mathematics

Geshu bu

Geshu bu 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 Geshu bu rather than just read about it. In short: The Geshu bu (格術補), translated to English as the Supplement to Geometric Optics, Science Updates, or Optic Updates, is a book on optics written by the Chinese Guangdong gentry and intellectual Zou Boqi (1819–1869). The book was written in the late Qing Dynasty period in China.

Key takeaways

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

Reference excerpt

The Geshu bu (格術補), translated to English as the Supplement to Geometric Optics, Science Updates, or Optic Updates, is a book on optics written by the Chinese Guangdong gentry and intellectual Zou Boqi (1819–1869). The book was written in the late Qing Dynasty period in China. It covers the principles of lenses and is based on mathematical theory.

Background

Zou Boqi wrote two significant works in optics: the Geshu bu and the "Notes on the Mechanism for Capturing Images" (Sheying zhi qi ji). The Geshu bu tackles the Chinese principles on optics and its related literature while the Sheyi zhi qi ji delves more on the results of Zou's experiments as well as principles on photography. The Geshu bu was published in 1874, after Zou Boqi's death. In the late nineteenth century, Western knowledge, especially in optics, began to influence China. Zou's book, Geshu bu, introduced basic concepts of optics and lens, building on earlier Jesuit translations. This work challenged the traditional Mohist views and laid the groundwork for geometrical optics in China.

Contents Based from one fascicle of the book, published in 1877, it aims to expand on ancient Chinese mathematics. The term geshu highlights thorough investigation as explained in the preface by the Chinese philosopher Chen Li, drawing from Western lens-making techniques. In the book, Zou discussed different mirror shapes and principles. He also explained convex lenses, focusing on how they concentrate sunlight to ignite a fire. The focal point determines how close or far an image appears. The text introduces trigonometric calculations for lens reflections, providing a mathematical basis for understanding convex mirrors as well as adding details on telescopes and microscopes. The book also corrected some mistakes made by J. Adam Schall von Bell and Zhen Fuguang, writers on optics in China.

Reception Due to its unique approach of integrating mathematical calculations in lens-making principles, the book received high praise from Qing scholars. In 1886, Zhu Kebao wrote about optical methods in his biography of Zou Boqi. Zou's book helped circulated the knowledge of optics and lenses in the print market. Such circulation was reflected in a winning essay from the 1889 Polytechnic Institute (Gezhi shuyuan, 格致書院) contest, linking optics and the "mirror that lights a fire."

References

External links Geshu bu (1877 edition), available on Google Books

Worked examples

Example 1 — a first encounter with Geshu bu

Start with the simplest possible case. Write down what Geshu bu 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 Geshu bu 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 Geshu bu 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 Geshu bu

In research: Geshu bu 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 Geshu bu 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: Geshu bu is common in secondary-school and first-year university syllabi. It links to neighbouring topics Chinese mathematics texts, History of optics, History of science and technology in China, so understanding it makes those chapters shorter.
In everyday life: Look for Geshu bu 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 Geshu bu in 20 minutes

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

Frequently asked questions

What is Geshu bu in simple terms?

Why does Geshu bu 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 Geshu bu?

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 Geshu bu.