Showing posts with label topology. Show all posts
Showing posts with label topology. Show all posts

Thursday, April 2, 2009

Discovering Visual Mathematics

Visual Mathematics is the study and use of images, objects, places and visual experiences to understand and communicate mathematical ideas. Some highly visual mathematical fields include geometry (left) and topology (right). Many mathematical investigations enter into such complex mental manipulations that they can not be accomplished without the use of computers and visual imaging.

Design educators can contribute to the growth of knowledge and understanding by helping prepare future scientists, technologists, engineers and mathematicians so that they develop strong visual skills.

For many science, technology, engineering and mathematics students, visual literacy is a foreign language. They are used to thinking and communicating with numbers. In order to help broaden math students' intellectual skills, design educators need to learn and use the concepts and vocabulary of mathematics and show students how to read and create visual images, manipulatives, models, and interactive objects to help them solve complex mathematical problems.

Design educators need to go beyond the aesthetic appeal of mathematical images to helping students understand how visual literacy skills will help them solve increasingly complex problems. As a starter, take a look at some simple mathematical knot problems moving from the trefoil knot (far right) to a true figure 8 knot. See if your students can draw such a knot and notice the visual and mathematical thinking involved.

Click on the heading above to see the math and visualization of a figure 8 knot in mathematics.