Hugh Nibley gave a lecture in 1975 on “Sacred Vestments” which was later transcribed and included in the collected works volume Temple and Cosmos (pgs. 91-132). The entire paper is fascinating, and highly recommended reading. One of the things he wrote about were certain Chinese artifacts which had been found depicting two mythological gods, Nüwa and Fuxi, and the tools they hold:
Most challenging are the veils from Taoist-Buddhist tombs at Astana, in Central Asia, originally Nestorian (Christian) country, discovered by Sir Aurel Stein in 1925… We see the king and queen embracing at their wedding, the king holding the square on high, the queen a compass. As it is explained, the instruments are taking the measurements of the universe, at the founding of a new world and a new age. Above the couple’s head is the sun surrounded by twelve disks, meaning the circle of the year or the navel of the universe. Among the stars depicted, Stein and his assistant identified the Big Dipper alone as clearly discernable. As noted above, the garment draped over the coffin and the veil hung on the wall had the same marks; they were placed on the garment as reminders of personal commitment, while on the veil they represent man’s place in the cosmos. (pg. 111-12)
Nibley included drawings of this depiction found on veils in the Astana Tombs in Xinjiang, China, with a caption that reads:
In the underground tomb of Fan Yen-Shih, d. A.D. 689, two painted silk veils show the First Ancestors of the Chinese, their entwined serpect bodies rotating around the invisible vertical axis mundi. Fu Hsi holds the set-square and plumb bob … as he rules the four-cornered earth, while his sister-wife Nü-wa holds the compass pointing up, as she rules the circling heavens. The phrase kuci chü is used by modern Chinese to signify “the way things should be, the moral standard”; it literally means the compass and the square. (pg. 115)
See the photos at the end of the post for more examples of this icon. The veil redrawn in Temple and Cosmos is shown photographed in the second row, fourth from the left.
Wikipedia notes, “Nüwa and Fuxi were pictured as having snake like tails interlocked in an Eastern Han dynasty (206 - 220 A.D.) mural in the Wuliang Temple in Jiaxiang county, Shandong province.” It also notes the various roles of Nüwa (and sometimes with Fuxi) in Chinese mythology:
- Tribal leader (emperor)
- Sun god/moon god
- Adam and Eve
Some have even suggested that “Nüwa” might be related to “Noah” from the Genesis account, with some parallels between the accounts, such as Nüwa’s sealing of the sky with five colored stones connected with Noah’s rainbow.
Another description of Nüwa and Fuxi and their tools is found in a book entitled The Magic Square: Cities in Ancient China by Alfred Schinz:
It appears from these legends that civilization, i.e. ordered human life, begins with two personages, both portrayed as being semi-human and with mermaid tails. Nüwa and Fuxi, originally sister and brother, later became wife and husband after they had invented proper marriage procedures and family names to prevent marriages between people from the same family. Nüwa, in her own legend, had restored order between heaven and earth after a horrible catastrophe had caused heaven to tilt to the north so that it no longer covered all of the earth. This may refer to the first observation of the oblique elliptic and the angle of the pole star. Nüwa found it necessary to reestablish the four cardinal points, which she did, thereby creating the prerequisites for further observations. In the oldest pictures of her she carries a compass, the instrument related to heavenly observations. Her brother Fuxi became the first legendary emperor, which also implies the establishment of government, of law and order… On another, more practical level he is said to have invented axes for splitting wood, the carpenter’s square, ropes for hunting and fishing nets. It is worthy of special attention that the two words for compass and square, gui ju, used together denote -the rule, custom, usage- and -good behavior-, i.e., keeping order. Furthermore, it should be observed that the male-female system, the yang-yin philosophy, is expressed here in a complex manner, first as Fuxi and Nüwa, second as compass (male) and square (female), and third as Nüwa (female) with compass (male) and Fuxi (male) with square (female). The compass-square dichotomy is similar to the heaven-earth, yang-yin, relationship, which in this case means that man (Fuxi) establishes harmonious order between heaven and earth. This is also expressed in the Chinese character for king, wang, the upper and lower line indicating heaven and earth and the middle line man, all three connected by the vertical line. This represents the position and function of the ruler; it is he who establishes and keeps order by placing himself in a balanced and harmonious position between heaven and earth, so that yang and yin cooperate in a beneficial way.
[Caption] Fuxi and his sister Nüwa, he with the carpenter’s square and she with the pair of compasses. From the decoration incised in the wall of the Wu Lang tombs in Jiaxiang, Shandong, second century AD. The Chinese words for carpenter’s square, ju, and a pair of compasses, gui, together form the expression to establish order. This is what, according to their legends, Fuxi and Nüwa did. The carpenter’s square also stands for the square that is the symbol of the earth, while the pair of compasses represent the circle, the symbol of heaven. Fuxi, the male (yang), gives order to the earth (yin), and Nüwa, the female (yin), gives order to the heaven (yang).
A book entitled The Mathematics of Egypt, Mesopotamia, China, India, and Islam by Victor J. Katz and Annette Imhausen relates a practical tradition about the use of these tools in Chinese history:
Here Fu Xi - the first of the “Three Sovereigns” - is shown on the right holding a ju or carpenter’s square. In some versions of this legend Fu Xi is said to have invented both the carpenter’s square and the compass, or gui - which is held in the above depiction by his consort Nü Wa (on the left). According to the Chronicles of the famous Chinese historian Sima Qian, the Emperor Yu of Xia (who reigned in the twenty-first century BCE), when attending to floods, carried with him “a plumbline in his left hand and a gnomon and compass in his right” in order to do the surveying required to bring the floods under control [Li and Du 1987, 3].
The Silk Road by Susan Whitfield and Ursula Sims-williams connects the concepts of the compass and the square with the circle and the square:
In traditional Chinese cosmology the earth was square and the heavens round and thus Fuxi holds a set square to draw the former, and Nüwa a pair of compasses to draw the circle of the earth.
Noted by Mark Edward Lewis in Writing and Authority in Early China, these symbols were used to represent cosmic order, a link between heaven and earth, and a favorable environment for the deceased:
This role of linking Heaven to Earth also figures in the depictions of Fu Xi and Nü Wa. First, in Han tombs their elongated, serpent bodies stretch from the bottom of the register to the top, and in later depictions this vertical ascent becomes even clearer. In Sichuan sarcophagi they play the iconographic role of the dragons on the Mawangdui banners who physically link the earthly realm to that of Heaven. This idea is reinforced through the regular inclusion of two other iconogrpahic traits. Fu Xi and Nü Wa are often depicted with the sun and moon, and they are shown holding a carpenters square (Fu Xi) and a drawing compass (Nü Wa). The former are metonyms for Heaven and the celestial equivalents of yin and yang. The latter suggests the linking of square Earth to the round Heaven. Most scholars agree that the role of the intertwined Fu Xi and Nü Wa was to depict the interaction of yin and yang that underlies cosmic order and thereby secure an auspicious environment for the denizen of the tomb.
Santillana and Dechend offer more explanation for the figures of Nüwa and Fuxi:
The Chinese picture illustrates in true archaic spirit (which means that only hints are given, and the spectator has to work out for himself the significance of the details) the surveying of the universe. The two characters surrounded by constellations are Fu Hsi and Nu Kua, i.e., the craftsman god and his paredra, who measure the “squareness of the earth” and the “roundness of heaven” with their implements, the square with the plumb bob hanging from it, and the compass. The intertwined serpent-like bodies of the deities indicate clearly enough, although in a peculiar “projection,” circular orbits intersecting each other at regular intervals. 
In another place some Chinese commentators have noted the uses of these tools in construction or building:
All “great instruments” were invented by the ancients to help lesser men “first rule the self and then rule others.” Although all are needed in construction, by no means do all these tools work in the same way. Level and line determine straight horizontal and vertical lines, while compass and square are needed to form perfect circles and corners. By analogy, each of the social institutions, including ritual, has its own function in building civilization, with each addressing a separate human need. It is characteristic of the sage-ruler that he always knows which tool to apply to the specific problem at hand.
There are probably hundreds of other sources which describe these symbols in Chinese tradition and mythology. You can find more by doing a Google Books search for “nuwa square compass.”
I’ve done some image searching and these two figures are almost always depicted holding the same symbols in their hands, and which have been described by many different scholars as the tools of creation and divine order. See the images below.
- Schinz, The Magic Square: Cities in Ancient China, 25-26, link.
- Katz and Imhausen, The Mathematics of Egypt, Mesopotamia, China, India, and Islam, 191, link.
- Whitfield and Sims-williams, The Silk Road, 329, link.
- Lewis, Writing and Authority in Early China, 204, link.
- Giorgio De Santillana, Hertha Von Dechend, Hamlet’s Mill, 272, link.
- Yan Hsiuing, Xiong Yang, Michael Nylan, The Elemental Changes: The Ancient Chinese Companion, 54, link.
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