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Peer Review

Dimensions (geometry)

by Multiple others in credits , , √Čtienne Ghys , Jos Leys , Aur√©lien Alvarez


Overall Numeric Rating:

4.75 stars
Content Quality: 4.75 stars
Effectiveness: 4.5 stars
Ease of Use: 5 stars
Reviewed: Jun 30, 2009 by Mathematics
Overview: This site visually presents topics in 2, 3 and 4 dimensional geometry with 9 online movies, each about 13 minutes in length. In each movie a narrator describes a geometrical construct which is being animated on the video.
Type of Material: Lecture/Presentation
Recommended Uses: These videos can be used as a supplement to a lesson on geometry (i.e. introducing proofs), topology (i.e. converting 3D sphere onto 2D map) or even algebra (introducing imaginary numbers). These would be especially effective for the visual learner who can appreciate the intrinsic beauty of geometry. There is also a page on the site with an overview of each video, including links to find out more about the mathematicians that introduced the various ideas and concepts. Students in a math appreciation class, or doing a math research project could use these links to begin searching for a research topic that would be of interest to them.
Technical Requirements: Any web browser.
Identify Major Learning Goals: To gain a visual understanding, artistic appreciation, and historical perspective of Stereographic Projection, fourth dimensional geometry, and complex geometry.
Target Student Population: Students in a higher level geometry or topology class or student in a liberal arts math class. Note: The authors suggest the following videos for these various groups of viewers: Lower secondary school (ages 12-15) : 1 or 1-2 or 1-2-9 Higher secondary school (ages 16-18) : 1-2-(3-4)-9 Higher secondary school with science major : 5-6 University sciences student (lower cycle): 2-3-4-5 or 5-6-(7-8-9) University science student( higher cycle) : 7-8-(9) General public : 1-2-3-4-(9)
Prerequisite Knowledge or Skills: None if the intent is just math appreciation. Basic ideas of topology and complex analysis if the intent is to understand the math behind the videos.

Evaluation and Observation

Content Quality

Rating: 4.75 stars
Strengths: Each video incorporates exquisitely colorful graphics. The artistic quality of these videos is impressive. The topics flow together well and the use of narrators who portray the mathematician who developed the concept is effective. Even though the geometric and topological ideas are complex, the use of soft color and light background music creates a soothing atmosphere. Viewers can choose from 9 major languages, so that these videos can be viewed worldwide. For each of the 9 videos there is a page giving a basic overview of the topic as well as links for some additional information. The videos are also kept at a manageable size (about 13 minutes) making it easy to fit one into a regular class period.
Concerns: The pages containing the introduction/overview of the 9 videos were very useful, but not easy to find right away. The website could be structured a little different, encouraging the viewers to read those pages first. Also, having no closed captioning raises accessibility issues. The pace of the videos may be too slow for some students.

Potential Effectiveness as a Teaching Tool

Rating: 4.5 stars
Strengths: A student viewing these will certainly get an understanding of the beauty of mathematics. Those who are taking a related course will have a strong visual understanding of 4-dimensional geometry after viewing each of these videos. An instructor of liberal arts mathematics can assign these videos and have students write an essay on the artistic nature of math, the history of math or the work of a particular mathematician.
Concerns: None

Ease of Use for Both Students and Faculty

Rating: 5 stars
Strengths: A student just has to click on the language of choice and then click on the video to be viewed. The rest is automatic.
Concerns: None