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DEFENDING  THE  BRIDE

 

 
Print Free Pamphlet - - Brief Summary

Sections :

Introduction
Church Fathers : Sts. Jerome, Augustine, Gregory the Great, Cyril A.
No Reason ?
Why Church Fathers’ Answers Could Not Be John’s
Problems with Square Root of 3 Answer
Context Points to the Answer : An Explanation That Works
Archimedes : Context of Time and Place
Greeks and Wisdom
Fish
Calculating the Measure of the Fish
John’s Purpose
Why Church Fathers Did Not (could not?) Give John’s Idea
Conclusion

 

The Solids named after Plato and Archimedes

All of these solids are mathematically associated with √3

In Plato’s Timaeus he explains the world according to geometric shapes.

Platonic Solids

There are five Platonic solids.  They are named for the ancient Greek philosopher Plato who hypothesized in his dialogue, the Timaeus, that the classical elements were made of these regular solids

 
 

Tetrahedron

Cube

Octahedron

Dodecahedron

Icosahedron

Four faces

Six faces

Eight faces

Twelve faces

Twenty faces

Tetrahedron.svg

Hexahedron.svg

Octahedron.svg

Dodecahedron.svg

Icosahedron.svg

 

Three of the five Platonic Solids use equilateral triangles.


Plato and The Elements

In Plato’s Timaeus he claims that the minute particle of each element had a special geometric shape: tetrahedron (fire), octahedron (air), icosahedron (water), and cube (earth).

 
 
 
Tetrahedron.gif Octahedron.gif Icosahedron.gif Hexahedron.gif  
Tetrahedron
(fire)
Octahedron
(air)
Icosahedron
(water)
Cube
(earth)
 
 

 

See Palto’s Timaeus.

 

The Timaeus makes conjectures on the composition of the four elements which some ancient Greeks thought constituted the physical universe: earth, water, air, and fire. Timaeus links each of these elements to a certain Platonic solid: the element of earth would be a cube, of air an octahedron, of water an icosahedron, and of fire a tetrahedron.

Each of these perfect polyhedra would be in turn composed of triangular faces,  the 30-60-90 and the 45-45-90 triangles.


Thirteen Archimedean Solids

Equilateral triangles, and therefore, the value of √3 figure prominently in the Thirteen Archimedean Solids

Nine of the thirteen Archimedean solids have some equilateral triangular faces:
truncated cube (1), truncated tetrahedron (2), truncated dodecahedron (3),
cuboctahedron (8), icosidodecahedron (9), (small) rhombicuboctahedron (10),
(small) rhombicosidodecahedron (11), snub cube (12) and snub dodecahedron
An Archimedean (semiregular) solid is a convex polyhedron composed of
two or more regular polygons meeting in identical vertices.
Archimedean Solids

Each of these perfect polyhedra would be in turn composed of triangular faces the a 45° - 45° - 90° Δ Triangle and the 30° - 60° - 90° Δ Triangle. These shapes also make extensive use of the equilateral triangle, 60° - 60° - 60° Δ Triangle.

The height of this equilateral triangle is one half times the length of the side times √3.   ( ˝  x  2  x  √3  =  √3 )

This triangle can be divided into two identical 30° - 60° - 90° Δ Triangles. And in the length of the longer leg of this triangle is equal to the length of the shorter leg times √3.

Consider below the equilateral Triangle ABC , a 60° - 60° - 60° Δ Triangle.
And the scalene right Triangle ABD, a 30° - 60° - 90° Δ Triangle.
 

 

 
 
 
 

See :

The Number 153 Was Very Prominent and Recognizable in Ancient Greek Culture

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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