As broad and as high a man standing with outstretched arms, since the times of the earliest writings and in the earliest stone engravings the square has stood for the idea of the enclosure, the house, the village.
Enigmatic in its simplicity, in the monotony of its four equal sides and four equal angles, it generates a whole series of interesting figures: a group of harmonious rectangles, the Golden Section and the logarithmic spiral which is found in nature in the organic growth of many forms of life.
The logarithmic spiral is based on a series of ‘golden’ rectangles arranged in progression around the smallest of them.
A square cut as shown in the above diagram can be turned into an equilateral triangle simply by turning the pieces round as on hinges at the points marked.
Its many structural possibilities have enabled artists and architects of every age to give a well-produced framework to their buildings and works of art. It is present in every style produced by every people on earth at any time, both as structural element and as the base and background of particular decorative motifs.
It is static when resting on one of its sides, dynamic when balanced on one of its angles. It is magic if it contains numbers, and can even be diabolic if these numbers are related between themselves and to the square or the cube. It is found in nature in many minerals. It is a curve, according to Paeanus. By cutting it up and putting the pieces together in a different arrangement you can make it into triangles or rectangles. In ancient times it had the power to keep the plague at bay. It has provided the proportions of famous ancient cities and of modern buildings: Babylon and Tel el-Amarnah were square, while of the buildings we may mention the Parthenon, the Cathedral at Pisa, the Palazzo Farnese in Rome, and Le Corbusier’s ‘square spiral’ museum. In the designs of many churches the square spaces beneath the semicircular domes are the most logical spaces possible, just as the square shape of a photograph corresponds to the round lens with a minimum of waste or distortion.
A square cut as shown by the white lines on the black figure at the top can be put together again in many different ways.
Proportioned rectangles obtained from the square by projecting its own dimensions outside itself.
On the Acropolis of Olympia the gymnasium, the the-ecoleon, the leonidaeum and other buildings had a square ground plan…
It has given birth to ancient games that are still played today: chess, draughts, halma, nine men’s morris.… Then there are the square dances of the American frontier, the hollow squares of the British redcoats.
At the time of the eastern Chin it gave a stable square form to Chinese ideograms. It contributed to the structure of the letters of our alphabet, as well as to the Hebrew and other alphabets. A double square of matting is the basic module of the traditional Japanese house. Twenty-eight squares compose the surface of a brick. According to an ancient Chinese saying, infinity is a square without corners.
Divisions of the inside of a square starting from the main combinations obtained between lines and curves derived from the dimensions of the square itself.
