1. Perspective

2. Similar triangles ratios of corresponding sides are equal

13. Mount Edith Cavell

14. Shen Zhou: Poet on a Mountain (c. 1500)

15. Claude Lorrain: Ascanius Shooting the Stag of Sylvia 1(1682)

16. John Constable: The Hay Wain (1821)

17. John Constable: Dedham Vale (1802)

18. John Constable: Wivenhoe Park (1816)

19. Claude Monet: Branch of the Seine near Giverny (1897)

20. Seoul

21. Giovanni Paolo Panini (1692-1765) Interior of St. Peters, Rome

22. vanishing point

24. Jan van Eyck The Arnolfini Portrait (1434) The way the perspective is drawn is seriously flawed. This painting is done with oil paint on a board, the first of its kind. There is great uncertainty about who the people in the painting are. The symbolism is complicated: the dog means loyalty, the clogs may be a wedding gift or a mark of respect, the oranges may be a sign of wealth or a sign of fertility.

26. American artist David Hockney developed a theory that artists around the time of Brunelleschi cheated. He claims that they used a camera obscura to project an image of a scene, which they could then copy. This painting is an important piece of evidence for his claim. He says that the image in the round mirror could not have been painted freehand: it must have been traced. An article in Scientific American in 2004 describes an analysis of the mirror image. The author concludes that it would have taken an enormous mirror, too big to fit in the room, to make this image. An even simpler objection is that, if the image was copied, the lines of perspective would have been more accurate.

27. Jacopo Tintoretto

28. Art historians talk about paintings in one point perspective or two point perspective. But actually, there is nothing all that special about either of these. It is perfectly possible to have seventeen point perspective.

30. In mathematical terms, a vanishing point is sometimes called a point at infinity. It represents the direction in which a family of parallel lines converge. There are infinitely many possibilities: one for each possible direction.

31. Brunelleschi used his trick to impress people with the power of perspective.