infinite or none? does a circle has infinite corners or none?
infinite or none? does a circle has infinite corners or none?
(OP)
Hi All:
infinite or none? does a circle has infinite corners or none?
I guess this could be a interesting or pointless discussion?
Can we say a shape with infinite number of corners, if it is not infinitely large, it has to be a circle? Then it becomes have no corners?
If true, how can one from linearly increasing number of certain property (in this case corners) to become none of that property?
infinite or none? does a circle has infinite corners or none?
I guess this could be a interesting or pointless discussion?
Can we say a shape with infinite number of corners, if it is not infinitely large, it has to be a circle? Then it becomes have no corners?
If true, how can one from linearly increasing number of certain property (in this case corners) to become none of that property?





RE: infinite or none? does a circle has infinite corners or none?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
The interior angle of a vertex is given by 180 - 360/n = 180 * (n-2)/n where n is the number of vertices. The only regular polygon with true corners is a square. As n goes to infinity, the interior angle approaches 180.
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
Per definition: 0 angles
for any practical use: finite number of angels.
NX 7.5.5.4 with Teamcenter 8 on win7 64
Intel Xeon @3.2GHz
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RE: infinite or none? does a circle has infinite corners or none?
i guess if you constructed a cirlce from a single piece of stuff (from a single line element) by bending it ... then it'd have no corners (or verticies)
if you constructed it by increasing the number of corners (or verticies) (like strethcing a piece of string around pegs) then it'd have an infinite number.
now i'll ponder the imminent end of the world (as we know it)
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
my memory thought of it that way.
a google search shows links to many definitions that say "touch" and "single point".
do you have a link that says "tangents intersect a circle at two infinitesimally close points" ?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
(x-a)^2 + (y-b)^2 = r^2
Anyone blathering about the approximation of a circle is simply not talking about a circle, but an entirely different shape with an entirely different definition, so their points are irrelevant.
RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
b'sides, it's silly season isn't it ? how is kate's pregancy ? (wtf cares ??)
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
So neither Icosoles (sp?) or equilateral triangles have no corners?
"Corner" implies a shift in direction, not 90 degrees - any percieved angle change.
I guess I'm using circuitous logic here...
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
There are no philosophical questions, only philosophical responses.
Personally, I'll stick to the engineering response; what we deal with are appoximations to circles, and you can approximate a circle to any precision you like with a finite number of straight lines.
As for a corner having 90 degrees, I don't know where that definition comes from, but the OP was clearly not talking about any such corners, and Google tells me that a corner is "a place or angle where two or more sides or edges meet".
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
- Steve
RE: infinite or none? does a circle has infinite corners or none?
http://www.physicsforums.com/showthread.php?t=4529...
Benta.
RE: infinite or none? does a circle has infinite corners or none?
A corner is a discontinuity of the first derivative of the curve. If that curve is a circle, it is clear its curve is an analytic function which means that it has one and only one first derivative at each point on the curve and therefore has NO corners.
To say it has an infinite number of corners would be to say it has an infinite number of discontinuities which is total nonsense.
RE: infinite or none? does a circle has infinite corners or none?
In the limit, the "corners" become straight angles, and there are no longer any discontinuities, and there are no longer "corners."
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
i don't think you're going to win this one ... a derivative is often a well behaved continuous mathematical function, the piece-wise approximation is just that, an approximation, and has no standing in this
argumentdiscussion"In the limit, the "corners" become straight angles, and there are no longer any discontinuities ..."
another IMHO lost cause ... though the idea is better expressed (IMHO) by saying the corner initially has a radius (so, yes, the derivative is continuous) and then reduce that radius to be infinitismally small (at which time the derivative is not continuous).
RE: infinite or none? does a circle has infinite corners or none?
btrueblood, your humor did not go unnoticed.
RE: infinite or none? does a circle has infinite corners or none?
Die Gerade schneidet die Ellipse in zwei reellen Punkten (Sekante), wenn b^2+m^2*a^2>n^2
die Gerade berührt die Ellipse in zwei zusammenfallenden Punkten (Tangente), wenn wenn b^2+m^2*a^2=n^2
&c
BTW, the similar formulation (tangent touching the curve in two points lying together) was used for circle, but it did not explicitly specify the line being a tangent, so I chose the quote from chapter on ellipses where it does. HTH
RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
i can see that a tangent could be viewed as a special secant, i still wouldn't say that a tangent intercepts the circle at two points (like a secant) and qualify the two points as being infintely close to each other.
RE: infinite or none? does a circle has infinite corners or none?
Sure it does. As engineers, the approximation is what we are concerned with.
In fact I'd go as far as saying that treating the mathematical idealisation as being more "exact" than a good approximation is a frequent cause of error.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
http://docs.mcneel.com/rhino/5/help/en-us/popup_mo...
John R. Baker, P.E.
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RE: infinite or none? does a circle has infinite corners or none?
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
I "know" a circle has 4x corners 'cause I drew one in AutomatiCAD the other day using a square and 4 fillets. Yah can't argue with success! (And duct tape.)
And, in the plant, I done did use a two bladed drill to drill me a hole with no corners!
RE: infinite or none? does a circle has infinite corners or none?
But you raise a more interesting mathematical problem. You can determine the constant "pi" using this method. Infact, this is a typical college type computing project, although I ran into it in mathematical physics. Essentially you begin with an equilateral triangle and determine the perimeter. For ease of the problem, you have the three apex of the triangle subtended (i.e. inscribed) in a circle of unit one. From the centroid of this equilateral triangle, you determine the distance to any apex, obviously 1/2 units. Then divide the perimeter of the triangle by twice the distance to the apex. This is the first approximation to "pi", our constant.
Now add one "side" to the figure. So from an equilateral triangle, you get a square. Repeat the process. Find the perimeter and divide by twice the distance from it's centre to any corner. You get a number which is slightly less than the first, a better estimate to "pi".
Repeat the process of another side added to the square, a pentagon. Repeat the process. You keep repeating for an added side to the figure at hand, hexagon...septagon...octagon...nonagon...decagon....eleven sided figure (whatever)....dodecagon.....and so on....
So eventually the computer program kicks out a constant for a figure of X sides, say X=250,000. Noting the number of sides of the polygon begin to approach the circumference of a circle. So at infinite number of sides, the constant begins to emerge as 3.1415692....whatever your level of significance may be.
Answering your question, a circle is a polygon of infinite sides, i.e. number of tangents is astronomically high. The constant of perimeter around the figure divided by twice the distance of centre to any corner is "pi".
And now you know.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
I just drew this in AutoCAD, where I found that the number of sides needed to make a polygon become indistinguishable from a circle is 42.
Hope you can all accept that as the ultimate answer.
STF
RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
Ho-hum
Watching grass grow is more interesting than this oversubscribed boring exercise in futility.
Why don't we let it go?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
Watching grass grow is more interesting than this oversubscribed boring exercise in futility.
Why don't we let it go?[/quote]
Why do people who have no interest in a topic take the time to open it, read through it, and then post an insulting response?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
If this where in the pub it could be appropriate as the pub is kinda for this type of thread, but this philosophical non engineering really does not belong in a serious forum, well at least in my view, so people do have a right to complain and even red flag it.
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
Thank for all the response.
I agree this question was a bit out of the scope of this forum, but I thought here I can get some intelligent response from some intelligent engineers. (even tho I do agree this topic is kinda of pointless of what we doing)
I thought my original question was more philosophic rather than mathematical. I was trying to emphasise on the question of how come when you increase something to infinite, at the end you could get zero(none).
When I say corner, I didn't mean corner by its narrow meaning, what I mean is more like a vertex formed by two (tangent lines). Starting with a basic shape with 3 corners(edges), a triangle, by increase the number of corners(edges) we get rectangle and so on. when your number of corners(edges) reaches infinite, geit becomes a circle, where all your increased number of your geometrical characteristic (corner,edges) has all gone.
Or perhaps you could never call a circle formed in such a way it a "true" circle?
To sum up, the question was, if something has a characteristic of A, and it has got so many of this characteristic, to an extend of infinite amount, can we say it has got none (or almost none) of that characteristic
RE: infinite or none? does a circle has infinite corners or none?
Consider your many sided polygon with 10000 vertices; that makes the interior angles equal to 180-360/10000 = 179.964° Not much of "corner" already, and still a long ways from infinity. You'd be hard pressed to tell that it wasn't just a straight line. Again, so what? There is nothing magical or inherent about the "corners" in this problem. The "corners" of a triangle don't really have anything to do with the corners of a square. They didn't morph into the corners of the square. From a topological math perspective, all polygons are essentially the same closed shape, like a rubber band. I think you have too much time on your hands
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
(too soon?)
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Intel Xeon @3.2GHz
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RE: infinite or none? does a circle has infinite corners or none?
as for "if something has a characteristic of A, and it has got so many of this characteristic, to an extend of infinite amount, can we say it has got none (or almost none) of that characteristic" i agree with IR ...
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
I start with a equi-sided polygon, the distance from the centroid to the vertex being 0.50000 units. Clearly I am referring to a equilateral triangle which is inscribed within a circle of radius 0.50000 units. I ask the question, "What is the perimeter of this figure?". Using the Law of Sines and noting that the sum of angles equals 180 degrees in a triangle I get a side length of 0.86603 units. So the perimeter around the equilateral triangle is three times this amount or 3 X 0.86603 units = 2.59808 units. Because I know that the circumference of a circle is PI times diameter, the value of PI is simply the perimeter of a polygon divided by twice the radius which is 0.50000 units. In other words, the value of PI is the perimeter of the polygon divided by "1.0" or my polygon perimeter, 2.59808. I claim this is the first approximation to PI.
Increase the number of sides by one. I am now referring to a square which would be inscribed within a circle of radius 0.50000 units. I ask the question, "What is the perimeter of this figure?". Using Pythagorous Theorem and noting any two sides are of equal length, I get a side length of 0.70711 units. The perimeter of the square is therefore 4 X 0.70711 = 2.82843 units. Therefore following the logic above, PI equals the perimeter of the polygon divided by "1.0", the second approximation to PI is 2.82843.
Increase the number of sides by one. I am now referring to a pentagon inscribed inside a unit circle. Same question, find perimeter. Noting the composite triangle of the radius between any two successive verticies and a side, the central angle is 360/5 = 72 degrees. The other two angles noting they are equal and triangle interior angles sum to 180, I get 54 degrees. So Law of Sines using one of the known radii of 0.50000 units, side length is 0.58779 units, perimeter is 5 X 0.58779 units - 2.93893 units. This is the third approximation to PI, 2.93893.
Increase the number of sides by one. I am referring to a hexagon inscribed inside a unit circle. Noting the logic used in the pentagon, side length is 0.50000 units and the perimeter is 6 X 0.50000 units = 3.00000 units. This is the fourth approximation to PI, 3.00000. It also is the proof that a hexagon is the only regular polygon that can be inscribed inside a circle using a compass and straight edge because the sides of the hexagon equal the radius of the circle to which it is inscribed. The fourth approximation to PI is 3.00000.
Increase the number of sides by one. This is now a heptagon or seven sided polygon inscribed in a unit circle. I find the angle between two verticies subtended by a side with the centre of the figure to be 360/7 = 51.42857 degrees. Noting the angle sum to 180 degrees in this composite triangle, I get a half angle vertex to be 64.28572 degrees. Apply the Law of Sines, a side equals 0.43388 units. Therefore the perimeter for the heptagon is 7 X 0.43388 units or 3.03719 units. The fifth approximation to PI is 3.03719.
So in this fashion, I continue increasing the sides to the polygon inscribed in the unit circle. Finding the perimeter will converge to the value of PI. But we will never get to PI as 3.1415692...simply because I can never stop adding a side to the polygon. For an infinitely large number sided polygon, the value of PI would be just that, PI.
THEREFORE it comes to pass that a circle is a polygon of equal sides because the value of the perimeter of that infinitely many sided polygon is PI. In this special circumstance, the perimeter is called the circumference and the circumference of the circle is PI times diameter.
And now you have it.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
By definition, a polygon is composed of straight segments. Segments are of finite length (therefore not infinitely small).
Next batter...
RE: infinite or none? does a circle has infinite corners or none?
You can't see the forest because of the trees. The method of calculating Pi in this fashion is sufficient to understand a circle is an infinitely sided polygon. Your freedom to note otherwise is noted, and wrong.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
A polygon is a planar closed chain of segments.
A circle is defined as the set of points in a plane equidistant from a given point.
A segment can not be fully coincident with any portion of a circle's circumference, as it will always have points that are not equidistant from the circle's center.
So... no, a circle is not a polygon.
RE: infinite or none? does a circle has infinite corners or none?
If it where a collection of infinitely short straight lines, it would also have infinitely small variations in distance from the central point and would therefore fail the definition of a circle.
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
But that's fine, you agree to disagree. I'm good with it.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
What is Engineering anyway: FAQ1088-1484: In layman terms, what is "engineering"?
RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
I've shown the convergence to Pi asymptotically from the left using inscribing of polygons of increasing sides. You could do the same thing by circumscribing that polygon and using the midpoint of the side as the tangent point to the circle. The arithmetic changes slightly, but it is the same process. In that case, you would converge on Pi from the right.
So we're showing the sum of an infinite series converging to a limit. The fact that circumference is Pi times diameter as a circle property falls out from the perimeter of the polygon. But the process, obvious to some in this forum, is the point I wanted to make.
I just wasn't expecting such a parochial mentality of some readers, which on occasion is refreshing, in an intuitively obvious demonstration. But I'm not in the faith conversion business, but I digress.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
As for lack of imagination, I suppose I would defer to those that do not have the ability to imagine curvature and are still stuck pasting straight segments together. Then again, there are no curves, but only straight lines travelling through curved space.
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
Asymtotic convergence from the left uses verticies of a polygon of increasing sides inscribed from a common point or centre of curvature. That from the right are circumscribed polygons of increasing sides that use the midpoint of a side tangent to a curve with common centre. Because of symmetry, such points, whether they are polygon verticies or midpoints to the sides of said polygon lying tangent to the curve, are equi-distant from the centre of curvature. Hence the notion of a "circle".
So a circle can be regarded as a polygon of infinite sides, no matter which way you choose to describe it. Points on a curve or tangent lines that are subtended at the midpoint of each side, convergence to a constant defined by perimeter divided by twice the radius of curvature, is a unique circular poperty that falls from the logic of the method. Regardless, the concept is a polygon of increasing sides thus geometrically forming a circle with points lying equi-distant from a common centre of curvature.
End of story.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
"I get a number approaching but never reaching Pi."
Most of us don't have the patience to wait for an infinite series to reach its asymptote.
We'd rather just reach for the pi.
STF
RE: infinite or none? does a circle has infinite corners or none?
Just because a CAD program cannot actually draw a circle, that does not mean it's best attempt at an approximation is a circle.
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
I think both "sides" (no pun intended) would agree with a statement worded as follows: In the limit as N approaches infinity, an N-sided polygon approaches a circular shape.
Personally I think the notion of a limit is a necessary part of that statement. The phrase "polygon with an infinite number of sides" does not seem mathematically precise and perhaps creates ambiguity which results in disagreement when people interpret the ambiguous phrase differently.
Sorry if someone else already said the exact same thing.
Also sorry for prolonging this. Barring any negative reply to my comments, I'm done.
=====================================
(2B)+(2B)' ?
RE: infinite or none? does a circle has infinite corners or none?
"In the limit as N approaches infinity, an N-sided regular polygon approaches a circular shape."
=====================================
(2B)+(2B)' ?
RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
Now that should really confuse people
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
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Siemens PLM:
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To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
Re. CAD analogy someone drew to Solidworks is not as to the point as someone did to AutoCAD (with answer being 42), because Solidworks and other modern CAD packages use 'proper' circles, and the limiting factor is resolution of the display, whereas AutoCAD actually (prolly for purposes of speed of display, &c) actually approximates circles with polygons (number of sides is set in options) to display, but calculates as it should with circles...
As for the intention of the OP, I must say the (intended) irony escaped me at the first, but I do see it. Admittedly, it's indeed not an engineering question per se, but interesting none the less. Increasing the number of sides of a polygon until there are none.
RE: infinite or none? does a circle has infinite corners or none?
ElectricPete brings to mind the notion of limit. I am not summing and allowing infinitesimal accumulations like an integration process. Rather, I an incrementally increasing the number of sides in a polygon from three to a very large number. The concept of circularity evolves out of the process as the circumference of a circle equals Pi times diameter. These fall out of the argument.
But two well thought out points, well presented, so I thank you. Try it for yourself, start with an equilateral triangle of any size and locate the centre. Then increase the sides of the polygon by one and recompute. You'll get the very same result whether you use the vertex of said polygons or midpoint of the sides. It is a beautiful proof! Try it for yourself over a few beers.
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
* the point in previous post was an attempt at a bit of joke- we show that polygons tend to approximate circle more closely as number of sides increases, and start doing it by inscribing a triangle in a circle... so the intended joke was why would we approximate the circle if we took a compass and have already drawn it?
RE: infinite or none? does a circle has infinite corners or none?
If my mom put me in a round room, and told me to go stand in the corner for 10 minutes..... I would be in there for the rest of my life.
Charlie
www.facsco.com
RE: infinite or none? does a circle has infinite corners or none?
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
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Pat
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RE: infinite or none? does a circle has infinite corners or none?
RE: infinite or none? does a circle has infinite corners or none?
The more points you make the closer you will be getting to the correct answer or will you?
A Circle is a Circle now a computer may come awfully close to representing a circle, but if you get a pushpin/thumbtack a piece of string and a pen and make two tiny loops the size of the pushpin diameter and the other the size of the pen tip. Push the pin through the pin hole into a piece of paper. stretch the string to it's max extent and put pen to page and go 360º around so you end where you start and you'll have a circle. Of course no one can draw a perfect circle although it may be possible it's highly not probable.
Everyone who thinks of a circle as an infinite sided polygon, let's have a race. you can start by drawing your polygon and I can start walking halfway to the nearest wall.
No one will win because you'll never have infinite number of sides because that number does not exist and I'll never reach the wall.
Cheers everyone and thank you for the mindlessly inane and quite stupid imho discussion.
The atom smiley is a Gif which is the closest that file type can get to a circle unless you make it ∞x∞ pixels and you may come close but never achieve a perfect circle.
Even with the best cad system and graphics card, if you zoom in far enough to a circle you'll see the linear approximation even with a Cray supercomputer. Pretty sure SolidWorks has a limitation to how many sides it can have in a polygon. If I find that out I'll post it on the SolidWorks forum which I recognize a few forum posters from.
One more thought before I leave the discussion Can you get a perfect circle from an etch a sketch with precisely programmed stepper motors at the knobs?
P.S. patprimmer If it's curved it's not a line at least not any longer.
Note: quote has been spell corrected were was "where"
But I completely agree with your point.
"It's not the size of the Forum that matters, It's the Quality of the Posts"
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RE: infinite or none? does a circle has infinite corners or none?
http://www.merriam-webster.com/dictionary/line
It seems Merriam Webster disagrees with your definition of a line around points 7, 8 and 9
Just to be pedantic about it.
Regards
Pat
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RE: infinite or none? does a circle has infinite corners or none?
I suspect that where this perception that somehow computers need to approximate a circle is when it needs to display one a computer screen, but this has absolutely NOTHING to do with how the computer software represents a circle mathematically. It's purely a 'mechanical' limitation of the display technology, but even that is not always what you'd think. There was a time before raster displays (like your TV) when we were using direct view displays, that is the displayes were not scan line based but with objects being directly drawn on the screen. However these were limited to monochromatic displays, the most common being White on Black with Display Refreash Devices...
...or Green on Black with Direct View Storage Terminals...
...but circles were circles, period.
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
TTFN
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RE: infinite or none? does a circle has infinite corners or none?
And then there's that small number of systems which don't depend on floating point computations at all, but rather uses integer math, which while it does limit the sorts of computations and geometric representations which can be handled, it's often sufficient for things like AEC and GIS applications. The advantage being that computations are generally fast resulting in efficient and compact data representations.
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
It is not possible to draw or simulate one with current technology. What we call a circle in drawings are not but they are a close enough approximation that it is acceptable.
That is all there is to it.
RE: infinite or none? does a circle has infinite corners or none?
What do you call a compass?
RE: infinite or none? does a circle has infinite corners or none?
I suspect that they only way this argument will be settled is when the primary protagonists agree to meet on the field of honor with Triangles and T-Squares
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
John R. Baker, P.E.
Product 'Evangelist'
Product Engineering Software
Siemens PLM Software Inc.
Industry Sector
Cypress, CA
Siemens PLM:
UG/NX Museum:
To an Engineer, the glass is twice as big as it needs to be.
RE: infinite or none? does a circle has infinite corners or none?
It is common engineering folly to confuse the representation or model of a phenomenon as the actual phenomenon.
A circle is an abstract, one with a clear definition. A drawing is only a representation. An n-sided polygon is only an approximation. Whatever intellectual gymnastics one performs to understand a circle is only a mental model.
Strangely, we can only tell how close something comes to being circular within an uncertainty, but we can never verify that something is perfectly circular.
RE: infinite or none? does a circle has infinite corners or none?
I wasn't referring to how it is represented graphically either, but I'm going to leave it at that.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: infinite or none? does a circle has infinite corners or none?
No corners... not an infinite number of them!
Dik
RE: infinite or none? does a circle has infinite corners or none?
Despite the second degree polynomial equation, I can produce a tangent at any point to the curve. Correct? The path can be said to contain infinitely many points, to which I can draw a tangent line.
So the circle, whose circumference is composed of many points approaching infinity in the limit, must have a tangent line associated with each of these infinitely many points. Hence the notion that a circle has infinite tangents, I.e. sides of a polygon circumscribed to such a circumference.
Pay attention to the geometry! Simple Archimedes with a little Euclid. Do the differential calculus, it is intuitively obvious! OMG!
Regards,
Cockroach
RE: infinite or none? does a circle has infinite corners or none?
Regards
Pat
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