The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification.

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Heron's Dioptra 35 is the unique witness of an ancient mathematical procedure for finding the great arc distance between two cities using methods of ancient spherical astronomy and simultaneous observations of a lunar eclipse. This paper provides a new study of the text, with mathematical and historical commentary. I argue that Heron's account is a summary of some longer work of mathematical astronomy or geography, which made extensive use of the analemma, an ancient model of the celestial sphere. Heron's text can be used to show the utility of the analemma model, both as a theoretical device and as a computational tool.

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This paper is a reassessment of the use of the use of Dioptra 35 for the purposes of dating the activity of Heron of Alexandra. It is argued that the text does not contain a carefully recorded eclipse observation that can be attributed to Heron. The most that can be said is that the lunar eclipse of 13 March 62 can probably be taken as a terminus post quem for Heron's activity.