Thursday, March 6, 2014

Blog Post #71 - Triangles and Circle of Life – Math fascination


1. Triangles in movies
2. Math refresher on triangles
3.Triangles in religion
   - 3a .  How the hindus relate om to triangles
  -  3b.   What is the meaning of Srichakra (or sriyantra)
   - 3c.    Ancients and Triangles
  -  3d.   Start of David Jews and Triangles
  -  3e    Christianity and Triangles
  -  3f      Islam and Triangle
4 Bermuda Triangle

How do we communicate to a tiny satellite in space and get pictures back to us ?
Religions love triangles - have you seen them?
Can the words you speak create triangles?
What does your GPS have to do with triangles?

The other day my friends daughter showed me this picture and asked find ‘x’.
Anjali's Question

Before I answered I thought I will collect all my thoughts about triangle and post (for the sake of mankind womenkind and be kind!)

1. Triangles in movies

I was thinking about movies and triangle love stories. As a professional movie goer and watcher of magic on screen I am a self declared expert in triangle love stories - 

2 heros 1 heroine - kill one hero or make him a swamiji (no premananda                                    nithyananda style but a real one like Osho?)
2 heros 1 heroine - get an extra heroine in the middle of the story or  twin                                   sister
1 hero   2 heroines - let them marry (hi - Rajini movie veera and other 2                                          wife/lover movies)
1 hero   2 heroines - obvious kill 1 heroine at the hands of the villain
1 hero   2 heroines - ask her to die while delivering a baby which the hero and                               heroine will raise and name her the dead heroine name                                 making this a movie worth a sequel
1 hero   2 heroines - introduce a brother or twin brother 

Always remember triangle love can be solved not the math Trigonometry problem though!! (What is trigonometry? - answer below) 

2. Math refresher on triangles

My red marker showed the answer and she was disappointed as I was supposed to say 5!. If she had marked this on any shaped other than a triangle I would have tried to calculate. The problem is - i have already read this question and lot more useless stuff about triangles and how we over analyze triangles for what it may or may not be! Let the journey begin on these knowledge....  


Basics

(From  http://home.avvanta.com/~math/triangles.html) 

Right angled triangle: Has one 90 degree angle 


Equilateral triangle: All angles are the same (60 degrees)
Isosceles triangle: Has two angles the same and two sides the same
Scalene triangle: Has all three angles and all three sides different
Obtuse triangle: Has one obtuse angle, greater than 90 degrees

The sum of all angles in a triangle is ___________ degrees. 

Answer = 180

Right Isosceles Triangle

Has a right angle (90°), and also two equal angles

Can you guess what the equal angles are? (from http://www.mathsisfun.com/triangle.html) 

Another way to remember

Equilateral - all 3 sides equal
Isosceles - 2 sides equal
Scalene - nothing is equal

Triangles can also have names that tell you what type of angle is inside:

Acute Triangle - all 3 sides have angles less than 90

Right Triangle-Has a right angle (90°)

Obtuse Triangle- Has an angle more than 90°



Right angle triangle form the basis of much useful and much dreaded field of Trigonometry.

How will you send instructions to satellites taking pictures of saturn from earth - use trigonometry. Out in the space the tiny spacecraft can be located anytime from earth using the magic of triangles. You can run but can't hide - I meant from trigonometry. Here are some more info from Wikipedia

Trigonometry (from Greek trigōnon, "triangle" + metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
The field emerged during the 3rd century BC from applications of geometry to astronomical studies.
The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically.

These calculations soon came to be defined as the trigonometric functions and today are pervasive in both pure and applied mathematics: fundamental methods of analysis such as the Fourier transform, for example, or the wave equation, use trigonometric functions to understand cyclical phenomena across many applications in fields as diverse as physics, mechanical and electrical engineering, music and acoustics, astronomy, ecology, and biology.
Trigonometry is also the foundation of the practical art of surveying.
Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. 


Triangles in religion

3a - How the hindus relate om to triangles

My obsession with triangles started a long time ago and specifically with Srichakra.

My house always had this - srichakra and that and that is = Kubera kolam 
Magic square - all squares add to 72 .

7+2 =9 to start with sounds good for a number associated with money but let us turn to science for fun (what else will be turn science for? we use powerful iphones and samsungs which are more powerful than computers that sent man to moon to play angry birds!)

According to wikipedia

In degrees Fahrenheit considered to be room temperature.

The average number of heartbeats per minute for a resting adult.
Percentage of water of which the human body is composed.
The life duration of the ovule is 72 hours.

The axis of the earth moves of one degree every 72 years compared to stars and to the vault of heaven.






Me being a hindu (Whatever it means – the religion was supposed to be Sanatana Dharma now they made this word sound like the hardcode militant hindus instead of the religion- another post later) one of the first places I observe this is in srichakram.

Dr Jenny invented a machine called a Tonoscope which allowed a human voice to vibrate the plate directly.  He had a voice sing 'OM' into a microphone and the result can be seen in mandala image . (according to http://www.unitedearth.com.au/sound.html)

Om Sound creates this image!!!!

 This mean when you say 'Om' you create triangles in sound waves whose final vibrations produce the image above!!!

3b - What is the meaning of Srichakra (or sriyantra)

Inside Homes




Outside Temple 


Cool 3D 


Four isosceles triangles with the apices upwards, representing Shiva or the Masculine.
Five isosceles triangles with the apices downward, symbolizing female embodiment Shakti.

Total 9 triangles

4 up 5 down but looking symmetrical forming 43 triangles

If number of triangles pointing up and down are equal then there is no fun (4 and 4 or 5 and 5) - Balanced means static.

It has 4 for male and 5 for female Imbalance makes this yantra dynamic.
Bindu is the center which is Jive(self),Soul,Spirit or atma (which reminds me of this song http://www.youtube.com/watch?v=hcCzEuNqD6g )


Great Ramana Maharishi pointed to srichakra as a symbol of how mind must be brought back using boundaries.  Adi Shankara wrote Soundarya lahari in which he describes how to create and workshop goddess in this shape. According to Shankara goddess is Srichakra and Sri Chakra is the goddess.


The five downward pointing triangles are Shakti triangles representing senses
SoundSightSmell
TasteTouch
Five sense organs

EarSkinEyesTongueNose
Five Organs of action

HandFeetMouthGenitalsAnus
Five Elements of body
SkinNerveFatBonesFlesh

Upward triangles are Shiva triangles or male energy
Being – ChittaBuddi  IntellectEgo  - AhamkarManas – Mind
Now it makes sense to have people brought back to earth – I told you women are always down to earth!!!




3c- Ancients and Triangles


According to ancient beliefs, an upright equilateral triangle, with one point at the top and two at the base, is a male and solar symbol representing spirit, divinity, fire, life, prosperity and harmony. In contrast, the reversed triangle is female and lunar, representing mother earth, water, rain and grace. 
(Sound familiar male and female theory - Ancients were everywhere the babylonians, mesopotamians, indus folks,greek ,romans and native tribes)
In magic it was seen as representing the element fire (with a downward meaning water)


3d - Star of David Jews and Triangles

When upright and downward triangles are put together, they form the Star of David and symbolize balance and knowledge. 



3e - Christianity and Triangles




Christianity's basic philosophy involves trinity . The God The Son and The Hold Spirit. To represent this concept the following symbol is used thus giving rise to an equilateral triangle. 





3f Islam and Triangle
(According to http://www.salaam.co.uk/themeofthemonth/march02_index.php?l=3) 

In islam - the circle, and its centre, are the point at which all Islamic patterns begin and is an apt symbol of a religion that emphasizes one God, symbolising also, the role of Mecca, the center of Islam, toward which all Muslims face in prayer.
The circle has always been regarded as a symbol of eternity, without being and without end, and is not only the perfect expression of justice-equality in all directions in a finite domain--but also the most beautiful parent of all polygons, both containing and underlying them.

From the circle comes three fundamental figures in Islamic art-
the triangle, square and hexagon.

The triangle by tradition is symbolic of human consciousness and the principle of harmony. The square, the symbol of physical experience and the physical world-or materiality-and the hexagon, of Heaven. Another symbol prevalent in Islamic art is the star and has been the chosen motif for many Islamic decorations. In Islamic iconography the star is a regular geometric shape that symbolizes equal radiation in all directions from a central point. All regular stars -- whether they have 6, 8, 10, 12, or 16 points -- are created by a division of a circle into equal parts. The center of the star is center of the circle from which it came, and its points touch the circumference of the circle. The rays of a star reach out in all directions, making the star a fitting symbol for the spread of Islam.

  



4. Bermuda Triangle

I am not planning to use this post and say I have cracked the mystery of bermuda triangle even though there is a program in netflix which claims to have done it and is in my instant queue to watch. This dreaded triangle has fascinated humans and the lots of people and property have been lost. While the scientist will uncover what Newton and Einstein didn't let's not forget all triangles are not friendly to humans!


Time to stop this post and start using triangles in visio and other microsoft tools.

Triangles are everywhere .. keep looking upward,sideward and onward.

Keep Learning
Sivakumar Manikanteswaran

1 comment:

  1. This is very good information. If you could add more info like the Pythagorean, Phil Jackson's (NBA) triangle, etc will add more value!

    ReplyDelete