mathematics

Hiroshi Haruki

Hiroshi Haruki 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 Hiroshi Haruki rather than just read about it. In short: Hiroshi Haruki (春木博, Haruki Hiroshi; died September 13, 1997) was a Japanese mathematician. A world-renowned expert in functional equations, he is best known for discovering Haruki's theorem and Haruki's lemma in plane geometry.

Key takeaways

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

Reference excerpt

Hiroshi Haruki (春木博, Haruki Hiroshi; died September 13, 1997) was a Japanese mathematician. A world-renowned expert in functional equations, he is best known for discovering Haruki's theorem and Haruki's lemma in plane geometry. Some of his published work, such as: "On a Characteristic Property of Confocal Conic Sections" is available (open source) on Project Euclid. Haruki earned his MSc and PhD from Osaka University and taught there. He was a professor at the University of Waterloo in Canada from 1966 till his retirement in 1986. He was a founding member of the university's computer science department (1967).

See also List of University of Waterloo people

References

News release, Department of Computer Science, University of Waterloo.

External links Haruki's theorem on MathWorld Hiroshi Haruki's Lemma (Interactive Mathematics Miscellany and Puzzles) Hiroshi Haruki's Theorem (Interactive Mathematics Miscellany and Puzzles)

Worked examples

Example 1 — a first encounter with Hiroshi Haruki

Start with the simplest possible case. Write down what Hiroshi Haruki 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 Hiroshi Haruki 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 Hiroshi Haruki 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 Hiroshi Haruki

In research: Hiroshi Haruki 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 Hiroshi Haruki 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: Hiroshi Haruki is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1997 deaths, 20th-century Japanese mathematicians, Academic staff of the University of Waterloo, so understanding it makes those chapters shorter.
In everyday life: Look for Hiroshi Haruki 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 Hiroshi Haruki in 20 minutes

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

Frequently asked questions

What is Hiroshi Haruki in simple terms?

Why does Hiroshi Haruki 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 Hiroshi Haruki?

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 Hiroshi Haruki.