Zhang Heng 張衡

**By: Tao Steven Zheng (鄭濤)**

### Known for

Seismometer, armillary sphere, theoretical astronomy, π approximation, grid maps, poetry

### Fields

Astronomy, mathematics, seismology, mechanical engineering, hydraulic engineering, cartography, metaphysics, poetry

### Notable works

"The Spiritual Constitution of the Universe" (靈憲 líng xiàn), "Western Metropolis Rhapsody" (西京賦 xī jīng fù), "Eastern Metropolis Rhapsody" (東京賦 dōng jīng fù), "Southern Capital Rhapsody" (南都賦 nán dū fù), "Rhapsody on Contemplating the Mystery" (思玄賦 sī xuán fù), "Rhapsody on Returning to the Fields" (歸田賦 guī tián fù), "Poems on Four Sorrows" (四愁詩 sì chóu shī)

**Zhang Heng** was a Chinese astronomer, mathematician, inventor, and poet who lived during the Han dynasty (206 BC - 220 AD). Perhaps the most famous scientist of Imperial China, Zhang Heng left a legacy in many fields. He was a celebrated literary figure most famous for his rhapsodies (賦 *fù*), a form of semi-poetic literary prose. Zhang is best known for his many inventions and for his accomplishments in astronomy, mathematics, and geography. He expanded the *hun-tian* cosmological theory (渾天說 *hùn tiān shuō*) to explain many celestial phenomena. Zhang mapped of the heavens and the Earth, employing more systematic methods compared to his predecessors.

## **Discoveries**

### **Astronomical Theories**

In his work *Ling Xian* (靈憲), Zhang Heng supported the *hun-tian* cosmological theory of Luoxia Hong (落下閎, c. 156 - 87 BC), which stated that the Earth is a sphere that lay in the center of a vast spherical universe, whereby all celestial bodies traverse in a fluid-like medium. Zhang theorized that the universe was like an egg as round as a crossbow pellet with the stars on the shell and the Earth as the central yolk. Following in the footsteps of Jing Fang (京房, 78 - 37 BC), Zhang advocated the "radiating influence" theory to explain solar and lunar eclipses. This theory posited that the light of the Moon was merely the light reflected from the Sun and that the celestial bodies were spherical.

### **Star Catalogue**

Zhang Heng compiled a star catalogue of 2500 stars and grouped them into 124 constellations.

### **Approximation of pi**

Zhang Heng used two approximations of pi:

(
1
)

# π

10

(
2
)

# π

365
116

{\displaystyle {\begin{aligned}(1)\;\pi ={\sqrt {10}}\\[5pt](2)\;\pi ={\frac {365}{116}}\end{aligned}}}

The method for obtaining the first approximation is uncertain. The second approximation, mentioned in the *Ling Xian*, was influenced by astronomical data.

## **Inventions**

### **Seismometer**

Zhang Heng invented the world's first seismometer and named it the "earthquake weathervane" (候風地動儀 hòu fēng dì dòng yí). The urn-shaped device was designed to detect the direction of seismic tremors in eight directions. It is theorized that the interior apparatus consists of an inverted pendulum that tips in the direction of a detected earthquake, which triggers the mouth of a dragon to drop a metal ball into the mouth of a frog.

### **Water-powered Armillary Sphere**

The armillary sphere was invented in China since the 2nd century BC. Zhang Heng improved the design and employed waterwheels to rotate the device.

### **Striking Odometer**

Zhang Heng is credited for inventing the striking odometer, a cart with gears that make puppets strike drums and gongs at different intervals of distance.

### **South-pointing Chariot**

The south pointing chariot is a mechanical chariot with a mounted figurine that points in one direction regardless where the chariot is moved. The direction is continually corrected to point south using a differential gear.

### **Grid Maps**

Zhang Heng is credited for introducing rectangular grids for scaling physical distances onto a map. His work influenced the research of surveying and cartography by later cartographers like Pei Xiu (裴秀, c. 224 - 271 AD).

## **Literary Works**

Aside from his scientific works, Zhang Heng was also an accomplished poet. Many of his poems and rhapsodies captured the spirit of society during the Eastern Han dynasty. His most notable literary works include:

*Poem of Four Sorrows* (四愁詩 sì chóu shī)

*Rhapsody of the Western Capital* (西京賦 xī jīng fù)

*Rhapsody of the Eastern Capital* (東京賦 dōng jīng fù)

*Rhapsody on Contemplating the Mysterious* (思玄賦 sī xuán fù)

*Rhapsody on Returning to the Fields* (歸田賦 guī tián fù).