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Question Number 29321 by JI Siam last updated on 07/Feb/18

is it possible to divide an angle into three equal parts?

$$\mathrm{is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{divide}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{into}\:\mathrm{three}\:\mathrm{equal}\:\mathrm{parts}? \\ $$

Commented by Rasheed.Sindhi last updated on 08/Feb/18

Some angles like right angle can be divided into three into three parts using Eucledean tools but not everyangle. Generally it is impossible to trisect an angle using a compass and a straight edge without any mark.

$$\mathrm{Some}\:\mathrm{angles}\:\mathrm{like}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{three} \\ $$$$\mathrm{into}\:\mathrm{three}\:\mathrm{parts}\:\mathrm{using}\:\mathrm{Eucledean}\:\mathrm{tools} \\ $$$$\mathrm{but}\:\mathrm{not}\:\mathrm{everyangle}. \\ $$$$\mathrm{Generally}\:\mathrm{it}\:\mathrm{is}\:\mathrm{impossible}\:\mathrm{to}\:\mathrm{trisect}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\mathrm{using}\:\mathrm{a}\:\boldsymbol{\mathrm{compass}}\:\mathrm{and}\:\mathrm{a}\:\boldsymbol{\mathrm{straight}} \\ $$$$\boldsymbol{\mathrm{edge}}\:\boldsymbol{\mathrm{without}}\:\boldsymbol{\mathrm{any}}\:\boldsymbol{\mathrm{mark}}. \\ $$

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