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## infinite or none? go a circle has actually infinite corners or none?

Spoonful (Mechanical)
Hi All: boundless or none? go a circle has actually infinite corners or none?I assumption: v this can be a amazing or pointless discussion? deserve to we to speak a shape with infinite number of corners, if it is not infinitely large, it has to be a circle? climate it becomes have actually no corners?If true, how have the right to one indigenous linearly increasing variety of certain residential or commercial property (in this situation corners) to come to be none of the property?

### RE: limitless or none? walk a circle has actually infinite corners or none?

IDS (Civil/Environmental)6 Dec 12 02:27
Since this is an engineering site I"ll say that a one (or any other smooth curve) has a finite number of corners, for any type of desired level that precision.

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### RE: unlimited or none? walk a circle has actually infinite corners or none?

IRstuff (Aerospace)6 Dec 12 02:47
Your premise is not correct. A circle is approximated through a continuous polygon through an infinite number of vertices, which room not necessarily "corners" since "corner" means a right angle. As the number of vertices increase, their included angle increases, till every vertex i do not care a right angle, i m sorry is the limiting case for the circle, and why tangent lines intersect at only one point.The internal angle the a crest is given by 180 - 360/n = 180 * (n-2)/n whereby n is the variety of vertices. The only continuous polygon v true corners is a square. As n goes come infinity, the internal angle viewpoints 180.

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### RE: limitless or none? go a circle has infinite corners or none?

WolfHR (Mechanical)6 Dec 12 04:50
Sorry to it is in pedantic, IRStuff, yet as much as i recall- together per definition, tangents intersect a one at two infinitesimally nearby points.

### RE: unlimited or none? does a circle has infinite corners or none?

Walterke (Industrial)6 Dec 12 05:05
That"s exactly the same thing. Every definition: 0 anglesfor any practical use: finite variety of angels.

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wolf ... ? a tangent touches a circle at one point.i guess: v if you built a cirlce from a solitary piece of ingredient (from a single line element) by bending the ... Then it"d have no corners (or verticies)if you constructed it by boosting the number of corners (or verticies) (like strethcing a piece of string about pegs) then it"d have actually an limitless number.now i"ll ponder the imminent finish of the civilization (as we recognize it)

### RE: limitless or none? go a circle has actually infinite corners or none?

WolfHR (Mechanical)6 Dec 12 08:29
Well, rb1957, I recognize a appropriate mathematical definition of a tangent, otherwise i wouldn"t presume to correct as knowledgeable and respected member as IRStuff. Friend may pick to adopt an ext practical, if less accurate, translate but... The an interpretation I provided is as much as I recognize the just correct one (for every curves, incl. A circle) and if girlfriend look at it more closely it will lead you come a much more recognizable, derivative form.
sorry wolf yet every definition of tangent i recognize says a tangent touches a circle at a single point.my memory believed of it that way.a google search shows web links to plenty of definitions that say "touch" and "single point".do you have a attach that states "tangents intersect a one at 2 infinitesimally near points" ?

### RE: unlimited or none? go a circle has actually infinite corners or none?

WolfHR (Mechanical)6 Dec 12 09:19
OK, I"ll look it up rb1957- yet I"m optimistic it"s the definition I to be taught in ~ high school (math oriented gymnasium) and at college, as well as my grandfather, who was university professor of descriptive geometry, using it...
Don"t confused the border equation meaning with the result. Per the an interpretation of the derivative, i beg your pardon is a "slope", that does involve two points that technique each other, but, in the limit, the result is for a single, identified point. Otherwise, you could never effectively quantify a numerical derivative. Refer to http://en.wikipedia.org/wiki/Tangent_line#Intuitiv... Because that the description.

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The same dispute can be applied to the derivative of any type of curve. The derivative is approximated through a series of piecewise linear approximations taken to the border of a infinitely tiny span.In the limit, the "corners" come to be straight angles, and also there space no longer any kind of discontinuities, and also there are no much longer "corners."

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