B What could prove this wrong? I'm having a dispute with friends

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The discussion centers on the concept of infinity and its implications in mathematics, particularly regarding convergence and limits. Participants debate whether infinity can be treated as a number and how it varies in meaning depending on context, emphasizing that mathematical definitions and applications of infinity are context-sensitive. The conversation highlights that while infinity is a useful mathematical concept, it raises philosophical questions about understanding and definition. The example of measuring perimeters illustrates the complexities of infinite subdivisions and their implications on speed and distance. Ultimately, the discourse suggests that while infinity is a challenging concept, it remains a vital part of mathematical discourse.
  • #91
Gavran said:
What about using a microscope?
That raises the question, what does ##\pi## look like under a microscope?
 
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  • #92
BWV said:
Is that what you saw of my post?
No. That's the 0.1% of the pixels in your post 84 I would have had to notice, in order to get the joke.

'Subtle' is an understatement. ;)
 
  • #93
PeroK said:
That raises the question, what does π look like under a microscope?
It looks like a circle with a diameter of 1. The same can not be said for the figure in the original post.
 
  • #94
ducknumerouno said:
TL;DR Summary: Pi = 4?
I know it theoretically never touches the circle, but does the circle ever really become a circle?

problem-webp.webp


This iterative approximation reduces the area-error in each step, but it doesn't reduce the perimeter-error at all. So, it can used to derive the area of the circle but not its circumference (and pi from it).

See also this video:

 
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  • #95
Old thread but it dives up as a hot thread every time . I just want to say that there are several definitions of arc length. Math begins from definitions.
 
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