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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 Number 153 Was Very Prominent and Recognizable in Ancient Greek Culture

In modern speech a person can use the number 3.14 and or the number 9-11 to convey a meaning that is much greater than just the numerical value. And he knows that the average person will associate the appropriate meanings that go with those numbers. And he can be reasonably assured that the person will make the proper association without him having to explain it.

The ancient Greek culture in which John the Evangelist lived, pastored, and wrote his Greek Gospel would not have attached any special meaning to either one of those numbers. They did not yet have the decimal system. Nor did they yet have the horizontal fraction bar. So, they would have had to express fractions as linear ratios. They would not have used 3.14 to refer to π . They would have expressed the value as
π ≈ 3 and 1:7

Today we usually express the values of irrational numbers as below.

π = 3.14…

e = 2.71828…

Now, π does not equal 3.14.  The dots following the numbers above denote that this is just an approximation.  The value of Irrational numbers when expressed using digits can only be expressed by way of approximation when using digits.  In an exact equal equation the numbers would go on forever and therefore, be impossible to write.  See endnote on Irrational Numbers.

See separate article on how
 “153” is an allusion to the wisdom of Archimedes because 9 out of his 10 equations end with that number 153.

Greek  Culture :  √3  and  153

As demonstrated below the √3  figured very prominently in ancient Greek culture.  It is also an irrational number.  So, its value when expressed in digits can only be done by way of an approximation.  The closest approximation of  √3   when using small whole numbers is

http://www.defendingthebride.com/ss/fish/fish_files/image002.gif

And since they did not have the decimal system they did use this approximation as the best possible. It is the most accurate while still being manageable.  This is because mathematical computations become very elaborate when using large denominators. And finding the lowest common denominator is essential to combining fractions.  However, at the time John had written his Gospel since the Greeks also did not yet have the horizontal fraction bar so, they would have written it as

√3   ≈   265 : 153.

So, 153 is essential as the final number when expressing the value of  √3.  


Greek  Geometry and  √3

And the value of  √3  figures quite prominently in geometry which was the core of the Greek cultural view of the world and those things important to them.  Notice below how prominent the equilateral triangle is in Greek culture.  See below. .

The height of an equilateral triangle with a measure of two is √3. 
An equilateral triangle separated in the middle produces two 

30° - 60° - 90° Δ Triangles.
The ratio of sides of a 30° - 60° - 90° Δ Triangle is the following :
1 : 2 : √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

 


Conclusion

Geometry was essential to Greek philosophy. Plato, the philosopher, had an inscription carved over the archway of his Academy:
“Let no one ignorant of geometry enter here.”
All the elements of creation could, in their view, be reduced to these geometric shapes.

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.

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.

 

 

 
The √3 had to be expressed, as close as reasonably possible, in rational terms in order to calculate distances for example. So, the final number in value for √3 was the number 153.

√3 ≈ 265 : 153

Greek philosophy and mathematics was highly valued in ancient Greek culture. So, John knew he could safely use 153 as an allusion. It would bring to mind in his Greek parishioners the great Greek mathematicians and philosophers who made extensive use of that number. That number would bring to their minds Greek wisdom just as surely as 9-11 brings to our minds the events in New York City on September 11, 2001.
 
 
 
End note
An irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction. Therefore, irrational numbers, when written as decimal numbers, do not terminate, nor do they repeat. For example, the number π and √3 are irrational numbers. The number π the starts with 3.141592653589793238462643 … but it goes on forever and ever.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Continue ...

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

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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