The 9th- and 10th-century mosaics of the Hagia Sophia in Constantinople are truly classical Byzantine artworks. The north and south tympana beneath the dome was decorated with figures of prophets, saints and patriarchs. Above the principal door from the narthex we can see an Emperor kneeling before Christ (late 9th or early 10th century). Above the door from the southwest vestibule to the narthex another mosaic shows the Theotokos with Justinian and Constantine. Justinian I is offering the model of the church to Mary while Constantine is holding a model of the city in his hand. Both emperors are beardless this is an example for conscious archaization as contemporary Byzantine rulers were bearded. A mosaic panel on the gallery shows Christ with Constantine Monomachos and Empress Zoe (10421055). The emperor gives a bulging money sack to Christ as a donation for the church.
If it is possible to answer this question, answer it for me (else, reply "unanswerable"): Who was depicted with the Empress Zoe on a panel in the gallery of the Hagia Sophia?
Ah, so.. Constantine Monomachos

One of the Han's greatest mathematical advancements was the world's first use of negative numbers. Negative numbers first appeared in the Nine Chapters on the Mathematical Art as black counting rods, where positive numbers were represented by red counting rods. Negative numbers are used in the Bakhshali manuscript of ancient India, but its exact date of compilation is unknown. Negative numbers were also used by the Greek mathematician Diophantus in about 275 AD, but were not widely accepted in Europe until the 16th century AD.
If it is possible to answer this question, answer it for me (else, reply "unanswerable"): How were negative numbers first described during the Han period?
Ah, so.. as black counting rods

The Ptolemaic Kingdom was a powerful Hellenistic state, extending from southern Syria in the east, to Cyrene to the west, and south to the frontier with Nubia. Alexandria became the capital city and a centre of Greek culture and trade. To gain recognition by the native Egyptian populace, they named themselves as the successors to the Pharaohs. The later Ptolemies took on Egyptian traditions, had themselves portrayed on public monuments in Egyptian style and dress, and participated in Egyptian religious life.
If it is possible to answer this question, answer it for me (else, reply "unanswerable"): What were the reaches of the Ptolemaic Kingdom?
Ah, so..
Syria in the east, to Cyrene to the west, and south to the frontier with Nubia