**Zhang Heng** was a Chinese mathematician, astronomer and geographer. He became chief astrologer and minister under the Emperor An'ti of China.

- At the time of Zhang Heng's birth the Emperor was Chang-ti, the third of the Eastern Han emperors.
- Over the years that Zhang Heng grew up, Chinese influence and prestige were growing rapidly and reached their peak in around 90 when he was about 12 years old.
- We shall give more information below on these aspects of Zhang's achievements as well as examples of his poetry.
- Zhang was thirty years old before his interests turned from literature to scientific matters, and at that time he became particularly interested in astronomy.
- If China began to suffer due to ambitious people seeking to further their own influence, this was certainly not the case for Zhang.
- We will describe below some of Zhang's outstanding scientific achievements.
- Zhang wrote the Four Stanzas of Sorrow which is the first seven-syllabic poem which we know of in China.
- It was natural therefore that Zhang having become an expert in astronomy should become involved in calendar reform by the year 123.
- In 132 Zhang invented the first seismograph for measuring earthquakes.
- Zhang's device, which he called Hou Feng Di Dong Yi, was made of copper.
- The seismograph detected an earthquake in February of 138 and Zhang reported this fact to the Emperor despite no other evidence of the earthquake being felt in the capital Lo-yang.
- Zhang appears to have been the first person in China to construct an equatorial armillary sphere.
- With this instrument Zhang was able to make more accurate star maps than earlier Chinese astronomers.
- Only the first part of this text by Zhang has survived.
- In mathematics Zhang studied 3 by 3 magic squares.
- As Mo notes, the significance here is that all earlier attempts to calculate were based on practical measurement, whereas the work by Zhang was based on a theoretical calculation.
- Zhang also gave formulae for the volume of a sphere in terms of the volume of the circumscribing cube.
- One interesting point to note in some of Zhang's mathematical work is that he leaves square roots as unevaluated.
- Some historians believe that Zhang understood the difference between rational and irrational numbers but this seems to be stretching things a bit too far.

Born AD 78, Nan-yang, China. Died AD 139, China.

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Astronomy, Origin China

Epochs: 1

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive