### Isosceles Right Triangle

 Triangular representation of the Blessed Trinity. Photo: Marthworld

Isosceles right triangle is the triangular structure of the Blessed Trinity whereby the two congruent sides are the axis of the Father and the axis of the Son respectively, and the hypotenuse is the Holy Spirit.

Congruent means agreement or harmony; which implies that the Father (the Eastern Orthodox Church) and the Son (the Catholic Church) are in harmony in the Blessed Trinity.

Jesus presented the two-dimensional structure of the Holy City (the New Jerusalem) as follows:
And the city lieth foursquare, and the length is as large as the breadth" (Revelation 21:16) "KJV"

Length = Axis of the Son
= X-Axis
= AC (Horizontal Line)
= Catholic Church

Breadth =  Axis of the Father
= Y-Axis
= BC (Vertical Line)
= Eastern Orthodox Church

And the city lieth foursquare: the city is a square made up of four smaller squares

This means that the holy city is a square whose breadth (the Father) is at right angle to its length (the Son).

We know that the Father is David:
I, Jesus, have sent my angel to give you this testimony for the churches. I am the Root and the Offspring of David, (Revelation 22:16) "NIV"

I = Jesus

Offspring of David = Son of David

David's kingdom is the Twelve Tribes of Israel. Since Jesus is the Son of David, Jesus' kingdom is the son of David's kingdom. The 12 Disciples constitute Jesus' kingdom; therefore,

Father = 12 Tribes of Israel
Son = 12 Disciples of Jesus

The Eastern Orthodox Church is the 12 Tribes of Israel lifted from the surface of the earth to heaven, the Catholic Church is the 12 Disciples of Jesus in heaven, and the Holy Spirit (the Pentecostal Church) is the resultant of the Father (the 12 Tribes of Israel) and the Son (the 12 Disciples of Jesus).

The relationship between the Father, the Son, and the Holy Spirit is summarised into the Isosceles Right Triangle ABC above. The Son (the length) is AC, the Father (the breadth) is BC, and the Holy Spirit (the Hypotenuse) is AB.

Number of Tribes of Israel = 12
Number of Disciples of Jesus = 12

Therefore line BC (the Father) is equal to 12, and line AC (the Son) is equal to 12.

Line AB (the Holy Spirit) is calculated by Pythagoras Theorem as follows.

It appears, in fact, from this, as well as from the extant fragments, that the first book (from Philolaus) of the work contained a general account of the origin and arrangement of the universe. The second book appears to have been an exposition of the nature of numbers, which in the Pythagorean theory are the essence and source of all things.Wikipedia

|AB|2 = |BC|2 + |AC|2                               (Pythagoras Theorem)
|AB|2 = 122 + 122
= 144 + 144
= 288
AB    = (288)
= (144 × 2)
= 122
= 12 × 1.41
= 16.92
= 17

1 = First (the first day of creation)
7 = Last (the last day of creation)

Therefore,
17 = the First and the Last
= the Beginning and the End
= the Alpha and the Omega
I am the Alpha and the Omega, the First and the Last, the Beginning and the End. (Revelation 22:13) "NIV"

Since AB is equal to 17, the Hypotenuse (the Holy Spirit) is the Father BC and the Son AC.

The simplest structure of the Blessed Trinity is calculated as follows:
BC (Father) = 12
AC (Son) = 12
AB (Holy Spirit) = 122

Dividing the magnitudes of the three persons of the Blessed Trinity by 12,
BC\12 = 12\12
= 1
AC\12 = 12\12
= 1
AB\12 = (122)\12
= 2

This means that the simplest structure of the Blessed Trinity is an Isosceles Right Triangle whose length AC (the Son) is equal to 1, breadth BC (the Father) is equal to 1, and base AB (the Holy Spirit) is equal to 2.

2 is the root or the foundation of the New Jerusalem, and 2 inside 2 is the Father and the Son. The Father (the First) is equal to 1, the Son (the Last) is equal to 1, and the Father and the Son are equal to 1 + 1 = 2.

The three angles of the Isosceles right triangles are calculated as follows:

Let angle ABC equal to A (Alpha).

Opposite = AC = 1
Hypotenuse = AB = 2

Sine A = Opposite/Hypotenuse
= AC/AB
= 1/2

A = Sine-1(1/2)
= 450

Let angle CAB equal to Ω (Omega).

Angle BCA = 900,               (Right Angle)

Therefore,
A + Ω + 900 = 1800       (Sum of angles of a triangle)
Substituting 45for A,
450 + Ω + 901800
Ω + 1350  1800
Ω = 1800  - 135
=  450

Since Alpha (A) = 45, and Omega (Ω) = 450
Alpha (A) and Omega (Ω) = 4545 900

This means that 'the Alpha and the Omega' is at the right angle where the Father (the vertical line) and the Son (the horizontal line) meet in the Isosceles Right Triangle representing the Blessed Trinity.

The twelve tribes of Israel and the twelve disciples of Jesus are congruent at the Alpha and Omega.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. - Wikipedia
The Omega (angle CAB) is the mirror image of the Alpha (angles ABC). Therefore Jesus (the 12 Disciples) is the image and likeness of the Father (the 12 Tribes of Israel).