mathematics

Muramatsu Shigekiyo

Muramatsu Shigekiyo 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 Muramatsu Shigekiyo rather than just read about it. In short: Muramatsu Shigekiyo (村松茂清; 1608 – 1695) was a Japanese mathematician and curator in the Edo period. He is known for being the first to calculate the volume of a sphere using very thin slices, and to use inscribed and circumscribed polygones to approximate the circumference of a circle, and hence π.

Key takeaways

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

Reference excerpt

Muramatsu Shigekiyo (村松茂清; 1608 – 1695) was a Japanese mathematician and curator in the Edo period. He is known for being the first to calculate the volume of a sphere using very thin slices, and to use inscribed and circumscribed polygones to approximate the circumference of a circle, and hence π. And by using a 32768-gon, he calculated its perimeter as 3.141592648... He published his value of π to 22 decimal places in his 1663 book Sanso (Stack of mathematics), but only 8 were correct. Later, in 1681, Seki Takakazu used the same method with a 131072-gon, and got π correct to 11 decimal places.

References "Muramatsu Shigekiyo", Sacred Mathematics: Japanese Temple Geometry, Hidetoshi Fukagawa & Tony Rothman (2008), p. 65

Worked examples

Example 1 — a first encounter with Muramatsu Shigekiyo

Start with the simplest possible case. Write down what Muramatsu Shigekiyo 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 Muramatsu Shigekiyo 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 Muramatsu Shigekiyo 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 Muramatsu Shigekiyo

In research: Muramatsu Shigekiyo 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 Muramatsu Shigekiyo 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: Muramatsu Shigekiyo is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1608 births, 1695 deaths, 17th-century Japanese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Muramatsu Shigekiyo 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 Muramatsu Shigekiyo in 20 minutes

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

Frequently asked questions

What is Muramatsu Shigekiyo in simple terms?

Why does Muramatsu Shigekiyo 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 Muramatsu Shigekiyo?

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 Muramatsu Shigekiyo.