Everyone who has visited an art museum and stood before a masterful painting has admired the artist’s clever use of accurate perspective to bring a third dimension to the flat canvas. The mathematical theory of perspective is almost 600 years old, having been pioneered by Leon Battista Alberti (1404–1472) in his treatise De Pictura (1435). Standing in front of a painting, you usually give little thought about precisely where to stand, relative to the canvas, in order to appreciate the three-dimensionality of the scene. Yet Alberti writes, on p. 57, “Know that a painted thing can never appear truthful when there is not a definite distance for seeing it.” You, the viewer, must assume the responsibility for accurately viewing the perspective intended by the artist. This article is intended to help viewers of art determine where to stand before a painting or a photograph. It is based on the idea from ray optics that light travels in straight lines from its source to the viewer’s eye.

2.
Annalisa
Crannell
,
Marc
Frantz
, and
Fumiko
Futamura
, “
Dürer: Disguise, Distance, Disagreements, and Diagonals!
Math Horizons
22.2.8
,
8
11
(
Nov.
2014
). Available online at http://www.maa.org/sites/default/files/pdf/horizons/durer.pdf.
3.
Marc
Frantz
and
Annalisa
Crannell
,
Viewpoints
(
Princeton University Press
,
2011
).
5.
An online appendix can be downloaded at TPT Online under the “Supplemental” tab at https://doi.org/10.1119/1.5003742 .
6.
A high-resolution image of Vermeer’s The Love Letter may be viewed at https://www.rijksmuseum.nl/en/collection/SK-A-1595.
7.
Philip
Steadman
,
Vermeer’s Camera
(
Oxford University Press
,
2001
).
8.
P. T. A.
Swillens
,
Johannes Vermeer: Painter of Delft 1632 – 1675
(
Spectrum
,
1950
).
9.
Trumbull’s Declaration of Independence
may be viewed online at https://www.aoc.gov/art/historic-rotunda-paintings/declaration-independence.

Supplementary Material

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