- #91
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That raises the question, what does ##\pi## look like under a microscope?Gavran said:
What could prove this wrong? I'm having a dispute with friends
- Context: High School
- Thread starter ducknumerouno
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Discussion Overview
The discussion revolves around the concept of infinity and its implications in mathematics, particularly in relation to limits, convergence, and the treatment of infinite quantities. Participants explore various perspectives on how infinity is defined and used across different mathematical contexts, as well as the philosophical questions it raises.
Discussion Character
- Debate/contested
- Conceptual clarification
- Exploratory
Main Points Raised
- Some participants question how convergence is defined—whether in shape, perimeter, or area—and whether properties like length are preserved in limits.
- Others argue that treating infinity as a number leads to contradictions, citing examples where incorrect conclusions can be drawn from misusing infinite quantities.
- A participant raises concerns about the trustworthiness of using infinity in mathematics, noting that some infinities are considered larger than others.
- There are discussions about the context-dependence of infinity, with some suggesting that this variability adds to the confusion surrounding the concept.
- One participant presents a thought experiment involving walking the perimeter of a square versus a circle to illustrate the differences in perceived speed and distance, questioning the nature of walking a circle.
- Another participant suggests that the philosophical implications of infinity should not overshadow its mathematical utility, while others express skepticism about the clarity of the concept.
- Several participants emphasize the need for context when discussing mathematical concepts, including infinity, and challenge the idea that it is merely a philosophical notion.
Areas of Agreement / Disagreement
Participants express a range of views on the nature of infinity, with no clear consensus reached. Some agree on the importance of context in understanding infinity, while others maintain that its utility in mathematics is undeniable. Disagreements persist regarding the clarity and philosophical implications of the concept.
Contextual Notes
The discussion highlights the limitations in understanding infinity, including its dependence on context and the unresolved nature of certain mathematical principles related to infinite quantities.
- #92
DaveC426913
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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.BWV said:
'Subtle' is an understatement. ;)
- #93
Gavran
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It looks like a circle with a diameter of 1. The same can not be said for the figure in the original post.PeroK said:
- #94
A.T.
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ducknumerouno said:TL;DR Summary: Pi = 4?
I know it theoretically never touches the circle, but does the circle ever really become a circle?
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:
Last edited:
- #95
wrobel
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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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