proportioned angles

Jan 2012
80
0
Required accessories - pencil, compass, unmarked straightedge


slika 1.png
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 \(\displaystyle 45 ^ o\) (which can be any angle which is obtainable by means of compass and straightedge)


The angle CAB \(\displaystyle 45 ^ o\) can be obtained with a compass and unmarked ruler, he added angles (each have \(\displaystyle 45 ^ o\)) DAC and EAD, obtained angle EAB \(\displaystyle 135 ^ o\)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 \(\displaystyle 15 ^ o\) get the angle FAB \(\displaystyle 150 ^ o\) - continued in the next post
 
Jan 2012
80
0
- previous post was in error -

slika 1.png

Required accessories - pencil, compass, unmarked straightedge

basic angle - can be any angle that can be construction using compass and unmarked straightedge, angle CAB \(\displaystyle 45 ^ o\)

starting angle - sum of 2, 3, 4, 5, ... basic angles , EAB \(\displaystyle 135 ^ o\)
sum angles CAB \(\displaystyle 45 ^ o\) DAC \(\displaystyle 45 ^ o\) EAD \(\displaystyle 45 ^ o\)

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 \(\displaystyle 30 ^ o\)

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
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will continue - if there are errors
 
Jan 2012
80
0
basic angle CAB \(\displaystyle 45^o\)

starting angle EAB \(\displaystyle 135^o\) consists of the sum of the angles CAB \(\displaystyle 45^o\) DAC \(\displaystyle 45^o \)EAD \(\displaystyle 45^o\)

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 \(\displaystyle 30^o\)

section IA and longer circular arc FG is a point J

slika w.png
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
What was your purpose in posting this? Do you have a question? You are doing a construction but you do not say what you are trying to construct.
 
Jan 2012
80
0
applies this photo
slika 3.png
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
slika 3a.png
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
So you are just going to keep chattering without telling us what you are talking about?
 
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