I think I trisected an angle. SERIOUSLY.

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SUMMARY

The discussion centers on the impossibility of trisecting an angle using only a compass and straightedge, a well-established theorem in classical geometry. The user initially believed they had trisected an angle using Geometer's Sketchpad but later realized their mistake, confusing slope with angle measurement. The specific angles mentioned include \(\tan^{-1}(3)\) approximately equal to 71.6 degrees and its incorrect trisection yielding approximately 26.6 degrees. The user seeks resources to better understand geometric proofs involving circles and angle relationships.

PREREQUISITES
  • Understanding of basic trigonometry, including tangent functions.
  • Familiarity with classical geometric constructions using compass and straightedge.
  • Knowledge of angle measurement and properties.
  • Experience with geometric software tools like Geometer's Sketchpad.
NEXT STEPS
  • Research the impossibility of angle trisection in classical geometry.
  • Learn about geometric proofs involving circles and angles.
  • Explore advanced trigonometric concepts, particularly tangent and its applications.
  • Investigate the use of Geometer's Sketchpad for visualizing geometric constructions.
USEFUL FOR

This discussion is beneficial for students of geometry, educators teaching geometric principles, and anyone interested in the limitations of classical constructions in mathematics.

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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.
 
Last edited:
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The angle you made seems to be \tan^{-1}3-\frac\pi4\approx26.6^\circ which isn't a trisection of the \tan^{-1}3\approx71.6^\circ 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 270^\circ angle...
 
Nevermind. I assumed that slope was the same as an angle.
 
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.
 
Dad, are you SURE you can't get something for nothing?
 
mathwonk said:
Dad, are you SURE you can't get something for nothing?

Is that directed at me?
 
Last edited:

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