Theon of Smyrna facts for kids
Theon of Smyrna was an ancient Greek thinker. He lived around 100 CE. He was a philosopher and a mathematician. Theon was very interested in the ideas of Pythagoras. His most famous book is called On Mathematics Useful for the Understanding of Plato. It teaches about Greek mathematics.
Contents
The Life of Theon of Smyrna
We do not know much about Theon's life. A statue of him was found in Smyrna. It was made around 135 CE by his son. Another famous ancient scholar, Ptolemy, mentioned a Theon who studied the stars in Alexandria. But we are not sure if this was Theon of Smyrna. There is a lunar impact crater called Theon Senior named after him.
The Works of Theon
Theon wrote many books. Most of them were about the ideas of other mathematicians and philosophers. He also wrote about Plato's philosophy. Sadly, most of these books are now lost.
His most important book that we still have is On Mathematics Useful for the Understanding of Plato. Recently, another one of his books was found. It was about the best way to study Plato's works. This book was found in an Arabic translation.
The Book: On Mathematics Useful for the Understanding of Plato
This book is not a direct comment on Plato's writings. Instead, it is a helpful guide for students learning mathematics. It brings together many ideas that were already known at the time. This makes it a valuable book. It shows us what people knew about math back then.
The first part of this book has two main sections. The first section is about numbers. The second section is about music and harmony.
Numbers and Number Theory
The section on numbers focuses on what we now call number theory. It talks about odd numbers, even numbers, prime numbers, and perfect numbers. It also explains "side and diameter numbers." This was a special method used by the Pythagoreans. It helped them find good guesses for the square root of 2. The book also tells us about the famous problem of Doubling the cube.
Music and Harmony
The section on music has three parts. These are:
- Music of numbers
- Music played with instruments
- "Music of the spheres" (the harmony of the universe)
The "music of numbers" explains how ratios and proportions create harmony. The part about instrumental music looks at intervals and consonance. This is similar to how Pythagoras studied music. Theon thought about how simple the ratios of musical intervals were. For example, an octave has a simple 2:1 ratio.
Music of the Cosmos
Theon believed the "music of the cosmos" was the most important part. He put it after the other sections because you needed to understand them first. Theon included a poem by Alexander of Ephesus. This poem gave a specific musical note to each planet. This idea was popular for over a thousand years.
Astronomy and the Earth
The second book of Theon's work is about astronomy. In this book, Theon states that the Earth is round and very large. He also describes events like occultations, transits, conjunctions, and eclipses. However, some experts like Otto Neugebauer felt Theon did not fully understand all the astronomy he wrote about.
Theon's Ideas on Pythagorean Harmony
Theon was a great thinker about harmony. He wrote about semitones in his book. In ancient Greek music, there were two common semitones. These were the "diatonic semitone" (16/15) and the "chromatic semitone" (25/24).
The Pythagoreans did not like using numbers that were not whole numbers for harmony. Theon, however, talked about this. He showed that a musical tone with a value of 9/8 could not be divided into equal parts. This meant it was a number on its own. Many Pythagoreans knew about irrational numbers. But they did not like using them because they seemed unnatural.
Theon also did a great job connecting fractions to musical intervals. He showed this in his writings and through experiments. He explained the Pythagorean way of looking at harmonies and consonances. He talked about experiments with half-filled vases. He showed that octaves, fifths, and fourths match the fractions 2/1, 3/2, and 4/3. His work greatly helped the fields of music and physics.
See also
In Spanish: Teón de Esmirna para niños
