Have you noticed that all statues (particularly old ones) are raised? Not only to be seen from far afield but also to assert the importance of the person or object depicted. They are raised on a platform, which is in fact a parallelepiped.
Power and platforms go together.A king’s throne sits on a platform. Sometimes the platform is high and reachable by stairs. The more authoritative the leader, the higher the platform. Old museums, universities, banks are raised from the ground by almost one floor. Their platform is disguised as stairs.
In an auditorium (that is a large space for performances and lectures) the speaker stands on a platform called stage. This helps the audience to see better but it also empowers the speaker and formalize the encounter (that is it makes it more sober and serious). Nowadays you can see that speakers and actors (especially in children theaters) get off the stage to connect better with the public. Some contemporary performance hall designs have no platform at all. No mistake. It means that the performers are meant to empathize with the public.
Take a look at the Violin Museum’s Auditorium in Cremona (http://www.museodelviolino.org/en/auditorium/auditorium-idea), a small but famous city in northern Italy for the renown luthiers (that is violin makers) Guarnieri, Stradivari and Amati. Do you see any platform? The space winds and whirls around the performers’ chairs as if the public embraces them.
Without pressing a rectangle to get an array of parallelograms or squeezing it in the middle to get a ribbon, a rectangle seems dull and boring. But draw it on the ground, raise it a bit, give it some height, just a couple of cm/ inches (with the help of stones, wood, or cardboxes) and you built a platform! For what? For persuading others that you’re special, why not? By forcing people to step up you make them aware that they enter a different place (maybe you plant there something or build a playhouse). By raising up your place others can easier see you (and your performances in case you sing, act, play). By standing a bit above, you tell the others without words that you are important. Sooo many meanings in a couple of stones organized in a pattern.
Most of our activities are organized in a rectangle-like pattern. The rooms at home, the classrooms, the offices, the buses, the public gardens, the malls, have in general a rectangular plan. It may be dull but it’s convenient. A triangular room has been found psychologically difficult to live in and financially hard to furnish it (you need tailored furniture). Thus, having neither the sturdiness of a triangle nor the spirituality of a circle, the rectangle found its way into the building world as the most common architectural plan, as a platform and as a wall.
It seems too simple shape to trace and build a rectangle. But did the ancient people have the same tools as we have today to measure exactly an angle of 90 degrees? No. They used other tricks to draw perpendicular lines.
Try this: draw a triangle with the edges 3, 4 and 5 cm/ inches (or any unit you want). You can do it by cutting 3 stripes of paper of the following lengths: 3, 4 and 5 units long. Now arrange them in a triangular shape. You get a right triangle. This is Pythagoras’ theorem: In any right triangle, the sum of the legs’ squares is equal to the hypotenuse’s square. Find other 3 number with this property and build a right triangle. Then mirror it and you get a perfect square.