One of the things you must do if you visit Helsinki is going to Linnanmäki which is an amusement park in the north of the city. It’s not cheap but you will fun a lot! Furthermore, if you go down from the park to the center of the city through the Western shore of Töölönlahti, you will be lucky to find this curious bridge where trains pass over the cars and the people’s heads. This bridge is exactly 50 meters long and now you can wonder … why can we know this measure? Because there is a great ruler painted in it! This could be a mere bridge but the Finns have been able to bring joy to all those people who love Maths!
The exhibitions of the British Museum have some mathematical pieces which must to be mentioned in a blog like this and three of this objects are the three polyhedral stones that we can see in the picture. The first one is a green stone inscribed with Roman numerals dated around the 1st-2nd century AD; the second is a stone inscribed with letters of the Greek alphabet dated in the 1st century AD and the third stone is also dated in the same century and it’s inscribed with Greek letters. We can see their polyhedral shapes and stones number 2 and 3 are two regular cuboctahedra:
Why Romans would like to have this kind of stones?
The Nuremberg Chronicle was written by Hartmann Schedel (1440-1514) in the XVth century to illustrate the human history from the Biblical passages up to the Middle Ages. It was printed in Nuremberg in 1493 and it became one of the best documented early printed books. The illustrations were drawn by Michael Wohlgemut (1434-1519) and his stepson Wilhelm Pleydenwurff (c. 1450-1494) and it’s not impossible that Albrecht Durer (1471-1528) also collaborated in them.
The Chronicle also contains numerous genealogies and family trees and a lot of portraits of gods, kings, writers and philosophers and Schedel wrote about the great mathematician Thales of Miletus among them (folios LIX recto and XL verso):
Thales, the Asiatic philosopher and first among the Seven Sages of Greece, flourished in Athens at this time. The Seven Sages were named after him.
The Seven Wise Men of Greece, or the Seven Sages, as they are also called, were the authors of the celebrated mottoes inscribed in later days in the Temple of Apollo at Delphi: “Know yourself” by Solon of Athens, “Consider the end” by Chilon of Lacedaemon, “Know your opportunity” by Pittacus of Mitylene, “Most men are bad” by Bias of Priene, “Nothing is impossible to industry” by Periander of Corinth, “Avoid excesses” by Cleobulus of Lindus and “Certainty is the precursor of ruin” by Thales of Miletus.
The origin of the title “Seven Wise Men” was this: Some fishermen of Miletus sold a draught of fish to some bystanders before the net was drawn in. When the draught came in, there was also in the net a golden tripod. The fishermen claimed they had sold only the fish, while the buyer insisted he had bought the whole draught. To settle the dispute they referred the matter to the Oracle of Delphi. Being ordered to adjudge the tripod to the wisest man in Greece, they offered it to their fellow citizen Thales; but he modestly replied that there was a wiser man than he, and sent it to Bias. He also declined, and sent the tripod to another; and thus it passed through seven hands, and these seven were afterward called the “Seven Wise Men of Greece.” It was finally placed in the Temple of Apollo at Delphi. These seven men met together but twice—once at Delphi, and again at Corinth.
Thales was the first among the philosophers to practice astrology and to predict an eclipse of the sun. He acquired a knowledge of geometry from the Egyptians. He was also an excellent counselor in matters pertaining to civic customs. He had (as they say) no wife, and when asked why he did not take one, he replied that it was because of his love of children. He contended that water is the origin of all things, and stated that the world was associated with and born of the devil. It is said that he also invented the year, and divided it into 365 days. He wrote on the subject of astronomy, and his writings are comprehended in 200 verses. When a golden table (tripod) was accidentally found, and there was a misunderstanding as to whom it belonged, Apollo answered that it should be awarded to him who excelled all others in wisdom. So it was offered to Thales, but he gave it to Bias and Bias Pitachus. At last the table came to Solon, but he turned it over to Apollo, as a token of most renowned wisdom. Thales was poor and he devoted himself to the acquisition of wisdom. Item: By means of astronomy he was able to predict fruitfulness in future years. One night when he was led out of his house by an old woman to study the stars he fell into a hole. And the old woman said to him, If you cannot see what lies at your feet, how can you expect to recognize the things that are in the heavens? He died at 78 years of age. Thales of Miletus was born about 636 BCE, and according to the weight of authority he died about 546 at the age of 90; however, both dates are uncertain. Some say he was of Phoenician extraction, and this is probably the reason why the chronicler calls him an Asiatic philosopher. It is more probable, however, that he was born in Miletus. As a Greek natural philosopher his fame among the ancients was remarkable. He is said to have predicted the eclipse of the sun which occurred in the reign of the Lydian king Alyattes; to have diverted the course of the Halys, or Red River, the greatest stream of Asia Minor in the time of Croesus; and later, in order to unite the Ionians when threatened by the Persians, to have instituted a federal council in Teos, as the most central of the twelve cities. The application of wise man was conferred on him, not only for his political sagacity, but also for his scientific eminence. He became famous by his prediction of the eclipse that did actually take place during a battle between the Medes and the Lydians, and being total, caused a cessation of hostilities and led to a lasting peace between the contending nations. Thales was one of the founders of philosophy and mathematics in Greece. He maintained that water is the origin of all things. […]
Thales the Milesian, one of the Seven Sages, is considered famous. After the theologians and the poets, they were called ‘Wise’, that is, ‘Sages’. This Thales was the first who was able to predict an eclipse of the sun and moon (as Augustine says). The preceding folios make clear the accomplishments and words of these men […]
Talking about Pherecydes, Schedel says that he was master of Pythagoras and…
wrote many letters to Thales the natural philosopher, receiving many from him in return.
He also says that…
Anaximander, philosopher and celebrated scholar, was at first a disciple of Thales.
In his Commentary to the Book I of Euclid’s Elements, Proclus (412-485) says that Thales…
first went to Egypt and thence introduced this study [geometry] into Greece. He discovered many propositions himself, and instructed his successors in the principles underlying many others, his method of attack being in some cases more general, in others more empirical.
Plutarch (c.46-120) says of him as one of the Seven Wise Men:
he was apparently the only one of these whose wisdom stepped, in speculation, beyond the limits of practical utility: the rest acquired the reputation of wisdom in politics.
[We can observe as a curiosity how the portrait of Plutarch is similar to the portrait of Thales!]
I am going to look for another touristic reference to Thales to explain more things about him. He was the man who is supposed to introduce the geometry in Greece so I think he deserves another post.