infinity in geometry

[3timer]

I was just recently taught about Cantor and infinity in relation to the geometry of a circle. It was explained that you could have infinite radii coming out of the center of the circle because of the fact they get farther apart as they radiate outwards.

Isn't the actual issue that the radii has as a width of 0 which makes it unrealistic. So therefore, the fact there is an infinitely small number involved (0), it leads to an infinitely large number (infinity)?

So, I drew this in paint to explain what I mean:

In this picture the radius (B) has an obvious width. If you were to add another radius right next to it, it would overlap a bit. The amount it overlaps is proportional to the width and/or the area of B. Generally when there proportions involved a formula can be made?

Ha, am I crazy? or over thinking this?

 

[mmm4444bot]

Your diagram does not show any radii. :?

 

[Grant Bonner]

Yeah, the block is supposed to be the radius of width b. See how it's kind of centered? But your over-thinking it. It's similar to the idea of there being an infinite amount of points between 1 and 2 on a numberline. Infinity is an idea, not really a number of things and I think that may be what is throwing her off.

 

[mmm4444bot]

… the block is supposed to be the radius …

The radius of a circle is not a 2-dimensional object. Therefore, a "block" cannot represent the radius of a circle.

The radius of a circle is the straightline distance from the center of the circle to any point on the circle.

In other words, the radius is shown as a line segment, drawn from the center of the circle to any point on the circle.

It makes no sense to describe the radius of a circle as a rectangular shape.

If the numbers A and B in your diagram represent the lengths of the sides of the block, then neither A nor B is the radius.

The radius is not shown anywhere in your diagram.

If you're still confused, look up the geometric definitions for the following words: radius, chord.

 

[Denis]

Yeah, the block is supposed to be the radius of width b. See how it's kind of centered? But your over-thinking it. It's similar to the idea of there being an infinite amount of points between 1 and 2 on a numberline. Infinity is an idea, not really a number of things and I think that may be what is throwing her off.

Grant, did YOU post the original under 3timer?
If so, you're not making much sense under both names.

 

[mmm4444bot]

I didn't notice the different user names.

(Maybe, I'm overthinking that, too.)

 

[Grant Bonner]

No, I'm not 3timer. I was trying to explain that the block drawn was supposed to represent the radius. Obviously a radius has no width. I think 3timer's problem was trying to understand how an infinite amount of radii or "lines" can equal the area of the circle. When 3timer wrote the question, I think it should have read: " The radius has width (b)." Not that it does, but I think that statement clarifies 3timer's question more. Understand?

 

[Mrspi]

No, I'm not 3timer. I was trying to explain that the block drawn was supposed to represent the radius. Obviously a radius has no width. I think 3timer's problem was trying to understand how an infinite amount of radii or "lines" can equal the area of the circle. When 3timer wrote the question, I think it should have read: " The radius has width (b)." Not that it does, but I think that statement clarifies 3timer's question more. Understand?

Not at all.

You know, this whole argument makes NO sense. If someone can understand that there are an infinite number of points between 1 and 2 on the number line, then it should be an easy step to believe that there are an infinite number of points on the circumference of a circle between any two defined points ON that circle.

"The radius has width b"?????

 

[mmm4444bot]

OIC, now. :roll: The block is a surrealistic representation of a single radial line. (I never really understood Dali, either.)

In his book "Zero: The Biography of a Dangerous Idea", Charles Seife writes "Adding infinite things to each other can yield bizarre and contradictory results."