mathematics

Isidore of Miletus

Isidore of Miletus is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Isidore of Miletus rather than just read about it. In short: Isidore of Miletus (Greek: Ἰσίδωρος ὁ Μιλήσιος; Medieval Greek pronunciation: [iˈsiðoros o miˈlisios]; Latin: Isidorus Miletus) was one of the two main Byzantine Greek mathematician, physicist and architects (Anthemius of Tralles was the other) that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537. He was born c. 475 AD.

Key takeaways

Isidore of Miletus belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Isidore of Miletus to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Isidore of Miletus from memory before moving on to harder problems.

Reference excerpt

Isidore of Miletus (Greek: Ἰσίδωρος ὁ Μιλήσιος; Medieval Greek pronunciation: [iˈsiðoros o miˈlisios]; Latin: Isidorus Miletus) was one of the two main Byzantine Greek mathematician, physicist and architects (Anthemius of Tralles was the other) that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537. He was born c. 475 AD. The creation of an important compilation of Archimedes' works has been attributed to him. The spurious Book XV from Euclid's Elements has been partly attributed to Isidore of Miletus.

Biography

Isidore of Miletus was a renowned scientist and mathematician before Emperor Justinian I hired him. Isidorus taught stereometry and physics at the universities of Alexandria and then of Constantinople, and wrote a commentary on an older treatise on vaulting. Eutocius together with Isidore studied Archimedes' work. Isidore is also renowned for producing the first comprehensive compilation of Archimedes' work, the Archimedes palimpsest survived to the present.

Teachings and writings A majority of Isidore's preserved work are his edits and commentaries on older Greek mathematical texts. For example, Isidore is known to have revised and checked some of Archimedes' works and also Book XV of Euclid's elements. That being said, claims from Alan Cameron have been made about a hypothetical "School of Isidore". Between his work on architectural exploits, Isidore taught about math and geometry of the time. The School of Isidore is supported more by the presence of his teaching's in much of his students (such as Eutocious) works rather than his own writings. In an edit of the fifteenth book of Euclid's Elements, for instance, the editor quotes Isidore, but then proceeds to explain that Isidore did not publish much of his work himself. Instead, he taught, and once he himself could understand the material, did not see a need to write it down. It is because of this that Cameron claims that Isidore helped to revitalize interest in ancient mathematicians in Constantinople and Alexandria circa 510. In addition to editing the works of others, Isidore is known to have written his own commentary on Hero of Alexandria's "On Vaulting", which discussed aspects of vault construction and design in relation to geometry. While this commentary is lost Eutocius makes mention of it in his own writings. It is when referring to this work that Eutocius credits Isidore with designing a special compass for the purpose of drawing parabolas. Isidore's invention allowed for the drawing of parabolas with a greater level accuracy than that of which many previous methods were capable. From Eutocius (or his copyist) it is believed that one notable use for Isidores invention was to visually solve the problem of doubling the volume of a cube. This was said to be done by drawing two parabolas and finding the point where they intersect. In addition to their mathematical applications, Isidore is believed to have highlighted the uses of applying the use of parabolas to the construction of vaults.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Isidore of Miletus

Start with the simplest possible case. Write down what Isidore of Miletus claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Isidore of Miletus before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Isidore of Miletus ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Isidore of Miletus

In research: Isidore of Miletus appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Isidore of Miletus in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Isidore of Miletus is common in secondary-school and first-year university syllabi. It links to neighbouring topics 470s births, 6th-century Byzantine scientists, 6th-century Byzantine writers, so understanding it makes those chapters shorter.
In everyday life: Look for Isidore of Miletus outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Isidore of Miletus in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Isidore of Miletus means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Isidore of Miletus out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Isidore of Miletus in simple terms?

Why does Isidore of Miletus matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Isidore of Miletus?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Isidore of Miletus.