. The initial preprint is from 2015, and it went through several versions, but the main results are unchanged, though some figures and section/theorem numbering are different, and there are several minor modifications in the text.
### Citation:

You can cite the published version as:
António Bandeira Araújo (2018) Ruler, compass, and nail: constructing a total spherical perspective, Journal of Mathematics and the Arts, 12:2-3, 144-169, DOI: 10.1080/17513472.2018.1469378

### Corrigenda:

Please let me know if you find any typos or errors in the article. At the moment the known corrections are as follows:
1 - On page 153, line 19 (the line above equation 1), where it reads

" the perspective map f " it should read " the perspective map p "

### What is the article about?

In the 1960s, Barre and Flocon wrote a seminal book (* La perspective curviligne*, 1967, Flammarion, Paris) wherein they defined a spherical perspective in a way that allowed for systematic drawing by elementary means, that is, by ruler and compass. However, "spherical perspective" was a bit of a misnomer since those rules were only specified for half the sphere. In this paper I extend those systematic constructions to the whole sphere. This extension had been attempted before, but either not successefuly or not systematically/completely. With this paper I solve the total spherical perspective in the same sense that Barre and Flocon solved the hemisphere: that is, I give a systematic method to calculate and draw all lines and vanishing points with ruler and compass (or even freehand). I also summarize Barre and Flocon's method in a very simple way (reduced to about two pages). Furthermore, I take the opportunity to consider what is the nature of a perspective as a mathematical object. I think it should be seen as a game of compactification that has anamorphosis as its central player (see the paper for details).

###
What's with the * nail *?

The initial title of the paper was "A construction of a spherical perspective in ruler, compass, and nail". It alludes to the fact that a set of (abstracted) mechanical apparatus defines a scope - it permits a certain class of points to be obtained from another through its action. Although you can construct the total spherical perspective with ruler and compass operations, I found that a more natural way to think about it is to imagine that you are using (or actually use) a third mechanical implement - namely, a * nail * fixed at the center of the page. This nail, interacting with a ruler, allows the construction of the antipodal image of a given meridian, and hence to construct the total spherical perspective by piggybacking on the hemsipherical constructions of Barre and Flocon (you'll have to read the paper for details).

###
What's the purpose of this web page?

I intend to place here several helpful files:
- Additional illustrations and comments that I didn't fit onto the paper due to space limitations.
- High resolution charts and grids.
- Animations and videos of constructions in the paper.
- Geogebra tools and other software that I developed along with the paper.

All of these need some work before I place them here, so I'll ask you to come around somewhat later (hopefully not infinitely long); I'll be working on it as my other duties allow.

It goes without saying (but I'll say it nonetheless) that
this page is under construction.

António Araújo, DceT, Universidade Aberta