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Sum of the Angles of an n-sided Polygon

The sum of the angles of an n-sided polygon is (n - 2) × 180°; where n is equal to the number of sides of the polygon.

Example: A pentagon is a 5-sided polygon, and the sum of its angles is equal to (5-2)×180°. 5 - 2 = 3 and 3 × 180° = 540°, which means that the sum of the angles of a pentagon is equal to 540°.

In harmony, a standard pentagon is a regular pentagon. The beauty about a regular pentagon is that all its sides are of equal magnitude. After all, the harmonious world is about equality and balance.

Since there are five angles in a pentagon, each angle of a regular pentagon is equal to the sum of the angles of a regular pentagon divided by the number of sides of the pentagon.

Let the sum of the angles of the regular pentagon be S, the number of sides n and each angle A.


A = S/n

Since S = 540°,
n = 5 and
A = 540°/5
   = 108°

Question 1:
what is the sum of the angles of a regular hexagon?

A hexagon is a 6-sided polygon, which means that n = 6.

Sum of angles of a polygon = (n - 2) × 180°.

Sum of angles of a regular hexagon = (6 - 2) × 180°

= 4 × 180°
= 720°

Question 2:
What is the magnitude of each angle of a regular octagon?

An octagon is an 8-sided polygon, which means that n = 8.

S (Sum of the angles of a polygon) = (n - 2) × 180°.

Substituting 8 for n,
S = (n - 2) × 180°
   = 1080°

A (an angle) = S/n
                       = 1080°/8
                       = 135°



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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