Insert Equilateral Triangles and Rhombuses into number theory and instantly there is a problem.
Number Theory doesn’t count Equilateral Triangles.
Number to the power of one = number.
n¹ = n
Number to the power of two = number*number.
n² = n*n = Squared.
To the power of three = number*number*number.
n³ = n*n*n = Cubed
To resolve the triangled problem of n¹=n, within these pages, to the power of ¹ is to the power of Equilateral Triangled and has the same sum as the squared function.
1¹=1 triangle,
2¹=1+3=4 triangles,
3¹=1+3+5=9 triangles,
4¹=1+3+5+7=16 triangles…
Cwantum is using 2c¹ as containers
or containment skin for energy.
NOT Solid.
To the power of
a¹+b¹=c¹ has the same solution as
a²+b²=c² with half the area.
Equilateral Triangles doubled to
Rhombi instead of Squared.

Rhombic 6 Star; Order 3.
Rhombic equation in penned Triangles.
a¹+b¹=c¹
5 Triangles + 1+3 Triangles = 1+3+5 Triangles
5 + 2¹ = 3¹
Note: 1 between triangled sides b&c, 2&3.
a¹+b¹+c¹
5+4+9= 18 triangles = 9 Rhombuses.
The smallest Order 1 Rhombus within;
0¹+1¹+1¹= 2 Triangles.
Note: 1 difference between sides a&b, 0&1.
Number 2, the first and only Even Prime Number, the smallest Rhombus.

Inside the three sides of the 3',4',5' Pythagorean Triangle Triangled are 12 equilateral triangle areas.
6 Rhombic areas.
Rhombic 6 Star; Order 3.
Each Rhombus is populated with integers like a Magic Square.
All 8 variations to the magic 3 square are shown linearly from top to bottom.
834 672
159 159
672 834
294 438 276 618
753 951 951 753
618 276 438 294
492 816
357 357
816 492
Cwantum Templates.
Rhombic 6 Star; Order 1.
Cwantum Templates.
RhombicStars; Order 1.
Rhombic 6 Star (1*6).
Number 6.
The area inside the 3,4,5 Pythagorean Triangle.
Six the first Perfect Number.
32 Rhombic 3 Stars
96 Rhombuses 192 Equilateral Triangles.
Cwantum Templates.
RhombicStars : Order 2.
Cwantum Templates.
RhombicStars : Order 2.
36 Rhombic 4 Stars.
30 Rhombic 4 Stars.
24 Rhombic 4 Stars.
18 Rhombic 4 Stars.
Cwantum Templates
RhombicStars : Order 3.
Cwantum Templates.
RhombicStars : Order 4.