An attempt to create a model of Weave a Home with respect to traditional geometry

1. An Attempt to Create a Proportional
Model of “Weave a Home”
Sufian Ahmad

2. Platonic Solids and Regular Polygons
• Regular polygons are geometric shapes that
can be created by dividing a circle into a set of
sections

3. Platonic Solids and Regular Polygons
• A hexagon for example, is created by
connecting the intersection points (in red
circles) for three circles and the horizon line

4. Platonic Solids and Regular Polygons
• Basic trigonometry is applicable to regular
polygons, they are basically right angled triangles
and by applying Pythagorean theorem you can
calculate the length of the side (in green)
• Given that we start from a unit
circle (r = 1) in the figure to the right
the height of the rectangle is:
• 12 + X2 = 24
•X = √3 hence giving us
the root 3 ratio

5. Mystic Interpretations of Geometry
• Ancient civilizations believed that geometric
properties in platonic solids and polygons are
the same values governing the whole universe
• Because these ratios or proportions are very
common in nature, they look beautiful to the
human eye
• Therefore, it became a traditional “best
practice” to follow these proportions in design

6. Mystic Interpretations of Geometry
• Ancients believed that the universe was created the
same way we created the hexagon in slide 3, by
intersecting circles (the absolute world and the relative
world)
• That concept of intersecting world is symbolized by
the flower of life
• Below is another important symbol, Metatron’s Cube
• Metatron’s Cube is a hexagon with all the platonic
shapes appearing inside it, which symbolizes the
creation of the world

7. Root Ratios
• Root ratios are the
relationship
between the sides
of a proportional
rectangle and the
sides of another
proportional
rectangle created
inside it
• Lines A and B in
figure (green lines)

8. Root Ratios
• To create interesting shapes and ornamentations, geometers
create complex grids by repeating basic proportional divisions
over and over
• An example of a golden ratio grid creating an ornamentation

9. “Weave a Home” Grid
• The basic golden ratio is a simple relationship
between two lengths, which is not very
beneficial to create an interesting shape
• If we were to only use the basic ratio, we will
always have shapes that are divided into two
thirds

10. “Weave a Home” Grid
• To get a close match for the basic “Weave a
Home” design (10 bending points on frame) we
have to use the full range of ornamentation grids
• By full range of ornamentation grid, I mean
instead of just using the golden ratio I will extract
ratios from the pentagon and the decagon (10
sides) grid
• A process is similar to traditional ornaments
created (slide 8)

11. Animated Grid
• The animation below demonstrates how a golden ratio
ornamentation lines and parts all fit a repeated decagon grid

12. Polygenic grids and Values
• The red lines (pentagon
sides) gradually get
smaller and smaller
• The golden ratio governs
the relationship between
red sides
• Plotting the lengths of
the red sides onto a
line chart will give us
the ratio curve

13. The Roots Curves
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8
golden
root three
root 2
root 3 sides
pentagon sides
10 sides

14. Different Roots and polygons
A repeated 12 sided polygon (root 3) A repeated sqaure (root 2) A repeated pentagon (golden)
A repeated 10 sided polygon (golden)A repeated hexagon (root 3)

15. From Sides to Angles
• To divide a right angle into
8 proportional angles
rather than proportional
lengths I compared the
lengths of 8 sides of a
repeated polygon grid to 8
angles that sum up to 90
• E.g. A series of Hexagon
side lengths with a sum of
(visualized in the next
slide)
• A simple conversion to
sum 90 will give the right
column
Lengths Angles
470.094045 25.00313694
352.570534 18.75235272
264.4279 14.06426451
198.320925 10.54819838
148.740694 7.911148802
111.55552 5.933361575
83.66664 4.450021181
62.74998 3.337515886
Sum = 1692.126238 Sum = 90

16. Hexagon Grid Values

17. Hexagon Grid Values
•The values of 18 sided
polygon are plotted as
dotted lines vs. 16 sided
polygon in solid lines
•We have selected the 16
sided polygon convertion