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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°



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…


Space-time (also axis mundi) is the hexagon inside the hexagram where the three hands of time meet with three dimensional space.

In physics,spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensionalcontinuum. 
The hexagram ABCDEF above is the sum of two triangles: ABC and DEF. The three sides of the triangle ABC are the three hands of time, and the triangle DEF is three dimensional s[ace.

The three hands of time are:

HourMinuteSecond The three manifestations of three dimensional space are: LengthBreadthHeight In triangle ABC, Hour = AB, Minute = BC, Second = CA. In triangle DEF, Length = DE, Breadth = EF, Height = FD.
Time is the circle of the sky, and the clock is the physical manifestation of time. Since the clock is made up of hour, minute, and second, triangle ABC is Time (the clock).
The three hands of time are manifestations of the three persons of the Blessed Trinity.
Hour (AB) = Father Minute (BC) = S…


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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