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mathematics

Luopan

Luopan 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 Luopan rather than just read about it. In short: The luopan or geomantic compass is a Chinese magnetic compass, also known as a feng shui compass. It is used by a feng shui practitioner to determine the precise direction of a structure, place or item.

Luopan — main illustration
Luopan — illustration

Key takeaways

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

Reference excerpt

The luopan or geomantic compass is a Chinese magnetic compass, also known as a feng shui compass. It is used by a feng shui practitioner to determine the precise direction of a structure, place or item. A luopan contains information and formulas regarding its functions. The needle points towards the south magnetic pole.

Form and function Like a conventional compass, a luopan is a direction finder. However, a luopan differs from a compass in several important ways. The most obvious difference is the feng shui formulas embedded in up to 40 concentric rings on the surface. This is a metal or wooden plate known as the heaven dial. The circular metal or wooden plate typically sits on a wooden base known as the earth plate. The heaven dial rotates freely on the earth plate. A red wire or thread that crosses the earth plate and heaven dial at 90-degree angles is the Heaven Center Cross Line, or Red Cross Grid Line. This line is used to find the direction and note position on the rings.

A conventional compass has markings for four or eight directions, while a luopan typically contains markings for 24 directions. This translates to 15 degrees per direction. The Sun takes approximately 15.2 days to traverse a solar term, a series of 24 points on the ecliptic. Since there are 360 degrees on the luopan and approximately 365.25 days in a mean solar year, each degree on a luopan approximates a terrestrial day. Unlike a typical compass, a luopan does not point to the north magnetic pole of Earth. The needle of a luopan points to the south magnetic pole (it does not point to the geographic South Pole). The Chinese word for compass, 指南針 (zhǐnánzhēn in Mandarin), translates to “south-pointing needle.”

Types Since the Ming and Qing dynasties, three types of luopan have been popular. They have some formula rings in common, such as the 24 directions and the early and later heaven arrangements.

San He This luopan was said to have been used in the Tang dynasty. The San He contains three basic 24-direction rings. Each ring relates to a different method and formula. (The techniques grouped under the name "Three Harmonies" are the San He methods.)

San Yuan This luopan, also known as the jiang pan (after Jiang Da Hong) or the Yi Pan (because of the presence of Yijing hexagrams) incorporates many formulas used in San Yuan (Three Cycles). It contains one 24-direction ring, known as the Earth Plate Correct Needle, the ring for the 64 hexagrams, and others. (The techniques grouped under the name "Flying Stars" are an example of San Yuan methods.)

Zong He This luopan combines rings from the San He and San Yuan. It contains three 24-direction-rings and the 64 trigrams ring.

Other types Each feng shui master may design a luopan to suit preference and to offer students. Some designs incorporate the bagua (trigram) numbers, directions from the Eight Mansions (八宅; bāzhái) methods, and English equivalents.

History and development

The luopan is an image of the cosmos (a world model) based on tortoise plastrons used in divination. At its most basic level it serves as a means to assign proper positions in time and space, like the Ming Tang (Hall of Light). The markings are similar to those on a liubo board. The oldest precursors of the luopan are the 式; shì or 式盤; shìpán, meaning astrolabe or diviner's board—also sometimes called liuren astrolabes—unearthed from tombs that date between 278 BCE and 209 BCE. These astrolabes consist of a lacquered, two-sided board with astronomical sightlines. Along with divination for Da Liu Ren, the boards were commonly used to chart the motion of Taiyi through the nine palaces. The markings are virtually unchanged from the shi to the first magnetic compasses. The schematic of earth plate, heaven plate, and grid lines is part of the "two cords and four hooks" (二繩四鉤; èrshéngsìgōu) geometrical diagram in use since at least the Warring States period. The zhinan zhen or south-pointing needle, is the original magnetic compass, and was developed for feng shui. It featured the two cords and four hooks diagram, direction markers, and a magnetized spoon in the center.

See also Automatic writing Chu Silk Manuscript Dowsing Geomancy

References

Bibliography Cheng, Jian Jun; Fernandes-Gonçalves, Adriana (1998). Chinese Feng Shui Compass: Step by Step Guide. Nanchang, Jianxi: Jianxi Science and Technology Publishing House. ISBN 9787539014302. Campbell, Wallace H. (2001). Earth Magnetism: A Guided Tour Through Magnetic Fields. San Diego: Academic Press. ISBN 9780121581640. Kalinowski, Mark; Brooks, Phyllis (1998). "The Xingde 刑德 Texts from Mawangdui". Early China. 23: 125–202. doi:10.1017/S0362502800000973. S2CID 163626838. Yin, Difei (1978). "Xi-Han Ruyinhou de zhanpan he tianwen yiqi" 西漢汝陰侯的占盤和天文儀器 [Western Han Lord of Runyin's divining plate and astrological apparatus]. Kaogu. 5: 338–343. ISSN 0453-2899. Yan, Dunjie (1978). "Guanyu Xi-Han chuqi de shipan he zhanpan" 關於西漢初期的式盤和占盤 [Regarding Western Han's early shìpán and divining plates]. Kaogu. 5: 334–37. ISSN 0453-2899. Lewis, Mark Edward (2006). The Construction of Space in Early China. SUNY series in Chinese philosophy and culture. Albany, NY: State University of New York Press. Allan, Sarah (1991). "The shape of the cosmos". The Shape of the Turtle: Myth, Art, and Cosmos in Early China. SUNY series in Chinese philosophy and culture. Albany, NY: State University of New York Press.

Further reading Skinner, Stephen (2008). Guide to the Feng Shui Compass: a Compendium of Classical Feng Shui. Singapore: Golden Hoard Press. ISBN 9780954763992. An account of the various types of luo pan, and details of 75 separate rings. The Lowdown on the Luo pan - Feng Shui for Modern Living Magazine

Illustrations

Luopan illustration
Luopan: Small feng shui compass, c. 1800–1894, from the Oxford College Archives of Emory University.
Small feng shui compass, c. 1800–1894, from the Oxford College Archives of Emory University.
Luopan: Chinese geomantic compass c. 1760 from the National Maritime Museum in London
Chinese geomantic compass c. 1760 from the National Maritime Museum in London

Worked examples

Example 1 — a first encounter with Luopan

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

In research
Luopan 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 Luopan 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
Luopan is common in secondary-school and first-year university syllabi. It links to neighbouring topics Chinese inventions, Feng shui, Geomancy, so understanding it makes those chapters shorter.
In everyday life
Look for Luopan 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 Luopan in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Luopan means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Luopan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Luopan in simple terms?

The luopan or geomantic compass is a Chinese magnetic compass, also known as a feng shui compass. It is used by a feng shui practitioner to determine the precise direction of a structure, place or item.

Why does Luopan 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 Luopan?

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 Luopan.

Tags

  • Chinese inventions
  • Feng shui
  • Geomancy
  • Magnetic devices
  • Orientation (geometry)

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