- #1
mymachine
- 42
- 0
How do you construct the arc of the circle as a straight line by geometry not by an equation?
Thank you
Thank you
How To Create An Arc Of A Circle As A Straight Line?
- Context: High School
- Thread starter mymachine
- Start date
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- Tags
- Arc Circle Line Straight line
Click For Summary
Discussion Overview
The discussion revolves around the geometric construction of an arc of a circle as a straight line, exploring whether such a construction is possible without using equations. Participants engage with the concept from various angles, including theoretical implications and practical limitations.
Discussion Character
- Debate/contested
- Conceptual clarification
Main Points Raised
- One participant questions how to construct the arc of a circle as a straight line using geometry, explicitly stating a preference for geometric methods over equations.
- Another participant asserts that an arc of a circle cannot be a straight line, emphasizing the traditional geometric method of using a compass to draw a circle.
- A humorous suggestion is made about using a compass with infinitely long legs to create a straight arc, introducing a fantastical element to the discussion.
- One participant proposes that the original question might relate to constructing a line of length 2πr, but expresses skepticism about the feasibility of such a construction based on historical geometric limitations, such as those related to squaring the circle.
- A follow-up question about the availability of an infinitely long compass adds a playful tone to the discussion.
Areas of Agreement / Disagreement
Participants do not reach a consensus; there are competing views on the feasibility of constructing an arc as a straight line, with some arguing it is impossible and others presenting hypothetical scenarios.
Contextual Notes
The discussion includes references to geometric constructions and historical mathematical problems, such as squaring the circle, which may imply limitations based on classical geometry.
- #2
Mark44
Mentor
- 38,107
- 10,661
You can't. An arc of a circle is not a straight line. The geometrical way to construct a circle is to use a compass, which is not the same as the compass that is used to determine magnetic north. The compass I'm referring to has two legs that are hinged. One leg has a sharp point, and the other has a pencil or pen.mymachine said:
The end with the point is fixed, and the other end is used to draw the circle.
- #3
JJacquelin
- 801
- 35
Mark44 said:
Of course, you can : First, buy a compass with infinitely long legs. Then, go to the infinity. There put the sharp point and turn the compass : Very far from there, the straight arc is drawn.
Last edited:
- #4
Mentallic
Homework Helper
- 3,802
- 95
mymachine might be asking how to construct a line 2\pi r units long given the circle with radius r.
I don't believe it can be done because of a similar argument for why you cannot square the unit circle - i.e. to find a square with side length \sqrt{\pi} by geometric constructions.
I don't believe it can be done because of a similar argument for why you cannot square the unit circle - i.e. to find a square with side length \sqrt{\pi} by geometric constructions.
- #5
Mark44
Mentor
- 38,107
- 10,661
Where do you buy one of these?JJacquelin said:
JJacquelin said:Then, go to the infinity. There put the sharp point and turn the compass : Very far from there, the straight arc is drawn.
- #6
JJacquelin
- 801
- 35
You may ask Alice. She knows a good shop in Wonderland.Mark44 said:
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