- #1
Shackleford
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We're covering this in my History of Mathematics class. I'm not entirely sure what they're asking.
The three famous geometric construction problems
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Homework Help Overview
The discussion revolves around the three famous geometric construction problems: squaring the circle, doubling the cube, and trisecting the angle. Participants are exploring the context and requirements of these problems as part of a History of Mathematics class.
Discussion Character
- Exploratory, Conceptual clarification, Problem interpretation
Approaches and Questions Raised
- Participants are questioning the specifics of the problems, including the relationship between the areas of circular sections and their chords. There is also a request for clarification on the visual representation of the problems.
Discussion Status
Some participants have reached out to the instructor for clarification, while others are attempting to interpret the problems based on provided images. There is an ongoing exploration of how the geometric concepts relate to each other.
Contextual Notes
Participants mention the need for additional context and clarification from the instructor, indicating that the original problem setup may not be fully understood. There are also references to specific geometric properties that need to be confirmed.
- #2
Mark44
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Is there some more context to this that you haven't shown? Are they slicing up a cone with circular sections that are perpendicular to the central axis of the cone?
- #3
Shackleford
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The notes cover squaring the circle, doubling the cube, and trisecting the angle.
This might be the construction I need to look at.
http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png
This might be the construction I need to look at.
http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-1.png
- #4
Shackleford
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Any ideas?
- #5
Mark44
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Your image seems related to the problem, but the best source for clarification would probably be the instructor for the course.
- #6
tiny-tim
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Shackleford said:We're covering this in my History of Mathematics class. I'm not entirely sure what they're asking.
Hi Shackleford!
It's talking about two sections of different circles but with the same shape (ie the same angles at the corners).
- #7
Shackleford
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tiny-tim said:Hi Shackleford!
It's talking about two sections of different circles but with the same shape (ie the same angles at the corners).
Hello, tiny-tim.
I emailed the professor. He said, "You need to show: the ratio of the areas of these two slices is equal to the ratio of the squares of their chords."
Is this correct?
http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110902_190701.jpg
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- #8
tiny-tim
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sorry, can't read it 
EDIT: oh, and i think the question means a region with one straight side (the "chord"), not two straight sides meeting at the centre
can you type it, please?
EDIT: oh, and i think the question means a region with one straight side (the "chord"), not two straight sides meeting at the centre
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- #9
Shackleford
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tiny-tim said:sorry, can't read it
can you type it, please?
EDIT: oh, and i think the question means a region with one straight side (the "chord"), not two straight sides meeting at the centre
The picture enlarges. It's readable.
In each of the circles, I forgot to draw the chord. Is that what you're talking about?
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