You are watching: How do you divide a circle into 3 equal parts

geometry circles area edge

share

mention

follow

edited Mar 18 in ~ 20:50

Andrei

29.3k44 yellow badges2121 silver- badges4646 bronze badges

request Mar 18 at 20:40

JonasHausJonasHaus

21

$endgroup$

1

add a comment |

## 4 answers 4

active oldest Votes

1

See more: Wilson In The Red Badge Of Courage What Happens To Wilson, The Red Badge Of Courage Chapters 13

$egingroup$

Given the edge $ heta$, split by the diameter comprise $B$, consider the complying with diagram:

$overlineBO$ is the line v the center and $overlineBA$ is the chord cutting turn off the lune whose area we wish come compute.

The area the the one wedge subtended by $angle BOA$ is$$fracpi- heta2r^2 ag1$$The area of $ riangle BOA$ is$$frac12cdotoverbracersinleft(frac heta2 ight)^ extaltitudecdotoverbrace2rcosleft(frac heta2 ight)^ extbase=fracsin( heta)2r^2 ag2$$Therefore, the area that the lune is $(1)$ minus $(2)$:$$fracpi- heta-sin( heta)2r^2 ag3$$To acquire the area separated into thirds, we want$$fracpi- heta-sin( heta)2r^2=fracpi3r^2 ag4$$which method we desire to solve$$ heta+sin( heta)=fracpi3 ag5$$whose solution deserve to be completed numerically (e.g. Use $M=fracpi3$ and also $varepsilon=-1$ in this answer)$$ heta=0.5362669789888906 ag6$$Giving us

**Numerical Details**