

Race cars with constant speed around curve | Physics | Khan Academy source: Khan Academy

**Circumference**

*"The circumference (from Latin circumferentia, meaning "carrying around") of a closed curve or circular object is the linear distance around its edge.[1] The circumference of a circle is of special importance in geometry and trigonometry. Informally "circumference" may also refer to the edge itself rather than to the length of the edge. Circumference is a special case of perimeter: the perimeter is the length around any closed figure, but conventionally "perimeter" is typically used in reference to a polygon while "circumference" typically refers to a continuously differentiable curve."*

https://en.wikipedia.org/wiki/Circumference#Circumference_of_a_circle

**Do The Experiment For Yourself**

How to Measure Bicycle Wheel Circumference For A Cycling Computer source: BikemanforU

**Don't Believe Your Eyes: Instead Believe Some Illogically Minded Guy Online**

"*When you roll a wheel along the ground, and then monitor that line created, you aren't actually monitoring one point or one event. You are monitoring a series of events in a very offhand and imprecise manner. The claim at the end that points have matched up or that distances are equal is just a claim, with nothing at all to support it.*

*Miles Mathis, "The Cycloid and the Kinematic Circumference*

**Miles & Miles of Confused Ideas About How To Model Reality**

Can you explain how this makes any sense? Miles Mathis points us to an imagined arc that has no bearing on how a wheel rolls. We can use the classical value of Pi in a 3d animation program and create expressions that mimic the real world physics and kinematics of wheels rolling. Mr. Mathis seems to be grasping at allegorical strawmen. How is he defining reality? How is a rolling wheel not one event? How is it that we can indeed unspool wire and thread and string?

**How can he seriously claim that the demonstrations in these two videos are "imprecise" and "offhand"?**

How is that we can easily demonstrate the validity of mainstream geometry and kinematics and yet Mr. Mathis insists we cannot? Not all of mainstream education is wrong just as not all of the News is made of 100% lies. All religions contain doses of truth and all of us like to breathe air. A broken clock is correct twice a day and all the rest. 1+1 really does equal two and the alphabet and grammar matter too.

Miles Mathis has not shown us that his way models reality better at all. In fact it seems there is no reason to even consider his idea as it does not seem to model anything. If you want to get into modeling planets moving around suns, making Pi = 4 is probably not the best way to go about it. Would you model the motion of the Earth around the Sun based upon a point on the Earth's circumference or would you use traditional geometry to model the Earth's near perfectly circular orbit and proceed from there? If you find you have problems with the kinematics of your resulting model, I don't think additional ad hoc mathemagical explanations are the tool to use. I would think that one would be better served by questioning all underlying assumptions instead, but hey what do I know... I am no NASA "Math Wiz". Please keep in mind Mr. Mathis seems to believe in the feats of NASA and other space programs.