mathematics

Jinkōki

Jinkōki 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 Jinkōki rather than just read about it. In short: Jinkōki (塵劫記) is a three-volume work on Japanese mathematics, first edited and published by Yoshida Mitsuyoshi in 1627. Over his lifetime, Mitsuyoshi revised Jinkōki several times.

Key takeaways

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

Reference excerpt

Jinkōki (塵劫記) is a three-volume work on Japanese mathematics, first edited and published by Yoshida Mitsuyoshi in 1627. Over his lifetime, Mitsuyoshi revised Jinkōki several times. The edition released in the eleventh year of the Kan'ei era (1641) became particularly widespread. The last version personally published by Mitsuyoshi was the Idai (井大), which came out in the eighteenth year of the Kan'ei (1634). Subsequent to that, various editions of Jinkōki were released, one of which includes Shinpen Jinkōki (新編塵劫記). Jinkōki is one of the most popular and influential Japanese mathematics books in history, having influenced Seki Takakazu, Kaibara Ekken, and many other later Japanese mathematicians. It is partly based on the works of Yuan dynasty mathematicians in China.

Etymology The name Jinkōki is derived from jintenkō (塵点劫), an immeasurably long span of time mentioned in the Lotus Sutra, hence the nuance of permanence in the Sino-Japanese word jinkō and its reflection in English title.

Content The book contained instructions for dividing and multiplying with a soroban and mathematical problems relevant to merchants and craftsmen. The book also contained several interesting mathematical problems, and was the first Japanese book to use printing in colour. As a result, the Jinkōki became the most popular Japanese mathematics book ever and one of the most widely read books of the Edo period. Mitsuyoshi made reference to everyday problems, such as buying and selling rice. The book was originally published in three volumes, the first of which mainly describes multiplication and division using the soroban. The second and third volumes include an assortment of practical and recreational problems. The included problems are not arranged according to any specific order. The book includes ideas that aimed to keep readers from boredom by adopting a wide variety of problems such as calculations of areas of rice fields, problems related to the construction of rivers and riverbanks, geometric progression, and the Josephus problem. The Shinpen Jinkōki was the most widespread version among the copies of Jinkōki, and widely used as a textbook for use of the soroban throughout the Edo period. In addition to fundamental knowledge such as numerical notation, units, and multiplication tables, it also included slightly more specialised topics, such as methods to find square roots and cube roots, practical calculations of area, currency conversion, and interest calculation. The content covers almost all arithmetic needed in daily life at that time, and it is a characteristic of the book that explanations are given using familiar topics, such as using the increase of mice as an example for geometric progression. Many different versions were published, with slightly modified content, and by the time of the Meiji era, over 400 editions of Jinkōki had been published.

Gallery

Illustrations

Worked examples

Example 1 — a first encounter with Jinkōki

Start with the simplest possible case. Write down what Jinkōki 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 Jinkōki 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 Jinkōki 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 Jinkōki

In research: Jinkōki 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 Jinkōki 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: Jinkōki is common in secondary-school and first-year university syllabi. It links to neighbouring topics Books about mathematics, Japanese mathematics, so understanding it makes those chapters shorter.
In everyday life: Look for Jinkōki 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 Jinkōki in 20 minutes

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

Frequently asked questions

What is Jinkōki in simple terms?

Jinkōki (塵劫記) is a three-volume work on Japanese mathematics, first edited and published by Yoshida Mitsuyoshi in 1627. Over his lifetime, Mitsuyoshi revised Jinkōki several times.

Why does Jinkōki 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 Jinkōki?

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 Jinkōki.