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Isosceles Right Triangle

An isosceles right triangle is a triangle with two 45° angles, a right angle and two equal sides. The side opposite the right angle is the base and the two equal angles are the base angles. The ratio of the sides opposite the two 45° angles is 1:1.

Isosceles right triangle is the product of an  isosceles triangle and a right triangle.

The three sides of the isosceles right triangle correspond to the following three sides of a right triangle:
  1. Opposite
  2. Adjacent
  3. Hypotenuse
The three sides are equal to the three persons of the Blessed Trinity as follows:

Opposite = Father (First Person)
Adjacent = Son (Second Person)
Hypotenuse = Holy Spirit (Third Person)

The linear magnitude of each person of the Blessed Trinity can be calculated via any of the six trigonometric ratios if either the angle facing the opposite side or the angle facing the adjacent side is known.

Let the angle facing the opposite side be Y. The side opposite the right angle is the hypotenuse and the remaining side is the adjacent. 

Therefore we can calculate angle Y via any of the following three of the six trigonometric ratios:

Sin Y = Opp/Hyp
Cos Y = Adj/Hyp
Tan Y = Opp/Adj


Sin = Sine
Cos = Cosine
Tan = Tangent
Opp = Opposite
Adj = Adjacent
Hyp = Hypotenuse

A side of the right triangle can be calculated via Pythagorean theorem if the other two sides are known.

Pythagorean theorem states that the square of the hypotenuse of a right triangle (a right-angled triangle) is equal to the sum of the square of the opposite side and the square of the adjacent side.

|Hyp|² = |Opp|² + |AdJ|² (Pythagorean theorem)

Since the Father is one person, Opp (the vertical line) is equal to 1. And since the Son is one person, Adj (the horizontal line) is equal to 1. The Holy Spirit is the Hypotenuse whose magnitude is calculated via Pythagorean theorem as follows:

Opp (Son) = 1
Adj (Father) = 1

Substituting 1 and 1 into the Pythagorean theorem,
|Hyp|² = 1² + 1²
          = 1 + 1
          = 2

Hyp = 2

Therefore the isosceles right triangle is a right-angled triangle whose opposite and adjacent sides are equal or an isosceles triangle that has a right angle.

The angle Y facing the opposite side and the angle X facing the adjacent side can be calculated via Sin Y = Opp/Hyp and Sine X = Opp/Hyp.

Opp = 1 (Father)

Hyp = 2

Sin Y  = Father/Holy Spirit
           = 1/2
       Y = 45°

Opp = 1 (Son)

Sin X = Son/Holy Spirit
          = 1/2
       X = 45°

This means that the base angles of the isosscles right triangle are equal to 45°.



Four-dimensional Space

In harmony, 4-D space (four-dimensional space) is a tesseract comprised of an outer large cube representing 3-D space and a small invisible inner cube representing the fourth dimension.

The two cubes are space and time, such that the tesseract is spacetime.

Spacetime implies equilibrium between space and time.

A cube is made up of the following three equal sides:

1. Length (l)
2. Breadth (b)
3. Height (h)

The three sides are three dimensions of space such that the cube represents three-dimensional space.

Time (the fourth dimension) has the following three sides:

1. Hour
2. Minute
3. Second

Time is the reflection of space, which means that time is a cube in another dimension.

Since length is l, breadth is b and height is h, hour is l', minute is b' and second is h'. l', b' and h' are reflections of l, b and h respectively, such that time is the image of space.

There is a mirror between time and space. When a cube is placed in front of a mirror, the image in the…

Yinyang in the Holy Bible

Yinyang is the pillar of cloud and the pillar of fire described in Exodus 13:21-22. The pillar of cloud is darkness (Yin), the pillar of fire is light (Yang), such that the two pillars are Yinyang.

"During the day the LORD went in front of them in a pillar of cloud to show them the way, and during the night he went in front of them in a pillar of fire to give them light, so that they could travel night and day. The pillar of cloud was always in front of the people during the day, and the pillar of fire at night." (Exodus 13:21-22)

Note that Yinyang is not 'Yin Yang'. Yinyang implies unity or reconciliation and 'Yin Yang' means division or conflict.

The Israelites left Egypt as a united people, which implies that their journey from Egypt to the Promised Land was governed by the force of Yinyang (not Yin Yang).

Yinyang is only one word. Yin Yang are two words.

Yinyang = 1 (unity or neutrality)

Yin Yang = 2 (division or polarity)

Day and night are two equal hal…

Circumscribed Circle

In geometry, a circumscribed circle (also circumcircle) of a polygon is a circle enclosing a cyclic polygon such that the circumference of the circle passes through all the vertices of the polygon.

All triangles and all regular simple polygons are cyclic polygons, which means that equilateral triangle, regular cyclic quadrilateral, regular pentagon, regular hexagon and regular octagon are cyclic polygons.

Recall that an octet is a regular octagon comprised of regular hexagons and equilateral triangles. Since these three geometric shapes are cyclic polygons, an octet is a circle comprised of circles.

In logical reasoning, the intersection between two equilateral triangles is a conjunction between two circles or two rings. Two circumscribed equilateral triangles are merged to form a circumscribed regular hexagon, and eight circumscribed regular hexagons are fused to form a circumscribed regular octagon.

Since the three geometric shapes are circumscribed polygons, each one can be substi…



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