The picture probably explains my inquiry best.I require to discover a method to division a circle right into 3 parts of equal area with just 2 currently that intersect each other on the rundown of the circle.Also I must check, if whatever diameter is in between those lines, likewise splits circles with a different diameter into equal parts.And lastly, and also probably the most an overwhelming question: exactly how do I need to calculate the angle in between x lines the all crossing in one point, so that the circle is split into x+1 components with area = 1/(x+1) of the circle?I tried my best, yet couldn"t even discover a solitary answer or the appropriate strategy to tackle the question... 1

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edited Mar 18 in ~ 20:50 Andrei
asked Mar 18 in ~ 20:40 JonasHausJonasHaus
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Given the edge \$ heta\$, split by the diameter comprise \$B\$, take into consideration the complying with diagram: \$overlineBO\$ is the line through the center and \$overlineBA\$ is the chord cutting off the lune who area us wish to compute.

The area of 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 the the lune is \$(1)\$ minus \$(2)\$:\$\$fracpi- heta-sin( heta)2r^2 ag3\$\$To obtain the area separated into thirds, us 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 achieved numerically (e.g. Use \$M=fracpi3\$ and also \$varepsilon=-1\$ in this answer)\$\$ heta=0.5362669789888906 ag6\$\$Giving us Numerical Details