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Regular Octagon

A regular octagon is an eight-sided polygon with eight equal sides and eight equal angles.

The sum of its angles, derived from the formula (n-2)180°, is equal to 1080°.

Since there are eight equal angles in a regular octagon, each angle is equal to 1080°/n; where n is equal to 8 (the number of sides of the octagon).

1080°/n = 1080°/8
               = 135° (an obtuse angle)

The eight angles of the regular octagon are the following eight directions of an 8-point compass rose (the eight-pointed star): north, east, west, south, north-east, north-west, south-east and south-west.

This means that the regular octagon is the geometric representation of a compass.

In Chinese Cosmology, Bagua (heaven) is an octagon. We know that heaven is the celestial sphere, which means that Bagua is an octagonal representation of the celestial sphere. The celestial sphere, with the cubicle representing the holy city, and the eight directions of the compass are the eight edges of the cube.

Note that an octagon can either be regular or irregular. Though a regular octagon represents balance, peace and harmony, an irregular octagon means conflict and chaos. Unlike a regular octagon, one or more angles and sides of an irregular octagon are different.

The term balance here implies equality between people of different religions, race, tribe, nation and language.

The most kept secret is that the world is a white light and diversity is a rainbow. We all constitute a white light and the diverse colours constituting the rainbow are products of a discriminating medium placed on our path.

White light is heaven. The light is a rainbow on earth because it is separated into the constituent colours of the rainbow by a glass ceiling placed between heaven earth.

Divided, the world is broken and the octagon is Yin or 2 (even number). United, the world is unbroken and the octagon is Yang or 1 (odd number).

This means that Bagua could either manifest as Yin or Yang. Yin is the sky of the underworld and Yang is the sky of the world above.

Yin = 'Yin Yang' (polarity or judgement)

Yang = Yinyang (neutrality or non-judgment)

Judgement or Yin is the irregular octagon symbolising a compass pointing downwards to the south (the ancient world). Non-judgment or Yang is the regular octagon symbolising a compass pointing upwards to the north (heaven or paradise).

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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…

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:
OppositeAdjacentHypotenuse 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 adja…

Mandala

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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