Optical Illusions Essay

! Optical illusions are images that are visually perceived differently than how they actually appear in reality. These images can be very entertaining, but also very deceiving. Optical illusions are caused by either an error with oneʼs visual sense or an error of intellect. This " error of intellect " occurs when the visual senses correctly interprets an image, but the mindʼs imagination, false assumptions, or inexperiences causes the illusion. Visual illusions with different effects can be found in numerous places, challenging the interests of scientists, artists, and artisans. Artist M. C. Escher utilized several optical illusions in his works, baffling the minds of mathematicians, scientists, and all other viewers. Optical illusions play an important role in our appreciation of both the physical world and the perceived physical world. Many optical illusions are very mathematical and geometric in nature. Implementing activities in the classroom involving such types of visual illusions could be intellectually stimulating, mathematically enriching, and thought-provoking for many students. The illusions described and explained below could be presented to students at the secondary level when studying several geometric concepts. For each illusion below, the instructions for constructing the illusion in The Geometerʼs Sketchpad (GSP) follows each explanation. All images below with the exception of the three dimensional Poggendorff image and the stereokinetic phenomenon image were constructed using GSP. Background Information/History: The prefix " stereo " comes from the Greek meaning " solid. " It is used with reference to hardness, solidity, and three-dimensionality in the formation of compound words. Kinetic describes an object in motion. Thus, as the name might suggest, stereokinetic phenomenon are three-dimensional objects assembled by two-dimensional shapes in slow rotatory motion, making them appear solid. They were first investigate by C. L. Musatti in the 1920s. Commonly produced by circles, stereokinetic phenomenon can also be created using ellipses, rectangles, and bars forming ellipsoids, cylinders, and other three-dimensional objects. Explanations and Mathematical Connections: The phenomena formed appears to have a defined length in depth. Through calculations of velocity and time, the depth of the three-dimension illusion can be predicted. The phenomenon is caused by the minimization of velocity differences. Our visual system minimizes relative velocity differences between the various points of the pattern, determining the apparent height of the three-dimensional object formed. When just looking at the image from a two-dimensional angle, however, it is merely just a set of circles. The circles are fixed to …