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Sacred Geometry of 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°.



Qibla Compass

Qibla compass is a compass design showing clearly that Islam is a direction, and Muslims constitute just one out of the many directions of a compass. Some of the other directions of the compass are Sikhism, Gnosticism, Judaism, Hinduism, Christianity, Atheism, Psychology, Philosophy, Jainism, Zoroastrianism, Buddhism, Taoism, Baha'i Faith, Babism, Rastafarianism, etc.

Qibla compass is designed specifically to help Muslims locate the direction of Mecca and pray facing the Kaaba. Some designs have the word "Mecca" inscribed as the most prominent direction on the compass; others have the image of the Kaaba or a Mosque signifying the qibla (Muslim direction) on the compass.
Although Judaism doesn't have a compass to show Jews what direction to face during prayers, the fact that Jews all over the world pray toward the Temple Mount is an evidence that Judaism is a direction and the Temple Mount is the qibla of the Jews.
Every religion is a compass - the centre of the comp…


The Monad (1) is an encycled dot or point O, representing the Alpha and Omega,  constructed using a compass and a pencil. The center of the circle is the origin or source of all things and the circumference of the circle is the end or crown of everything, such that the Monad is the first and the last; the beginning and the end.

Creation of the Cosmos is construction of geometric shapes. The most important part of the process of creation is the construction of the first day and the last day. The two days were constructed simultaneously.

God constructed the first day when he said "let there be light!" (Genesis 1:3) "NIV"

The light that appeared on the first day of creation of the Cosmos is the halo - a ring of light.

The last day is the seventh day when God rested from his work of creation of the harmonious world. "By the seventh day God had finished the work he had been doing; so on the seventh day he rested from all his work." (Genesis 2:2) 'NIV"…

Mandala, Israel and Geometry of the Axis Mundi

Mandala is a two dimensional representation of the axis mundi: the junction between the physical and the metaphysical. The physical is man or the earth, the metaphysical is God or heaven (sky), and Mandala is where God and man or heaven (sky) and earth are reconciled.

The universe is the sum of heaven and earth.

Universe = Heaven (Sky) + Earth

A mandala (emphasis on first syllable; Sanskrit मण्डल, maṇḍala – literally "circle") is a spiritual and ritual symbol in Hinduism and Buddhism, representing the universe(Wikipedia)
We learnt from the Taiji that the axis mundi represents balance or stability. Therefore the universe of the axis mundi is the orderly universe known as the cosmos, which means that Mandala is a two-dimensional representation of the cosmos.

"mandala" has become a generic term for any diagram, chart or geometric pattern that represents the cosmos metaphysically or symbolically; a microcosm of the universe. (Wikipedia)
Mandala is simply a square and …



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