MENTAL MODEL · M10805

Mirror for Measuring the Circle

TechnicalHigh supportMathematics

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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

A work by the Jin dynasty mathematician Li Ye, which developed the 'Tianyuan technique' to solve higher-degree equations. The core is to algebraize geometric problems.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

Transformation of problem domain. When geometric problems are difficult to solve, transform them into algebraic problems; similarly, difficult problems in any field can be attempted to be handled better in another field.

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Anchor fast decisions

Written by Li Ye in the Yuan dynasty, it uses the 'Tianyuan technique' (setting up unknowns and polynomial equations) to systematically solve problems of inscribed and escribed circles in right triangles, and is an important document in Chinese algebraic geometry and equation techniques.

MINIMUM ACTION

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Practice this model in one real situation:

Set the diameter of the circle as 'Tianyuan one'
according to the relationships of the right triangle, set up the Tianyuan expression
equate two expressions to eliminate the unknown and obtain a one-variable equation
extract roots to solve and verify the roots.

Check to track your progress (stored locally)

Learning progress0%

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Source support: Explicit

link
zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E6%B5%8B%E5%9C%86%E6%B5%B7%E9%95%9CZH · Explicit
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