 
Summary: 1 Introduction
In the littlestudied trianglebisection illusion (Piaget and Pe¨ ne 1955; Robinson 1972/
1998; Seckel 2000, illusion 108), a dot is inscribed exactly halfway up the height of an
equilateral triangle, but it looks apparently far more than halfway upömuch closer to
the apex than the base of the triangle. In this paper we examine various properties of
this illusion and show that it is strongest for equilateral triangles with angles of 608.
It still occurs for triangles that are defined by stereo depth (Julesz 1971) or by equi
luminous textures, and this rules out any explanation based upon simple spatial filtering
(Morgan 1996). It is isotropic, being equally strong along all three axes of an equilateral
triangle, so there is nothing special about vertical. It is much increased when the sides
of the triangle are curved inward to make a concave, bottomheavy triangle, and
reduced when the sides are convex and bulge outwards. It is stronger when the bisec
tion spot is replaced by a grey diamond (see figure 7). We conclude that observers are
responding, not to the halfheight of the triangle as they were asked to do, but to the
centroid of the triangle (Morgan and Glennerster 1991) as defined by its centre of area
or centre of gravity.
2 Experiment 1: Measuring the effect
Observers were undergraduate students who received course credits for their participa
tion. They viewed various forms of equilateral triangles on a computer monitor screen.
They adjusted the vertical position of a small spot inside the triangle, until it appeared
