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From Thales’ Theorems to His Discoveries

By Jess, published on 20/03/2019 Blog > Academia > Maths > Everything about Thales the Mathematician

Mathematics is a subject that often comes up in debates about the education sector, where it is repeatedly one of the subjects that school children struggle the most in. It is considered to be an essential step in the academic career of students, where students are expected to consolidate their knowledge every year in order to to be successful and understand new mathematical notions.

What is involved in the framework and what is at the origin of this discipline? Cosines, reciprocals, fractions, quadrilaterals, relative numbers, circumferences, symmetry, tangents, inequalities – revising over courses in mathematics can become less stressful when viewing it through the lens of history. One of the many great examples is the great scientist and mathematician: Thales. Check out his history to both unlock some of the strategic concepts you might be struggling with and improve your capabilities within them!

Thales of Miletus: The Life of the Mathematician

In the life of a mathematics student, there are two names that are impossible to forget: Pythagoras and Thales. The latter, a professor of the former according to historical texts, was a philosopher born in Miletus around 625 BCE. Aptly named, the Greek philosopher Thales of Miletus is considered as one of the seven sages of ancient Greece, along with other Greek philosophers: Solon, Chilon of Sparta, Pittacus of Mytilene, Bias of Priene, Cleobulus of Lindos and Periander of Corinth.

Founder of the school of Milesians, Thales started off his academic career as a philosopher and scientist by going to Egypt at a very young age, thanks to good relations that existed between the country and his maternal city, Miletus. It was there that a young Thales discovered the knowledge of Egyptian and Babylonian sciences.

Once there, he learned geometry, astronomy, and philosophy – all knowledge that was a core part of the educational training of Egyptian priests. This trip to Egypt is not really supported by data, according to ancient Greek historians. In fact, only some records written years after the death of Thales have been able to attest to the life of the scientist and place him in Egypt at the time.

Once he reached adulthood, Thales returned to the Greek city of Miletus to create the School of Milesians. Thales used his position to spread his knowledge in mathematics and Greek philosophy, all the while continuing to perform observations and scientific experiments.

Throughout his life, Thales used his observation in order to discover how the world functioned. According to the legend, he calculated the height of the great pyramid, helped predict a lunar and solar eclipse and put into practice the theorems of Thales.

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Thales, along with many philosophers, came from Miletus Ancient Greece, and especially Miletus, had a deep influence on Western philosophy

His mathematical and scientific research are considered as having revolutionized the times.

Considered as a sage, Thales always prided himself on explaining his discoveries from a rational point of view instead of a mythological one, las was tradition at the time. For him, the process of observation and creating proofs were the base of scientific reasoning.

According to some accounts written many years after his death, Thales died around 547 BCE in Miletus while attending a gymnastic competition. Found in the bleachers, he had apparently died of hunger, thirst and age.

Some other great mathematicians and philosophers from this area include Archimedes!

How Thales Influenced Math Courses

Everyone has heard of, and even learned, many of the theorems that Thales discovered. Thales was the first to mark the history of mathematics in the creation of his scientific formula and principle. Here are five of the geometric theorems he has been credited with:

  1. A circle is bisected by a diameter
  2. Angles in a triangle are equal if their opposites are two sides of equal length
  3. Intersecting straight lines produce opposite angles that are equal
  4. A right angle, and its corresponding right triangle, can be drawn inside of and using a semicircle
  5. If a triangle’s base and two angles are given, the triangle can be drawn

While these may sound too simple today to have ever been considered revolutionary, they actually give us a lot of information and were considered a major innovation at the time. Thales’ theorems are utilized to calculate certain relationships of longitude and proportions in geometric figures possessing parallel lines. They are also used to calculate many concepts in trigonometry, when there is the presence of two parallel lines.

According to legend, Thales discovered this theorems while calculating the height of a pyramid. To do this, the mathematician calculated the shadow of the pyramid to the floor. With the help of a cane, Thales was able to calculate the dimensions of the pyramid of Egypt in relation to the shadow of his cane.

While Thales is credited with these theorems, however, they were already known by the Babylonians and Egyptians. We know this most notably thanks to the proof elaborated in the book Euclid’s Elements, which deals with the proportionality of areas of triangles of equal height. However, Thales was credited with putting words to the latter.

Thales does not receive credit in many countries for some of his theorems. For example, the English call one of his theorems the Theorem of Interception, while for the same theorem the Germans call it the Theorem of Rays. However, these are all not completely identical and it resembles more the theory of Pythagoras.

Thales was an astronomer, philosopher and mathematician The history of Greek mathematicians is incomplete without the mention of Thales

Thales From Math to Astronomy

During the course of his life, Thales utilized mathematics to understand important notions of real life. Math exercises, prime numbers, decimals, equations, medians, subtraction, addition, philosophy, architecture – math served as a tool to understand the world around him.

Early on in his career, Thales developed a passion for astronomy and analyzing the sky. Because of this he is considered as one of the pioneering forces behind of Greek astronomy.

Similar to his research in mathematics, Thales utilized the method of observation for constellations in order to understand how the universe functioned. He made many discoveries in these areas:

  • Used the little dipper to guide sailors in the open ocean
  • Calculated the length of a year thanks to intervals of a solstice and equinoxes
  • Indicated the pathway of the son in between the two tropics
  • Listed the ephemeris

His discoveries were only a small part of his observations. Most notably, he analyzed the number of days in a year and concluded that the year is not 365 days but 365 days and a quarter. This discovery would later be the the base of leap years.

Thales also observed stars in movement, the diameter of the sun and the moon – all the while using the same system of measuring objects relative to the shadow of a cane. He also located the position of Pleiades, calculated the orbital inclination of zodiac, etc.

Thanks to his observations, Thales also could have predicted a large harvest of olives according to Aristotle. He applied these observations of nature in order to explain how the world functioned, but most often simply ended up ameliorating the lives of those around him. For example, sailors learned how to orientate themselves thanks to him and navigation advanced tenfold.

Astronomy and all of its associated fields owe a lot to Thales, who was not but a simple mathematician. To learn more about how these discoveries influenced the work of another great mathematician, Rene Descartes, click here!

Thales in the Context of the Greats

All of Thales’ discovers have placed a special mark on the field of mathematics. Arithmetic, complex functions, whole numbers, polygons, multiplication, factorization, probability – his knowledge and discoveries are still taught in our day and in our maths courses, which is what places Thales as one of the biggest mathematicians of history.

Thales and the history of philosophy Ancient philosophy was impacted by thinkers like Thales

However, more than his discoveries, Thales theorized knowledge that was already established by the Egyptians or Babylonians. The mathematician didn’t just content himself with this knowledge, laid out in mythological truths, but searched to observe and prove all these affirmations that he encountered during his studies through math. In this way, Thales baffled his contemporaries.

In a book by Jean Voilquin, the scientific French editor explained that Thales wanted to “replace mythological explanation” of phenomena “by physical explanation.” This is what leads Voilquin, along with many others, to name him as “one of the precursors to Greek science.”

Thales’ scientific legacy is magnified by the discoveries made by his School of Miletus. Called the Milesian school, or “Ionian School”, their work revolutionized the field of science and they have come to be known as pre-Socratic philosophers. His teaching, specific to Thales, favored visual perception and observation in order to inject practicality into knowledge.

The school included mostly geometry and astronomy, Thales’ two preferred fields, but it also worked on subjects like biology, physics, and metaphysics. They were the first students to be called Physics-ians and studied everything about nature.

The Miletus School disciples utilized concepts like the four elements in order to give explanations over the function of the environment. All these studies are considered as the first scientific investigations into nature and have left an indelible contribution to the sciences.

Thales didn’t just mark the field of mathematics in antiquity, but also the history of science  as a whole, inspiring works of even Sir Isaac Newton. For that, we should remember his name along with his achievements.

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