mathematics

School of Chios

School of Chios 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 School of Chios rather than just read about it. In short: The School of Chios (Ancient Greek: Σχολή της Χίου) was a mathematical school in ancient Greece that flourished from around 480 BC to 450 BC. Main Representatives of the School The School of Chios was a mathematical school established in the early 5th century, succeeding the Pythagorean School.

Key takeaways

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

Reference excerpt

The School of Chios (Ancient Greek: Σχολή της Χίου) was a mathematical school in ancient Greece that flourished from around 480 BC to 450 BC.

Main Representatives of the School The School of Chios was a mathematical school established in the early 5th century, succeeding the Pythagorean School. Its most prominent representative was Hippocrates of Chios (~470-400 BC), who flourished around 440 BC. His teacher was Oenopides of Chios, who was a generation older. Also, Anaxagoras (500-428 BC) was likely a member of the School.

The Mathematical Work of the School There is no information on whether the School of Chios was based in Chios or if its representatives hailed from there. However, it was the brief period between the Pythagorean School and the Platonic Academy. The Academy declined, and its traces were lost shortly after the mid-5th century, during a flourishing geometric tradition, where the central focus was on the three famous "unsolvable" problems of antiquity: the Doubling of the cube or Delian problem, the Trisection of the angle, and the Squaring of the circle. Anaxagoras is mentioned as the first to deal with the problem of squaring the circle. According to Proclus, Oenopides was involved in mathematics and gained fame from it; he also introduced the use of the rule and compass for geometric constructions. Hippocrates is mentioned as the first to reduce the problem of doubling the cube to its equivalent, the interpolation of two mean proportionals between two straight line segments a and b=2a, so that the continuous proportions a/x=x/y=y/2a hold. Hippocrates also squared lunules, according to Simplicius (4th century AD), in a text that is preserved to us. The peak of the School of Chios did not last long, and the scientific center soon after the mid-5th century BC shifted to Athens. The three above-mentioned main representatives of the School of Chios settled in Athens and continued their mathematical work.

Bibliography Sotiris X. Goudouvas, "Γεωμετρικές Διαδρομές / Geometric Pathways", Athens 2015 Σωτήρης Χ. Γκουντουβάς, "Το νόημα της κατασκευής στην πορεία εξέλιξης της Γεωμετρίας / The meaning of construction in the course of Geometry's evolution", Dissertation, NKUA, Athens 2009 Proclus the Successor, "Comments on the 1st book of Euclid's Elements", Leipzig 1897 Thomas Heath, "Ιστορία των Ελληνικών Μαθηματικών / A History of Greek Mathematics", KEPEK, Athens 2001 Β. L. Van der Waerden, "Η αφύπνιση της επιστήμης / The awakening of science", PEK, Heraklion 2003

References

Worked examples

Example 1 — a first encounter with School of Chios

Start with the simplest possible case. Write down what School of Chios 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 School of Chios 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 School of Chios 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 School of Chios

In research: School of Chios 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 School of Chios 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: School of Chios is common in secondary-school and first-year university syllabi. It links to neighbouring topics Ancient Greek mathematicians, Ancient Greek people stubs, Education in classical antiquity, so understanding it makes those chapters shorter.
In everyday life: Look for School of Chios 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 School of Chios in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what School of Chios 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 School of Chios out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is School of Chios in simple terms?

The School of Chios (Ancient Greek: Σχολή της Χίου) was a mathematical school in ancient Greece that flourished from around 480 BC to 450 BC. Main Representatives of the School The School of Chios was a mathematical school established in the early 5th century, succeeding the Pythagorean School.

Why does School of Chios 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 School of Chios?

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 School of Chios.