Basic Examples 
(2)
 

Using ϕ,
GoldenRatio
or Fibonacci’s rabbit constant, convert points to the algebraic number field
(ϕ)
and build the Fermat triangle:
In[7]:=
ϕ=GoldenRatio;​​points={{0,0},{0,1},{-Sqrt[ϕ],0}};​​Column
[◼]
SqrtSpace
[ϕ,points],Graphics[{EdgeForm[Black],Yellow,Polygon[points]}]
Out[9]=
{{{0,0},{0,0}},{{0,0},{1,0}},{{0,-1},{0,0}}}
———
Using ψ, the supergolden ratio or Narayana’s cow constant, convert points to the algebraic number field
(ψ)
and build the supergolden triangle:
In[26]:=
ψ=Root[-1-
2
#1
+
3
#1
&,1];​​points={0,0},
1
2
,
3
2
,{-ψ,0};​​Column
[◼]
SqrtSpace
[ψ,points],Graphics[{EdgeForm[Black],Yellow,Polygon[points]}]
Out[28]=
{{0,0,0},{0,0,0}},
1
4
,0,0,
3
4
,0,0,{{0,0,-1},{0,0,0}}
Convert back to the original points:
In[16]:=
[◼]
SqrtSpace
ψ,{{0,0,0},{0,0,0}},
1
4
,0,0,
3
4
,0,0,{{0,0,-1},{0,0,0}}
Out[16]=

Properties and Relations 
(2)
 


Neat Examples 
(3)
 
