I think I trisected an angle. SERIOUSLY.

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In summary, the conversation discusses the topic of trisecting angles using only a compass and straightedge, and how it is impossible to do so. The individual then asks for an explanation, but later realizes their mistake and states that the trisection must be of a general angle, not a specific one. They also mention wanting to learn more about using circles for geometric proofs.
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Angle Trisection

Hello, I know the stuff about how trisecting angles using only a compass and straightedge is impossible. So then could you explain this? I have posted some pictures at http://www.flickr.com/photos/14902182@N04/ which i made using geometers sketchpad.

Edit: Nevermind. I assumed that slope was the same as an angle.
 
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  • #2
The angle you made seems to be [itex]\tan^{-1}3-\frac\pi4\approx26.6^\circ[/itex] which isn't a trisection of the [itex]\tan^{-1}3\approx71.6^\circ[/itex] angle.

More importantly, the trisection must be of a general angle, not of a particular one you decide. I can drop a perpendicular to a line and call it the result a trisected [itex]270^\circ[/itex] angle...
 
  • #3
Nevermind. I assumed that slope was the same as an angle.
 
  • #4
can someone point me to a resource on reading about this whole using circles to do geometric proofs thing. i have no idea how any of these relationships are derived.
 
  • #5
Dad, are you SURE you can't get something for nothing?
 
  • #6
mathwonk said:
Dad, are you SURE you can't get something for nothing?

Is that directed at me?
 
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1. Can an angle really be trisected?

Yes, it is possible to trisect an angle, but it is a complex and challenging mathematical problem that requires advanced knowledge and techniques.

2. How do you know if you have successfully trisected an angle?

In order to prove that an angle has been trisected, one must demonstrate that the angle has been divided into three equal parts using a geometric construction or a mathematical formula.

3. What are some common methods for trisecting an angle?

Some common methods for trisecting an angle include using a compass and straightedge, using a protractor and ruler, and using trigonometric functions.

4. Are there any real-world applications for trisecting an angle?

Trisecting an angle has practical applications in fields such as engineering, architecture, and physics, where precise measurements and angles are crucial for accuracy and efficiency.

5. Why is trisecting an angle considered a challenging problem?

Trisecting an angle is considered a challenging problem because it requires advanced mathematical skills and techniques, and it is not always possible to trisect an angle using basic geometric tools.

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