# The Naked Scientists Forum

### Author Topic: Is this a valid way to trisect an angle?  (Read 2158 times)

#### f.point

• Jr. Member
• Posts: 30
##### Is this a valid way to trisect an angle?
« on: 07/01/2016 10:44:16 »
Required accessories - pencil, compass, unmarked straightedge

Odd proportion angles (there is a proportion of the steam angles) of the element 3 (which may be 5,7,9, ...) and the base angle (which can be any angle which is obtainable by means of compass and straightedge)

The angle CAB    can be obtained with a compass and unmarked ruler, he added angles (each have  ) DAC and EAD, obtained angle EAB is the starting angle

Merge points E (D, C, B) and get a longer ED (DC, CB)

Along the DC from the point C draw is normal that intersects the segment AB, the intersection is a point G

Divider AG and from point G draw a circular arc to a longer EA and H get the point, and the arc GH, join the dots G and H and get along GH

Longer GH (ED, DC, CB) are equal, the arc EB's first circular arc can be made smaller or larger with a constant radius AB, arc GH is the second circular arc can be made smaller or larger with a constant radius AG

INCREASING THE ANGLE
the starting angle EAB add angle FAE get the angle FAB - continued in the next post
« Last Edit: 13/01/2016 14:15:47 by chris »

#### chris

• Neilep Level Member
• Posts: 5337
• Thanked: 65 times
• The Naked Scientist
##### Re: proportioned angles
« Reply #1 on: 07/01/2016 11:19:11 »

#### f.point

• Jr. Member
• Posts: 30
##### Re: proportioned angles
« Reply #2 on: 12/01/2016 15:58:08 »
- previous post was in error -

Required accessories - pencil, compass, unmarked straightedge

basic angle - can be any angle that can be construction using compass and unmarked straightedge, angle CAB

starting angle - sum of 2, 3, 4, 5, ... basic angles , EAB

difference angle - the angle which increases or decreases the starting angle. difference starting angle and the angle of whom do not know the measure , this angle is known to see a procedure HAB

straightedge AB is divided into three parts AF , how we have a basis in the angles starting angle

divider AF from point A the circular arc FG

section straightedge AH the circular arc FG , point I

straightedges FG , ED
--------------------------------------
will continue - if there are errors

#### evan_au

• Neilep Level Member
• Posts: 4106
• Thanked: 245 times
##### Re: proportioned angles
« Reply #3 on: 13/01/2016 08:20:21 »
It is often useful to start a proof with a statement of what you are trying to prove.

This website is about asking and answering questions, so please phrase the thread as a question (even if it is "Is this a valid way to trisect an angle?").

#### f.point

• Jr. Member
• Posts: 30
##### proportioned angles
« Reply #4 on: 20/01/2016 09:53:28 »
basic angle CAB

starting angle EAB consists of the sum of the angles CAB DAC EAD

DC straightedge the normal to the point D , gets the point F

AF divider from point A, we get the point G

divider AB from point F, divider AB from point G, we get the point H

HG divider from point H, creates a circular arc FG

difference angle IAB

section IA and longer circular arc FG is a point J

#### Bored chemist

• Neilep Level Member
• Posts: 8655
• Thanked: 42 times
##### Re: Is this a valid way to trisect an angle?
« Reply #5 on: 20/01/2016 21:10:10 »
In the particular case of 45 degrees it's easy to trisect it.
You construct a triangle of 60 degrees and the difference is 15 which is a third of 45.
However that's not generally very useful.
Being able to construct an angle like 135 degrees by trebling some other angle, then dividing it back into three parts is even less use.

What would be interesting would be a general way of splitting an angle into 3 equal parts.
However that problem has been proven to be impossible.
Why spend time on it?

#### alysdexia

• Sr. Member
• Posts: 121
• Thanked: 3 times
##### Re: Is this a valid way to trisect an angle?
« Reply #6 on: 21/01/2016 13:43:12 »
Instructions unclear.  Pencil stuck in toaster.

Being able to construct an angle like 135 degrees by trebling some other angle, then dividing it back into three parts is even less use.

What would be interesting would be a general way of splitting an angle into 3 equal parts.
However that problem has been proven to be impossible.
Why spend time on it?

Only with a compass and edge, not with a ruler.  What if one uses two or three compasses at a time?

Anyway one could triple any angle, put a set of those angles in a table, then use that table as the ruler.

#### f.point

• Jr. Member
• Posts: 30
##### Re: Is this a valid way to trisect an angle?
« Reply #7 on: 30/01/2016 16:50:15 »
applies this photo

bisection angle DAC is obtained by point J
along AJ
GF section circular arc and along the AJ, obtained point L
AF divider, from the point J, we get the point O
divider AF, from point A circle c1
divider GL, from the point J, the circuit d1, get the points P and Q

#### The Naked Scientists Forum

##### Re: Is this a valid way to trisect an angle?
« Reply #7 on: 30/01/2016 16:50:15 »