Can a circle have an infinite diameter? I say no

[DeepBlueSea]

Ah, but an infinitely small circle is easy: it is but a single point.

That’s the wittiest oneIiner I have heard in quite a while.

 

[GEddie]

Something that complicated can not be reduced to these one-liners.

If you look at any point on a circle very closely, it may be taken as a “straight line” for mathematical purposes.

It’s not that complicated, in fact it is binary. Either infinite circles exist or they do not.

Because as someone said, infinity is not a number, I’d say that by the definition of a circle, no circle can be infinite.

And I think you misstated your argument, as there is no way that any point can approximate a straight line.

God Bless and ICXC NIKA

 

[Zosimus41]

Can a circle have an infinite diameter? I say no.

The circle portion of the madalbrot set if you include the fractals would be infinite.

z → z^2 + c iteration process goes on forever. These numbers are contained within the black of the Mandelbrot fractal.

In the Mandelbrot formula z → z^2 + c, where you always start the iterative process with z equals zero, and c equaling any complex number, an endless series of seemingly random or chaotic numbers are produced.

 

[InspiritCarol]

…And I think you misstated your argument, as there is no way that any point can approximate a straight line.

God Bless and ICXC NIKA

Ah… forgive my imprecise language. By “point” I meant “section” or short segment.

lol

… Engineers…

 

[InspiritCarol]

welltall.com/ymc/discovery/polygon.html

here’s a nice explanation with a neat java applet.

Basically, you take the formula for finding the circumference of an n-sided polygon.
Plug in infinty to n. As the limit approaches infintiy, the answer is pi(D).



It’s this kind of congruity that radiates the signature of the Creator to me and why I have always loved math.

The infinite may be expressed in the finite. God really can become man.

 

[mafh]

Yes, a circle can have an infinite diameter (or infinite radius… amounts to the same thing).

This is in fact one of the underpinings of an obscure type of mathematics called complex analysis (essentially integrals in the complex plane). There is a type of operation called a contour integral where you have to go around the ‘poles’, which are spots where the function blows up into infinity. To do this, you integrate along a path that goes around a little half-circle around the pole, and then along a huge half-circle with a radius of infinity.

So, not only does it exist, but it is useful!

 

[GEddie]

welltall.com/ymc/discovery/polygon.html

here’s a nice explanation with a neat java applet.

Basically, you take the formula for finding the circumference of an n-sided polygon.
Plug in infinty to n. As the limit approaches infintiy, the answer is pi(D).



It’s this kind of congruity that radiates the signature of the Creator to me and why I have always loved math.

The infinite may be expressed in the finite. God really can become man.

That’s not the same as the OP’s question.

As n approaches infinity, the number of sides and corners increases and smooths out until at infinity there is a circle. But the diameter does not change.

God Bless and ICXC NIKA

 

[Cristiano]

Can a circle have an infinite diameter? I say no.

If you accept that your circle can look like a square then the answer is yes and you get a Von Neumann neighborhood of infinite extent. Just be careful how you calculate your tangents

 

[InspiritCarol]

That’s not the same as the OP’s question.

Please review the thread.

Post #13 directly speaks to the OP & I only tossed in my 2 cents because of post #15.
IOW - my posts support #13’s point and refutes #15.

As n approaches infinity, the number of sides and corners increases and smooths out until at infinity there is a circle. But the diameter does not change.

Yes, now step outside the box and apply that understood expression, to what Nicholas of Cusa has shown.

Are you picturing an infinite line? It is only *part *of the circumference of the circle itself. It must be because it is infinite. In *this *case of the infinite, the diameter must be as well.