What are the labyrinths?
Labyrinths are one of the mathematical wonders, the origin of which is lost in the legendary twilight of history. Karl Lepsius, the famous Egyptologist, argued that the name "labyrinth" comes from the Egyptian words: "lery" - "holy institution" and "rå-hint" - "mouth of the channel". Other scholars believe that this is a word of Greek origin, meaning "underground passages". It is impossible to find out whether this word, concept and even the structures themselves appeared on Greek land or got there many centuries ago from Egypt.
From the works of Lepsius it is known that in Egypt over Lake Moeris there are still ruins of a labyrinth built in 2100 BC., therefore, the most ancient of the existing. Pliny recalls the other two ancient labyrinths, namely the Lemnos labyrinth on the island of Lemnos and the Italian labyrinth under Clusia. However, the most famous is the legendary Cretan labyrinth, in which, according to legend, the fabulous monster Minotaur stayed for many years, until, finally, the hero Theseus climbed into the labyrinth and killed the monster, and then safely and cunningly returned back thanks to the proverbial from those times of "Ariadne's thread".
In the early Middle Ages, the clothes of Christian monarchs were decorated with drawings of the labyrinth, and then, especially in the XII century, the walls and parquet floors of temples. It was a symbol of the confusion of earthly roads and human wanderings.
In later centuries, labyrinths lost their primary mystical-religious character and became the subject of decoration and entertainment in the huge princely parks, palaces, etc.
All known labyrinths can be divided into apparent and real, because in many cases a very intricate pattern is actually multiple bends of the same road.
If we define a real labyrinth as a confusion of roads along which it is very difficult to get to the center, as well as to go back, then in seeming labyrinths everything is the other way around: entering it and heading all the time forward, one cannot help but reach the center, and turning back, one cannot but get out of it.
Such a seeming labyrinth is the famous labyrinth in the Cathedral in Chartres (located at a distance of several tens of kilometers from Paris), 40 cubits in diameter, through the narrow passages of which believers made their way with penitential psalms.
An intermediate place between the seeming labyrinths and the real ones is occupied by labyrinths, in which you can move with complete confidence, if you know their secret, if there is at least one small pointer - like a key to this riddle, which seems extremely confusing.
This type of labyrinth is the garden labyrinth at Kemton Court (Fig. 1), near London, created from trellises of hornbeam trees, leading to two large trees, under which once stood a bench. This labyrinth, according to some historians, dates back to the time of Henry VIII. It occupied over 1200 sq. m. Its alleys stretched for half an English mile, that is, 800 m.
This is a labyrinth in which you can really get lost (fig. 2). But, if you know his secret, if you know that, moving forward, you should constantly stick to either the right or left side, you can go around without any difficulty.
In the very center of a beautiful park, an environment of a maze of alleys and hedges, a small palace is lost. In this secluded place, the English king Henry II, in love with the beautiful Rosamund, jealously hid her beauty from human eyes.
If we lived in the XII century and wanted to see the beauty of Rosamund, praised by many poets, we would have to find a path that led to her palace.
The English mathematician Rous Ball arranged an excellent labyrinth in his garden (Fig. 3). The question here is not how to get to a particular place, but rather how you can make the longest walk with the fewest possible alleys that you have to visit twice.
Although in everyday terms a labyrinth denotes a confusion of roads from which one cannot get out, however, after a little reflection, everyone must admit that there can be no labyrinth without an exit, if there is... an entrance.
The ability to solve every labyrinth, even without the "Ariadne's thread", will not surprise anyone anymore. At the same time, it may seem surprising to many that not only the rules for such solutions are known, but that there is almost a whole geometric theory of these solutions.
