### Abstract

Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.

Original language | English |
---|---|

Pages (from-to) | 278-284 |

Number of pages | 7 |

Journal | Shinrigaku Kenkyu |

Volume | 67 |

Issue number | 4 |

Publication status | Published - 1996 Oct |

### Keywords

- Non-Euclidean geometry
- Visual space
- Visual triangle

### ASJC Scopus subject areas

- Psychology(all)

### Cite this

*Shinrigaku Kenkyu*,

*67*(4), 278-284.

**The estimation of the curvature of visual space with a visual triangle.** / Watanabe, Toshio.

Research output: Contribution to journal › Article

*Shinrigaku Kenkyu*, vol. 67, no. 4, pp. 278-284.

}

TY - JOUR

T1 - The estimation of the curvature of visual space with a visual triangle

AU - Watanabe, Toshio

PY - 1996/10

Y1 - 1996/10

N2 - Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.

AB - Triangular properties which Blank (1961) proposed are useful in investigating the geometry of visual space. With this method, however, it is not possible to estimate quantitatively the curvature of visual space. In the present article, hyperbolic and elliptic triangles are described with mathematical equations in the two and three dimensional Euclidean maps, and a method is proposed to estimate the curvature with triangular properties. Further, one experiment is conducted to find how the curvature changes according to the experimental conditions. Visual triangles are constructed in an eye level plane, a slanted plane and a horopter plane. The result shows that the curvature is negative in the eye level plane and in the slanted plane, but positive in the horopter plane.

KW - Non-Euclidean geometry

KW - Visual space

KW - Visual triangle

UR - http://www.scopus.com/inward/record.url?scp=0030254423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030254423&partnerID=8YFLogxK

M3 - Article

VL - 67

SP - 278

EP - 284

JO - Shinrigaku Kenkyu

JF - Shinrigaku Kenkyu

SN - 0021-5236

IS - 4

ER -