Proving an Angle Cannot Be Trisected w/ Compass & Ruler

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Discussion Overview

The discussion revolves around the impossibility of trisecting an arbitrary angle using only a compass and straightedge, with references to specific angles where trisection may be possible. Participants seek resources and proofs related to this geometric problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant states that it has been proven that an angle cannot be trisected with a compass and straightedge, except for specific angles like 90 degrees or 180 degrees.
  • Another participant suggests obtaining an introductory book on algebra and group theory as a resource for understanding the proof.
  • Links to external resources are provided by a participant, which may contain relevant information about angle trisection.
  • A participant reiterates the impossibility of trisection with the tools specified but notes that if marking the straightedge is allowed, any acute angle can be trisected.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which angle trisection is possible, indicating that there is no consensus on the general applicability of the impossibility proof.

Contextual Notes

The discussion does not resolve the mathematical steps involved in the proof of angle trisection impossibility, nor does it clarify the implications of allowing markings on the straightedge.

murshid_islam
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i have read that it has been proven that an angle cannot be trisected using just a compass and a straight-edge (unless it is some specific angle, e.g., 90 degrees or 180 degrees). can anyone tell me where i can find the proof? can anyone suggest any website?
 
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murshid_islam said:
i have read that it has been proven that an angle cannot be trisected using just a compass and a straight-edge (unless it is some specific angle, e.g., 90 degrees or 180 degrees). can anyone tell me where i can find the proof? can anyone suggest any website?

If you are allowed to mark the straight edge with a pencil, then you can certainly trisect any acute angle. Of course, with marking not permitted you cannot.
 

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