99.99% Approximation to Angle Trisection

Notes

Fig. 4

Fig. 5

WITH COURTSY OF THE SOFTWARE AUTODESJ AUTOCAD 2016.

Fig. 6 Notes

Fig. 8

Fig. 9

Fig. 7

Fig. 10

Construction Steps: ABC is the given angle.

1. Construct a rhombus SBTB' & extend the lines SB' to C' & TB' to A',
2. Trisect the line BB' at point x & take two points y & z on the extended line SB'C so as B'x = B'y = yz,
3. Draw two circular arcs mn & op with radius By & Bz respectively from the center B.
4. Bifurcate both the arcs at point e & f,
5. Join point e & f intersecting the line SB'C at point r,
6. Now the constructed angle rBC is $\frac{1}{3}$ rd of original angle ABC approximately.

Fig. 12

Invented by: Mahesh R. Bubna Drawing by: Harish V. Shirke. Date: 15.10.2022 WITH COURTSY OF THE SOFTWARE AUTODESJ AUTOCAD 2016.

Contraction Steps: ABC is the given angle.

1. Construct a rhombus SBTB' & extend the lines SB' to C' & TB' to A'.
2. Trisect the line BB' at point x & take two points y & z on the extended line SB'C so as B'x = B'y = yz,
3. Draw two circular arcs mn & op with radius By & Bz respectively from the center B,
4. Bifurcate both the arcs at point e & f, (5) Join point e & f intersecting the line SB'C' at point r,
5. Now the constructed angle rBC is $\frac{1}{3}$ rd of original angle ABC approximately.

Invented by: Mahesh R. Bubna Drawing by: Harish V. Shirke Date: 15.10.2022

Fig. 11

Fig. 13

OF THE SOFTWARE AUTODESJ AUTOCAD 2016.

Contraction Steps: ABC is the given angle.

1. Construct a rhombus SBTB' & extend the lines SB' to C' & TB' to A',
2. Trisect the line BB' at point $x$ & take two points $y$ & $z$ on the extended line SB'C so as $B^{\prime }x=B^{\prime }y=yz$.
3. Draw two circular arcs mn & op with radius By & Bz respectively from the center B.
4. Bifurcate both the arcs at point e & f
5. Join point e & f intersecting the line SB'C at point r,
6. Now the constructed angle rBC is $\frac{1}{3}\mathrm{rd}$ of original angle ABC approximately.

Invented by: Mahesh R. Bubna Drawing by: Harish V. Shirke Date: 15.10.2022

• B

WITH COURTSY OF THE SOFTWARE AUTODESJ AUTOCAD 2016.

Fig. 14

1. Construct a rhombus SBTB' & extend the lines ${\mathrm{SB}}^{\prime }$ to C& TB to A'.
2. Trisect the line BB' at point x & take two points y & z on the extended line SB'C so as B'x = B'y = yz,
3. Draw two circular arcs mn & op with radius By & Bz respectively from the center B.
4. Bifurcate both the arcs at point e & f, (5) Join point e & f intersecting the line SB'C' at point r.
5. Now the constructed angle rBC is $\frac{1}{3}\mathrm{rd}$ of original angle ABC approximately.
6. Construct a bomb's SBTB & extend the lines SB' to C' & TB' to A'.
7. Trisect the line BB' at point x & take two points y & z on the extended line SB'C' so as B'x = B'y = yz,
8. Draw two circular arcs $mn$ & op with radius By & Bz respectively from the center B.
9. Bifurcate both the arcs at point e & f,
10. Join point e & f intersecting the line SB'C' at point r.
11. Now the constructed angle rBC is $\frac{1}{3}$ rd of original angle ABC approximately.

• Contraction Steps: ABC is the given angle.

• Invented by: Mahesh R. Bubna Drawing by: Harish V. Shirke. Date: 15.10.2022

B

WITH COURTSY OF THE SOFTWARE AUTODESJ AUTOCAD 2016.

Fig. 15

Fig. 16