THE ANGLE OF THE TRIANGLE

I ran into Isosceles. He had a great idea for a new triangle!

Woody Allen

My favourite geometrical shape  was the triangle, easier to draw than the others, in shapes considerably more than the straight line, circle and the quadrangle, with a large number of theorems constructed around it. It was also a liberally displayed geometrical shape in government advertisements during my childhood in 1970s, appearing as the Red Inverted Triangle or the R.I.T. The Hum Do Humarae Do pictorial ad, packets of Nirodh which were 'Especially Packed for Government of India"  alongside the picture of a couple in silhouetted anonymity moving away for a quiet, almost sinful, coitus, and Mala-D, the pill. The R.I.T accompanied all the Family planning and contraceptives' ads on TVs. Whenever it would float on the TV screen, it would cut the titters and giggles in the family TV Room and evoke a  muted consternation amongst the elders in the families whose 5000 year rich civilisation would be found impotently inadequate to tackle this triangular affront.

I used to doodle feverishly on the last pages of school exercise books to draw a star by superimposing two triangles pointed in opposite directions to create a hexagon and later became an expert in drawing the pentagram with pointed triangles without lifting the pen. The three dimensional or Solid Geometry cousin of the triangle , called a tetrahedron, was also a favourite due to two things - the Egyptian pyramids in my history book and the prisms we used in Fr. Kirsch's Physics laboratory to study refractive index. 

It took Sauniere's blood etched pentagram in Da Vinci Code for me to realise the deeper symbolism of what were just geometrical shapes I doodled more than drew. Place the triangle differently , inverted or pointed  and it means different things, astoundingly similar across cultures and religions, though . Some may call  those differences as opposites though in my view  they are complementary to each other: male - female; lunar-solar;yoni-lingam;shakti-shakta;water-fire;passive-active;cave-mountain; chalice-sword; mother-father, etc.  One sarkari babu Deep Tyagi tweaked this age old theological symbol of inverted triangle by painting it red to design the symbol of India's family planning , health and contraception services. But he was not the only person who painted the triangles. The Nazis had painted them much earlier in different colours in their concentration camps to classify the prisoners, these colours of repression were adopted by different repressed groups-  the lesbians painted it black as a symbol of defiance against repression and discrimination, the gay painted it pink and the Illuminati rainbow which the gays later adopted as well. 

Little did I know then that the superimposition of the inverted (water) and point-up ( fire)  triangle which formed a hexagon was one of the most important symbols  of balance and Divine Union.  In western tradition, it was called the Seal of Solomon while in Hindu religion, the hexagram or shatkona  is a combination of Shiv kona , the symbol of Lord Shiva, representing elements of fire and Shakti kona, representing the element of water , together they represent union of male and female. The Pythagoreans called the  pentagram hugieia or "health"  and used it as a greeting. To the early Christians it symbolised "five senses" or " five wounds of Christ", was used in Renaissance and post Renaissance occultism and in modern times even adopted by the Bahas for whom it is Haykal or temple.

The symbolism of the three dimensional cousins of the triangle and hexagram , the tetrahedron and the  Star Tetrahedron  respectively,  is no less interesting. The tetrahedron is one of the Platonic solids and is the most fundamental building block of life on earth- being the geometrical shape of the water molecule! It symbolises harmony and equilibrium since the four points in a tetrahedron are equidistant from one another.One form of the tetrahedron, the pyramid , is linked to creation itself, almost like a primeval mound,  as well to Fire and Ascension. The pyramid is the perfect shape for channelling energy. You pour water water over a sphere or a cube and it dribbles down unevenly but do it on a pyramid and it will flow down evenly- so now you understand the reasons behind the conical hats of witches and pyramid priestesses.

If the tetrahedron is the shape of the water molecule  which supports life, the Star or Double Tetrahedron is the shape of the new molecule of life, the Silicon which stores the data so efficiently in the computer. It is also the shape of the Egg of Life which is a stage reached after the binary division of a fertilised cell from 2 to 4 to 8, the stage through which all every single life on Earth must pass through.It also models the energetic body of the human being, the blending of Heaven and Earth, Male and Female, and was known in the esoteric knowledge of the Egyptians as Mer-ka-ba, a rotating light that would take the spirit and the body from one world to another.In Hebrew it means the Chariot of God. It is also known as Star of David , the symbol of Judaism. It represents the innermost law of the physical world - the inseparable relationship between two complimentary halves.

The triangle becomes important as symbol also  because its  three sides represent the number three, which as emblematic of the Trinity, has always been considered a Sacred number. Even though this concept was used very early in germatia, or the ancient Babylonian/ Hebrew numerology, it is meaningful to many groups. It is abundantly featured in the Celtic culture as triskelion, triquetra and various other trinity Celtic knot motifs, it represents the Christianity trinity of Father, Son, and Holy Ghost united in a single godhead , the Hindu Triad of Brahma, Vishnu, and Siva, and in mythologies of Assyrians, Phoenecians, Greeks, Scandinavians, and even Chinese and Japanese. To the Greeks , the triangle is seen as the delta glyph and is symbolic of a doorway. For the Egyptians , the right angle triangle was the symbol of universal nature; the base being Osiris ( male), ; the perpendicular Isis ( female); and the hypotenuse Horus ( son) or the product of that male-female principle. This  inspired Pythagoras's work in geometry and spawned a whole lot of historical and cultural trinities : Waxing, Waning, Full; Thought, Feeling, Emotion; Mother, Maiden, Crone, etc. 

And  if you think the triangle would be just what the Egyptians and Pyathagoreans  made of it or what the symbolists thought it to be, you are mistaken. Triangles are everywhere . They are there in literature, not only in the form of love triangles which were peppered in Shakespearean sonnets and countless other literary works, but more fundamentally as a prescriptive tool for good and effective writing in the form of Rhetorical Triangle which exhorts a balance of the Writer with the Context and the Audience through a trinity of Aristotelian  rhetorical techniques of ethos, logos and pathos. Actually, life is itself an eternal triangle and relationship triangles are an archetypal dimension of human life which we generally tend to handle badly when they enter our lives - being usually evocative of very painful memories. Not all triangles involve adult sexual relationship, though. Most relationship triangles are fundamentally  those involving parents and children or Freud's Oedipal Triangle ( not necessarily sexual in adult sense but more do with emotional fusion), some also involve friendships, and quite a few involve non- human companions which could be one partner's dedication to a pet or artistic involvement or even golf which has led to the coinage of the term  "golf widows" !

Compact touristy destinations are also marketed as ' triangles 'like the Delhi- Agra- Jaipur Golden Triangle, a term which  is  also an infamous drug producing  tri-junction of Laos, Myanamar and Thailand.Many geographical areas have been dubbed as Triangle of Death: an area south of Algiers during the Algerian Civil War; an area to the south of Baghdad during the Iraq War ; and even an area in southern Italy with an unusual high number of deaths caused by dumping of toxic waste. Another triangle which has been the theatre of much tragedy and even research has been the Bermuda Triangle. Paradoxically, a term which has gained currency in the spate of earthquake related deaths in recent years is actually called the Triangle of Life, a controversial theory , propounded by one Doug Copp, about how to survive a major earthquake , typically promoted via viral emails and  roundly criticised by  American Red Cross and United States Geological Survey.

The juggernaut of the triangle has carried on down the ages. It is there in your bicycle , it was liberally used in the modern art of Cubism and there is  a musical instrument which even goes by the name triangle- an idiophone type of musical instrument , a steel or copper bar shaped like a triangle. The Summer Triangle, an astronomical asterism involving an imaginary triangle drawn on the northern hemisphere's celestial sphere, was actually the Navigator's Triangle in the days before the INS, GPS and other electronic/mechanical equipment took their place in military aircraft.The Red Inverted Triangle of Deep Tyagi,  printed on packets of contraceptives, is not the only triangle which has entered our bedrooms. To spice up coitus from routine missionary position, bereft as it was of the zeal which is otherwise associated with missionaries ,  the Kamasutra had suggested a  more vigorous and  frenetic Glowing or Torrid Triangle which required activity by both the partners!

As a Boy Scout, I remember preferring  the pyramidal heap and the triangular layered arrangement of firewood over the rectangular as the latter tended to be more unstable. Ditto it has been with architecture- while rectangles have been the most popular and common form for buildings it is the triangle, more difficult to use conceptually,  which provides a great deal of strength. Push a rectangle at a corner and it loses shape to become a parallelogram , but a push or a shove at the more stable and rigid triangle  and the shape doesn't result in that. It has been a part of architecture,  used as a pediment and placed above above the entablature atop the columns  since the Hellenic Age and used extensively in churches and public buildings.  The triangular or planar truss and the space frame or tetrahadal  truss have been used in many engineering structures like bridges, beams, buildings, towers etc, not only for their strength but also to reduce cross sectional area for wind resistance. 

A few iconic buildings have actually been in the shape of a triangle like the Flatiron Building in NewYork City and now mathematics has totally revolutionised architecture with triangulation  of surfaces resulting in construction of such buildings as the Gherkin in London. You could be wondering at the sheer impossibility of a triangle to make its presence felt as a design of building, used as you are to the rectangular shape which accommodates your furniture much better. But if you ask me, much earlier the triangle did something which could have been thought most improbable a century ago. 

Unlike the square peg which cannot fit  in a  round hole,  the triangle triumphed significantly when it lent its versatility to cover a round object in the form of one of the truly modern women wears- the bikini! Designed in 1946 by Parisisan engineer Louis Reard, and made famous by Brigitte Bardot, Raquel Welch, Ursula Andress, et al, it was a kind of a bombshell, which if you ask me was only to be expected from an apparel which was named after a place where the atomic bomb was tested- the Bikini Atoll.

While you may gawk at the ouvre and oomph of the triangular bikini, you would definitely wonder as to why the bikini is such a red rag  to the sartorial and moral Talibanic bulls. To begin with, the Holy See  could see no merit in it declared the design sinful. I can't quite give a reason for such scathing criticism but it could probably also lie in  the significance of some symbols  which the design of the bikini might  approximate and evoke- I would illustrate with the pointed reference to the bikini  as triangle within a circle with a point inside in the triangle. To the occult group Lucy Trust, the dot inside the circle denotes Sanat which is an  anagram of Satan while the  eye in the Eye of Providence symbol of the Illuminati is deemed to be the representative of Satan. But amidst these Satanic verses aimed at it, the bikini marches ahead, fuelling spin off industries like bikini waxing and  sun tanning. 

Time to play the triangle!!