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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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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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