Concept explainers
To define : The portion of Mobius band left uncolored after coloring one side of it and the number of sides it has when the original strip of paper had two sides.
Answer to Problem 1E
None of the band is left uncolored. The band has only one side.
Explanation of Solution
Given information : Take a strip of paper. Give it a half roll. Bind the ends together. The resultant is a Mobius Loop. After one side of the loop is colored the portion of band left uncolored is to be defined. The original strip of paper had two sides. The number of sides in the Mobius Band is to be determined.
Consider the given strip of paper. After the strip of paper is given a half turn, bind it using a tape or any adhesive. Color it from one end and continue it. It can be noticed that the end is reached from where the task was started. So, no portion of the band will be left uncolored.
If someone starts to color Mobius Band from one side and moves on then nothing is left uncolored. It implies that Mobius Band has one side only.
Chapter 2 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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