Product ID: 99534

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Undergraduate

In this unit, the historical background of the study of stable illusions of angle is sketched to show how a 19th century conecpt leads to formalization of a first order differential equation model for the apparent curves in such illusions. Some difficulties with the model are identified, and these lead to a refined formulation based on parametrization by arc length and polar coordinate transformations to solve the refined equations. ** Table of Contents:1. BACKGROUND OF THE PROBLEM2. THE HOFFMAN MODEL** 2.1 Vector Interpretation of the Bretano Hypothesis

2.2 Parametrization of Curves

2.3 The Differential Equation Model

2.4 Another Example: The Hering Illusion

2.5 Some Difficulties with the Hoffman Model

3.2 The Orbison Illusion

3.3 The Hering Illusion

3.4 Polar Coordinate Transformations

5. PREVIEW OF UNIT 535

6. ANSWERS TO EXERCISES

7. REFERENCES

APPENDIX A: SPECIAL ASSISTANCE SUPPLEMENT

©1986 by COMAP, Inc.

UMAP Module

38 pages

- Calculus ,
- Differential Equations

- Psychological Sciences ,
- Visual Perception

vector differential calculus in the plane; parametric representations; polar coordinates; variable separable differential equations; techniques of integration

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