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Anthemius of Tralles (c. 474 - c. 534) (Greek Ἀνθέμιος από τις Τράλλεις) was a professor of geometry at Constantinople and architect, who collaborated with Isidore of Miletus to build Hagia Sophia by the order of Justinian I. Anthemius came from an educated family, one of five sons of Stephanus of Tralles, a physician. Of his brothers, Dioscorus followed his father's profession in Tralles; Alexander became at Rome one of the most celebrated medical men of his time; Olympius was deeply versed in Roman jurisprudence; and Metrodorus was a distinguished grammarian in Constantinople.

As an architect he is best known for replacing the old church of Hagia Sophia at Constantinople in 532; his daring plans for the church strikingly displayed at once his knowledge and his ignorance. His skills seem also to have extended to engineering for he repaired the flood defences at Daras.

Anthemius had previously written a book on conic sections, excellent preparation for designing the elaborate vaulting of Hagia Sophia. He compiled a survey of mirror configurations in his work on remarkable mechanical devices which was known to Arab mathematicians such as Al-Haytham.

One perhaps apocryphal story concerning Anthemius may illustrate the nature of his character. After a quarrel with his next-door neighbor Zeno, Anthemius simulated earthquakes, thunder, and lightning in the upper room in which the man entertained his guests, using curved mirrors and steam piped in through hydraulic leather tubes connected to the flooring.

A fragment of his treatise on burning-glasses was published as Περί παραδόξων μηχανημάτων ("Concerning wondrous machines") by L. Dupuy in 1777, and also appeared in 1786 in the forty-second volume of the Histoire de l'Academie des Instrumentistes; A. Westermann gave a revised edition of it in his Παραδοξογράφοι (Scriptores rerum mirabilium Graeci, "Greek marvel-writers"), 1839. In the course of constructions for surfaces to reflect to one and the same point

1. all rays in whatever direction passing through another point,
2. a set of parallel rays,

Anthemius assumes a property of an ellipse not found in Apollonius (the equality of the angles subtended at a focus by two tangents drawn from a point), and (having given the focus and a double ordinate) he uses the focus and directrix to obtain any number of points on a parabola—the first instance on record of the practical use of the directrix.

• Procopius, De Aedific. i. 1
• Agathias, Hist. v. 6-9
• Gibbon's Decline and Fall, cap. xl.
• This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.
• Huxley, G.L.. (1970). "Anthemius of Tralles". Dictionary of Scientific Biography 1: 169-170. New York: Charles Scribner's Sons.
• T L Heath, A History of Greek Mathematics(2 Vols.) (Oxford, 1921)
• G L Huxley, Anthemius of Tralles (Cambridge, Mass., 1959).

• O'Connor, John J., and Edmund F. Robertson. "Anthemius of Tralles". MacTutor History of Mathematics archive.